Multi-material mortise and tenon biomimetic configuration and additive method and device based on causal mechanics map inversion

Abstract

The application discloses a multi-material mortise and tenon biomimetic configuration and additive method and device based on causal mechanics atlas inversion, and comprises the following steps: receiving idealized mechanical performance indexes of a target component; based on the performance indexes, an artificial intelligence model with a built-in physical partial differential equation as a constraint is used to perform reverse calculation and solve optimal material physical properties and their spatial gradient distribution required to achieve the performance indexes; a multi-material continuous gradient three-dimensional geometric configuration is generated according to the material property field; and integrated manufacturing instructions are generated by optimizing additive manufacturing process parameters. The application provides an active generative design method, overcomes the limitations of existing verification digital twin technology, ensures the performance and reliability of the final physical entity from the source, and improves the manufacturing success rate and research and development efficiency of complex components.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, and more specifically, to a multi-material mortise and tenon biomimetic configuration and additive manufacturing method and apparatus based on causal mechanical spectrum inversion. Background Technology

[0002] Additive manufacturing, often referred to as 3D printing, has shown great potential in the reconstruction and optimization of biomimetic structures, such as traditional mortise and tenon joints. Mortise and tenon joints, with their ingenious mechanical interlocking mechanism, can achieve high-strength connections without the use of nails or adhesives. Multimaterial 3D printing, on the other hand, promises to further enhance performance by using high-rigidity materials at key stress points and flexible materials in areas requiring deformation or cushioning.

[0003] However, in the application of multi-material additive manufacturing to precision and complex interlocking structures (such as mortise and tenon joints), significant differences exist in the physical parameters of different materials, such as their coefficients of thermal expansion, cooling contraction rates, and Young's modulus. These differences accumulate as materials are deposited layer by layer, resulting in complex residual stress fields within the parts after printing. When the parts are removed from the printing platform or undergo subsequent heat treatment, these internal stresses are released, leading to uncontrollable, minute geometric deformations, warping, or even cracking. For precision structures like mortise and tenon joints that rely on micron-level tolerances, even local deformations greater than 0.15 mm are sufficient to cause severe jamming during assembly, or loosening of connections and performance degradation due to sustained stress after assembly, or even brittle fracture due to stress concentration at sharp geometric sections. This problem has become a key technical bottleneck restricting the application of multi-material 3D printing technology in high-precision and high-reliability fields.

[0004] To address this issue, the industry currently employs two main technological approaches. The first involves researchers using Computer-Aided Engineering (CAE) software, particularly topology optimization tools based on Finite Element Analysis (FEA), to optimize design models. This method applies pre-defined loads and constraints within a given design space, using iterative calculations to find the optimal material distribution for lightweighting or maximizing stiffness. The second approach involves researchers integrating various sensors (such as infrared thermal imagers and optical scanners) into additive manufacturing equipment to monitor physical parameters during the printing process in real time and compare them with an ideal digital twin model for quality control and defect identification.

[0005] However, existing technologies, whether in the design or manufacturing stages, have failed to effectively address the internal stress and deformation failures of complex multi-material structures caused by the disconnect between the physical realities of the design and manufacturing processes. The industry urgently needs a new technological approach that can break the traditional design-verification cycle, using the desired mechanical properties as the starting point for design, and working backward to derive an integrated solution that meets functional requirements while fully complicating the physical laws of the manufacturing process. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-material mortise and tenon biomimetic configuration and additive manufacturing method and device based on causal mechanical spectrum inversion. It aims to solve the technical problem in the prior art that the disconnect between the idealization in the design stage and the complex physical reality of the additive manufacturing process leads to assembly failure or structural damage of complex multi-material components after printing due to uncontrollable internal stress release and local deformation.

[0007] To achieve the above objectives, this invention provides a multi-material mortise and tenon biomimetic configuration and additive manufacturing method based on causal mechanical spectrum inversion. This method employs a reverse design process, starting from a preset product performance target and working backwards to find a design scheme that can achieve this performance target. The design scheme includes the component's geometric configuration, gradient material spatial distribution, and corresponding manufacturing process parameters.

[0008] Specifically, one aspect of the method provided by the present invention includes the following steps:

[0009] Obtain the target mechanical performance parameters of the target component under preset working conditions. This step defines the final goal of the reverse engineering. Specifically, this step may include receiving a series of quantitative performance indicators that the target component must meet, input by the user. These performance indicators may include: critical load, maximum permissible deformation, loading and unloading resistance threshold, or number of fatigue cycles.

[0010] In an optional implementation, prior to subsequent steps, a mathematical model for inverse computation may be constructed. For example, the design domain of the target component may be spatially discretized, and its geometric constraints and key functional nodes may be combined to abstract an initial mechanical graph containing nodes and edges. The nodes may represent material micro-elements, and the edges may characterize the physical connections and force transmission relationships between these material micro-elements. This initial mechanical graph provides structured computational input for subsequent artificial intelligence models.

[0011] Next, based on the acquired target mechanical performance parameters, an artificial intelligence model with embedded partial differential equations of solid mechanics as physical constraints is used to perform inverse calculations to obtain the optimal material physical property field within the target component design domain corresponding to achieving the target mechanical performance parameters. This step uses the target mechanical performance parameters as the solution objective and reversely deduces the material physical properties that each spatial point within the design domain should possess to achieve the performance target. The physical properties may include Young's modulus, Poisson's ratio, shear modulus, and density. The output of this step is a three-dimensional material physical property field characterizing the entire design domain.

[0012] In one specific implementation, to ensure the physical authenticity of the inverse calculation results, the artificial intelligence model can employ a hybrid deep learning architecture, which may include two stages: causal inference and configuration generation. In the causal inference stage, a physical information neural network can be used. The loss function of this network includes residual terms from one or more partial differential equations describing macroscopic physical laws. Specifically, the Navier-Cauchy equation can be used as a constraint on the mechanical behavior of solids. The goal of network training is to adjust the network weights through backpropagation, under the condition of satisfying the user-defined target mechanical performance parameters, so that the internal physical field predicted by the network conforms to the partial differential equations, thereby outputting an optimal material physical property field that both meets the target requirements and follows physical laws.

[0013] After obtaining the material property field, the model enters the configuration generation stage, which aims to transform the property field into a manufacturable geometric entity. Optionally, a conditional variational autoencoder can be used to achieve this transformation. The model is pre-trained using a dataset containing functionally graded material structures and their corresponding physical property fields, allowing it to learn the mapping relationship between physical property distribution and 3D geometric configuration. In practical applications, the optimal material physical property field output from the previous stage is used as the conditional input to the model, driving its decoder to reconstruct in the latent space to generate a high-resolution 3D digital model with a continuously gradient material distribution. The model reproduces the requirements of the optimal material physical property field at the voxel level. For example, when deriving regions requiring stress relief, the model can automatically generate a region with a smooth transition from rigid to flexible materials.

[0014] Subsequently, the method of the present invention further includes generating integrated manufacturing instructions based on the generated three-dimensional digital model. This step aims to connect virtual design and physical manufacturing. First, the three-dimensional digital model is analyzed. Then, based on the spatial changes of material components in the model, motion paths are planned for the actuators of the multi-material additive manufacturing equipment. On this basis, additive manufacturing process parameters are collaboratively optimized at each node of the path planning. This means that as the actuator moves, the system will synchronously and dynamically adjust a series of process parameters based on the material composition information of its current position. For fused deposition modeling (FDM) technology, these parameters may include the instantaneous extrusion rate ratio of multiple materials, nozzle temperature, printing platform temperature, layer height, and actuator movement speed. Through this process parameter control coupled with material distribution, the consistency of the final physical entity and the three-dimensional digital model in terms of microscopic material properties can be improved. Finally, the motion control instructions and process parameter adjustment instructions are compiled into an integrated manufacturing instruction file to drive the multi-material additive manufacturing equipment.

[0015] In another aspect, the present invention also provides an apparatus for implementing the above-described method. Specifically, the apparatus may include: a target input module, a causal dynamics graph inversion engine module, a model generation module, and an instruction generation module.

[0016] The target input module is configured to provide a human-machine interface to receive user input of target mechanical performance parameters that the target component must meet under preset working conditions, and to structure these parameters for use by subsequent modules.

[0017] The causal mechanical graph inversion engine module, as the core computing unit of this device, is configured to receive the target mechanical performance parameters and, through its internally embedded artificial intelligence model, execute the core inverse calculation task, ultimately outputting the optimal material physical property field that achieves the performance target. In a specific implementation, to ensure the physical authenticity of the inverse calculation results, the causal mechanical graph inversion engine module can be implemented by an inverse deduction unit based on a Physical Information Neural Network (PINN). This unit uses the target mechanical performance parameters as the optimization objective in its loss function and uses the residual of the embedded solid mechanics partial differential equation as the physical constraint penalty term in the loss function. By training the network through the backpropagation algorithm, the network must meet the target performance constraints while its internal physical field prediction results must also converge to the solution that conforms to the partial differential equation, thereby ensuring that the output optimal material physical property field has both target orientation and self-consistency with physical laws.

[0018] The model generation module is configured to receive the abstract, optimal material physical property field output by the causal mechanical map inversion engine module and transform it into a concrete, visualized, and fabricable three-dimensional digital model. Specifically, the model generation module can be implemented by a configuration generation unit based on a conditional variational autoencoder (C-VAE). This unit utilizes a pre-trained C-VAE decoder, taking the input optimal material physical property field as the generation condition. The decoder samples and reconstructs in a latent high-dimensional space, decoding and outputting a high-resolution three-dimensional digital model with a continuous gradient material distribution.

[0019] The instruction generation module is configured to parse the three-dimensional digital model output by the model generation module and generate integrated manufacturing instructions that are co-optimized with the manufacturing process. Furthermore, the instruction generation module is further configured to dynamically and synchronously optimize the additive manufacturing process parameters based on changes in the material gradient within the three-dimensional digital model, and generate time-series instructions containing refined process control parameters. Thus, the final output of the device is not a static geometric model file, but a complete integrated solution encompassing macroscopic geometry, microscopic material distribution, and dynamic control of the manufacturing process, ensuring that the physical manufacturing process can reproduce the digital design intent to the greatest extent possible.

[0020] Preferably, the apparatus of the present invention may further include a preprocessing and graph construction module, located between the target input module and the causal mechanical graph inversion engine module. This module is configured to discretize the design domain of the target component before the inverse calculation begins, and abstract information such as geometric constraints and key functional nodes into an initial mechanical graph composed of nodes and edges. Subsequently, the causal mechanical graph inversion engine module performs inverse calculations on this initial mechanical graph, assigning a set of optimal material physics parameters to each component of the graph, thereby constituting the optimal material physics property field.

[0021] More preferably, the device of the present invention may further include an online monitoring and feedback unit. This unit can acquire, in real time, geometric or physical state information of the physical component being formed during the additive manufacturing process using sensors such as high-resolution optical cameras, laser scanners, or thermal imagers, including actual dimensions, surface morphology, or temperature field distribution. The acquired state information is fed back to the causal mechanical map inversion engine module. Based on the feedback information, the engine module can perform near real-time dynamic correction and adjustment of the three-dimensional digital model or integrated manufacturing instructions upon which the ongoing or subsequent printing tasks are based, thereby forming a closed-loop control system within the device to further improve the manufacturing accuracy and performance reliability of the final product.

[0022] In summary, this invention provides a multi-material configuration and additive manufacturing method based on a causal inversion mechanism, along with corresponding systems and devices. The core technical solution of this invention lies in establishing a novel design and manufacturing logic: this logic uses the preset functions and performance indicators of the end product as the input and solution target for calculation. Through an artificial intelligence model embedded with objective physical laws (specifically manifested as partial differential equations in solid mechanics) as strong constraints, it performs reverse deduction to directly solve for the optimal material spatial distribution scheme necessary to achieve the preset target. Furthermore, this solution also includes a complete technical path that transforms this abstract material distribution scheme into a concrete three-dimensional digital geometric model with continuous gradient characteristics, and finally compiles and generates integrated and coordinated fine-grained processing instructions that can be directly executed by multi-material additive manufacturing equipment.

[0023] The present invention, through the above technical solution, can achieve the following beneficial effects:

[0024] Firstly, this invention provides a reverse design method driven by the final performance target, which solves the design scheme in reverse. This method can use physical laws as an inherent constraint in the solution process of the artificial intelligence model, so that the design result not only meets functional requirements but also conforms to objective physical laws, thereby reducing the risk of failure due to inadequate consideration of physical effects at the design source.

[0025] Secondly, this invention can improve the performance of multi-material components. By generating a continuous gradient material distribution, stress concentration at the interface of heterogeneous materials can be effectively mitigated, improving the structural integrity and durability of the components. Compared with traditional designs using discrete material interfaces, the precision mortise and tenon structure prepared by this invention shows improved connection reliability, fatigue life, and assembly accuracy.

[0026] Third, this invention can improve the efficiency of research and development design. It transforms a design process that relies on experience and repeated trials into a highly automated calculation process, shortening the design iteration cycle, reducing the number of physical prototypes produced, and thus reducing resource consumption in the research and development process. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1This is a flowchart of a method according to an embodiment of the present invention, illustrating the overall steps of a multi-material configuration and additive manufacturing method based on causal mechanical spectrum inversion.

[0029] Figure 2 This is a system functional architecture block diagram according to an embodiment of the present invention.

[0030] Figure 3 This is a schematic diagram of the core data flow according to an embodiment of the present invention.

[0031] Figure 4 This is a schematic diagram illustrating the internal working principle of a causal dynamics graph inversion engine according to an embodiment of the present invention.

[0032] Figure 5 This is a schematic diagram of the gradient material distribution profile of a three-dimensional model generated according to an embodiment of the present invention and applied to the design of a drone battery compartment clip. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0034] Example 1

[0035] This embodiment details a complete process for a multi-material mortise and tenon biomimetic configuration and additive manufacturing method based on causal mechanical map inversion. This process refers to... Figure 1 The overall steps shown, combined with Figures 2 to 4 The system, data flow, and core principles shown herein provide a specific implementation of the method of the core technical solution of this application.

[0036] Step S1: Obtain the target mechanical performance parameters of the target component.

[0037] This step is the starting point of the entire reverse engineering and manufacturing process. Its purpose is to transform an engineering application requirement into precise, quantifiable data input that can be understood and processed by machines. In this embodiment, this step is performed on a human-computer interaction interface equipped with the system described in this invention, and can be broken down into the following sub-steps:

[0038] First, the user imports or defines the geometric constraints of the target component. For example, for a complex mortise and tenon joint that needs to be designed, the user can provide a 3D CAD model that defines the maximum external contour that the joint must have, the mating interfaces with other components, and the geometric boundary conditions such as cavities where materials cannot be placed. After receiving this geometric information, the system will use it as the basic design domain for subsequent calculations.

[0039] Secondly, users annotate functional nodes or areas at key locations within the design domain. These annotations are interactive; for example, users can select and define on the 3D view which surfaces are primary load-bearing surfaces that need to resist external loads; which parts are latching arms that need to move or undergo elastic deformation; and which surfaces are mating surfaces that precisely engage with other components. Defining these functional areas helps the system understand the core functions of different parts of the components.

[0040] Next, the user inputs one or more sets of target mechanical performance parameters for the functional node or the entire component. These parameters are the final indicators that the design results must achieve. In this embodiment, the user can input parameters in the following form:

[0041] Static bearing capacity: When a pressure of 5000N in the X direction is applied to surface A, the maximum displacement of point B should be less than 0.05mm.

[0042] Dynamic fatigue life: Defines the requirement that a component must withstand 1 million cycles of cyclic load with a frequency of 50 Hz and an amplitude of 1 mm without breaking or permanent deformation.

[0043] Assembly performance: The maximum resistance of the mortise and tenon structure during insertion should be less than 50N, while the minimum pull-out force in the locked state should be greater than 800N.

[0044] Weight constraint: Defines that the total weight of the final finished component must not exceed a specified threshold, such as 25 grams.

[0045] Finally, the system integrates the aforementioned geometric constraints, functional area definitions, and performance parameters. At this point, an optional, preferred implementation method is to start... Figure 2The preprocessing and graph construction module (202) is shown to perform the following: First, the geometric design domain is voxelized to a high density, for example, divided into millions or even hundreds of millions of tiny cubic units. Then, based on these voxel units and combined with user-defined functional nodes, a mathematical graph structure, namely the initial mechanical graph G(V, E), is constructed. In this graph, the centroid of each voxel or a group of voxels can be abstracted as a node V; adjacent nodes or nodes with physical connections are connected by edges E. User-input loads, constraints, and other conditions are also mapped to specific nodes or edges in the graph. Thus, a complex engineering problem is completely transformed into a well-defined mathematical object that can be computed by an artificial intelligence model. The output of this step is the initial mechanical graph containing all the initial design information.

[0046] Step S2: Perform reverse calculations based on the artificial intelligence model to solve for the optimal material physical property field.

[0047] This step is the core technology of the method of the present invention. It takes the initial mechanical spectrum and target performance parameters generated in the previous step and outputs a solution that defines the optimal material properties at each point in the design domain through an innovative reverse solution process.

[0048] In this embodiment, the artificial intelligence model used is a specially designed hybrid deep learning model comprising two stages. The reverse computation process is first performed in the first stage, namely the causal inference stage. This stage employs a Physical Information Neural Network (PINN) based on a Graph Neural Network (GNN).

[0049] The input to the PINN model is the initial mechanical graph generated in step S1. The model's network structure (such as GCN, GAT, etc.) is designed to handle this non-Euclidean graph data, effectively learning and inferring the interactions between nodes. The network's goal is to predict and output an optimal material physics parameter vector for each node in the graph, for example, p_i = (E_i, v_i), where E_i is the ideal Young's modulus of the material at that node, and v_i is the ideal Poisson's ratio.

[0050] The key innovation of the PINN model lies in the construction of its loss function. Traditional neural networks rely on a large amount of input-output pairs for supervised learning, while the PINN loss function L_total in this embodiment consists of two parts: L_total = L_target + L_phy.

[0051] Here, L_target is the target performance constraint. It directly converts the target mechanical performance parameters input by the user in step S1 into mathematical constraints. For example, if the user requires the displacement u_B at point B to be less than 0.05 mm, then max(||u_B|| - 0.05, 0) becomes a sub-item of L_target. If the user requires the maximum stress σ_max in a certain area to be less than the safety threshold σ_safe, then max(σ_max - σ_safe, 0) also becomes a sub-item of L_target.

[0052] L_phy is the physical constraint term. This is crucial to ensuring that the model output conforms to the real physical world. In this embodiment, the residual of the Navier-Cauchy partial differential equation (PDE) in solid statics is used as this penalty term. Specifically, this equation describes the relationship between the displacement field u, stress field σ, and material properties (represented by Young's modulus E and Poisson's ratio v) of an object under given body force f and boundary conditions: During model training, the network deduces a predicted displacement field u based on its current predicted material property distribution p. This u is then substituted into the PDE equations to calculate the residual, the magnitude of which is the value of L_phy.

[0053] During training, the model continuously adjusts its internal weights using backpropagation algorithms (such as the Adam optimizer). The goal is no longer to fit a known correct answer, but to find a set of network weights that simultaneously makes both L_target and L_phy approach zero. This is essentially a performance-oriented optimization process strictly constrained by physical laws. When the loss function converges, it means the model has found an optimal material property distribution scheme. Under this scheme, the component's performance satisfies all the user's preset goals, and its internal mechanical behavior fully complies with the fundamental laws of solid mechanics.

[0054] The final output of this step is a high-dimensional tensor that assigns a set of optimal material physics parameters (E, v, etc.) to each node in the initial mechanical map, collectively forming an optimal material physics property field P(x,y,z) covering the entire design domain. (This relates to the residual field of the Western equations.)

[0055] Step S3: Generate a three-dimensional digital model based on the optimal material physical property field.

[0056] This step aims to transform the mathematically optimal but formally abstract material property field produced in step S2 into a concrete, visualized, geometrically continuous and smooth, manufacturable three-dimensional solid model.

[0057] In this embodiment, a pre-trained conditional variational autoencoder (C-VAE) is used to accomplish this task.

[0058] First, the C-VAE model needs to be pre-trained. This process can be done offline. Researchers can construct a large dataset containing tens of thousands of 3D model samples with functionally graded material (FGM) features. For each sample, the corresponding material physical property field under specific working conditions is calculated using high-precision finite element analysis software. This yields a large number of "3D geometric model-material property field" data pairs. These data pairs are then used to train the C-VAE model. The encoder in the model learns how to compress a specific 3D model into a low-dimensional, continuous latent space Z; while the decoder learns how to accurately reconstruct the original 3D model from an encoding in the latent space and a given material property field as conditions. In this way, C-VAE learns a profound mapping relationship between physical properties and geometric form.

[0059] In the actual implementation of the method of this invention, the optimal material physical property field P(x,y,z) output in step S2 is used as the conditional input to the pre-trained C-VAE decoder. After receiving this condition, the decoder samples in the latent space Z and begins the reconstruction (decoding) process. Due to the continuity of the latent space and the powerful nonlinear mapping capability of the decoder, its output is a high-resolution voxelized three-dimensional digital model M_3D.

[0060] This generated 3D model possesses the following key characteristics: First, its macroscopic geometry naturally adapts to the requirements of mechanical performance; for example, it automatically becomes robust in areas requiring high rigidity, while lightweight openings may appear in non-load-bearing areas. Second, and most importantly, it perfectly and continuously reproduces the requirements of the optimal material property field P at the microscopic voxel level. This means that the model no longer features the abrupt, black-and-white material interfaces found in traditional designs; instead, it exhibits smooth material gradients. For instance, a thin, tough layer of material may be generated at the contact surface between the tenon and mortise; while at the root of the connection, a soft transition zone automatically forms, smoothly transitioning from a high-rigidity matrix material to a tougher contact surface material. This biomimetic gradient design is crucial for mitigating stress concentration, improving structural toughness, and extending fatigue life.

[0061] The final output of this step is a 3D model file containing fine-grained material gradient information, which can be recognized by downstream software and hardware; for example, a specially expanded .3MF format file. Figure 5The image shown is a two-dimensional cross-sectional diagram illustrating the possible output of this step for a specific application scenario. For a more intuitive demonstration of the gradient material distribution characteristics within the three-dimensional model generated in this embodiment, please refer to... Figure 5 This figure is a rendered schematic diagram of a snap-fit ​​assembly cut along its plane of symmetry. The diagram clearly shows the material distribution in three different functional areas: Reference numeral 302 indicates the rigid main frame of the snap-fit, constructed of pure PA6-CF material to provide high strength and stiffness, ensuring structural stability under overload. Reference numeral 303 indicates the flexible contact surface, constructed of pure TPU95 material, located on the surface in direct contact with the battery casing, used to buffer vibration and resist wear from long-term insertion and removal. Most critically, reference numeral 301 indicates the gradient flexible transition zone, located in stress concentration areas such as the bend root of the snap-fit ​​tongue. Within this zone, the material transitions smoothly and continuously from pure PA6-CF to pure TPU95. This biomimetic design effectively mitigates stress concentration, which is key to improving the fatigue life of the component and the overall structural toughness.

[0062] In the actual implementation of the method of this invention, in order to connect the different computational power data structure characteristics between the physical inversion map engine and the image configuration decoding system, the optimal material physical property field obtained in the preceding steps will be subjected to an additional layer of arithmetic spatial to geometric three-dimensional resampling and rasterization processing mechanism (SpatialResampling & Voxelization) in the built-in module before being submitted as the upstream input as the C-VAE condition. For the initial irregular mechanical model features containing each node, using methods such as inverse distance weighted smooth interpolation (IDW) or fast discretization differential projection of unstructured polyhedral meshes, a standard spatial continuous material parameter input tensor map based on a cubic array framework, i.e., [N x N x N] dimensional, is uniformly quantized, reprojected, and reduced in dimension to a fixed resolution. This ensures the compliance of the preceding input and the equivalence of spatial coupling at the decoding network end.

[0063] Step S4: Collaboratively optimize process parameters and generate integrated manufacturing instructions.

[0064] This step is the final bridge connecting the digital world and the physical world, ensuring that the additive manufacturing process can reproduce the complex gradient material model designed in step S3 as faithfully and to the greatest extent possible.

[0065] First, this module receives and analyzes the gradient three-dimensional model file output by step S3. It reads out the spatial coordinates of each voxel and its corresponding material component information. For example, for a gradient material composed of material A (rigid) and material B (flexible), the material information of the voxel can be represented by a proportionality coefficient k. k = 1 represents pure material A, k = 0 represents pure material B, and 0 < k < 1 represents a mixture of the two.

[0066] Next, this module performs path planning for additive manufacturing. Based on the geometric shape of the model, it plans a three-dimensional motion trajectory for the print head (or laser beam, or other energy source) of the multi-material printing device layer by layer and path by path. This is similar to traditional slicing software, but the particularities of multi-material printing need to be considered, such as avoiding interference between different material nozzles and optimizing the waiting time during material change or mixing.

[0067] On this basis, the key process parameter co-optimization of the present invention is performed. At each tiny step when the print head moves along the planned path, this module will query the material component ratio k in the three-dimensional model corresponding to the current position in real time. Then, based on this real-time changing k value, a series of manufacturing process parameters closely related to the material properties of the final product are adjusted synchronously and dynamically.

[0068] In this embodiment, taking a dual-nozzle fused deposition modeling (FDM) device as an example, the co-optimized parameters may include:

[0069] Dual-material extrusion rate ratio: precisely control the number of steps of the two nozzle motors per unit time so that the volume ratio of the extruded material A and material B is strictly equal to the k value at the current position.

[0070] Nozzle temperature: For some materials whose viscosity is sensitive to temperature, the nozzle temperature can be fine-tuned when printing areas with different mixing ratios to achieve the best interlayer bonding strength and surface quality.

[0071] Printing speed: When printing the gradient transition area, appropriately reducing the printing speed can give the material more sufficient melting and mixing time to ensure the smoothness of the gradient change.

[0072] Finally, this module compiles and integrates the planned print head motion instructions (such as G0, G1 instructions) with these co-optimized process parameter control instructions (such as the extended usage of M instructions) that change in real time with the spatial position.

[0073] The final output of this step is an integrated manufacturing instruction file (such as a highly customized G-code) containing extremely rich and detailed process control information, which can be directly loaded into Figure 2The multi-material additive manufacturing equipment (207) shown is used for this process. This ensures that the entire process, from an abstract performance requirement of the user to the final driving of the physical equipment for precise manufacturing, forms a complete, intelligent, and highly integrated closed loop.

[0074] To more clearly illustrate the data flow process in the method of this invention, please refer to... Figure 3 The entire process begins with a user-defined, parameterized target mechanical property T. This property parameter, along with geometric constraint information, is processed by the preprocessing and graph construction module (202) and abstracted into a mathematically rigorous initial mechanical graph G(V, E), which becomes the carrier for subsequent calculations. The core causal mechanical graph inversion engine (203) executes an inverse inversion function P = f_inverse(T), guided by the target T, to directly solve for the optimal material physical property field P(x,y,z). This property field P, as a condition for the subsequent generation stage, is input into the model generation module (204) to perform the configuration decoding process M_3D = g_decoder(P), thereby generating a specific three-dimensional digital model M_3D containing gradient material information. Finally, the instruction generation module (205) parses the model and compiles the instructions I_gcode = h_compile(M_3D), ultimately outputting an integrated manufacturing instruction I_gcode that can be executed by physical devices. This process clearly demonstrates how data is gradually transformed from an abstract performance requirement into a concrete representation and ultimately into physical manufacturing instructions.

[0075] Example 2

[0076] This embodiment details the specific technical implementations of several core computational modules used to implement the method of the present invention, particularly the causal dynamics graph inversion engine module (203) and the model generation module (204). The present invention is not limited to employing a specific artificial intelligence model architecture; those skilled in the art can select or combine different technical paths to implement the core ideas of the present invention based on specific application scenarios, computational resources, and performance requirements.

[0077] I. Detailed Implementation of the Causal Mechanics Graph Inversion Engine Module (203)

[0078] The core task of the causal mechanical graph inversion engine module (203) is to perform the inverse calculation of step S2, that is, to solve for the optimal material physical property field starting from the target mechanical properties. The preferred implementation of this module is to use a Physical Information Neural Network (PINN). The following will describe in detail the model architecture selection, loss function design and training process of the PINN unit.

[0079] 1.1 Model Architecture Selection

[0080] In step S1 of Embodiment 1, the design domain has been abstracted into an initial mechanical spectrum G(V, E). Therefore, the neural network model used to process this graph data is preferably a graph neural network (GNN) or a variant thereof.

[0081] Compared to traditional finite element methods (FEM) based on regular meshes or image-based representations using convolutional neural networks (CNNs), graph structures can characterize the irregular geometric shapes and topological relationships of complex components in a more efficient and flexible way. The geometric boundaries of biomimetic structures such as mortise and tenon joints are often highly irregular. Using fixed-resolution grids or pixels to represent them introduces quantization errors and makes it difficult to accurately capture key curved and sharp-corner features. In contrast, nodes and edges in a graph can directly correspond to discretized infinitesimal elements of arbitrary shapes (such as tetrahedral or hexahedral mesh elements) and their connections, thus representing the true topological structure of the component without loss of quality. This is fundamental to ensuring the accuracy of subsequent mechanical analysis.

[0082] The message-passing mechanism of Generative Neural Networks (GNNs) naturally aligns with the physical essence of local interactions in physical fields (such as stress and displacement fields) that are transmitted globally through a continuous medium. In each layer of a GNN, a node updates its state by aggregating information from its neighbors, which is highly isomorphic to the principle that the stress state of a point in the physical world is determined by the states of its surrounding points. By stacking multiple layers of GNNs, the model can automatically learn complex mechanical transmission paths and stress distribution patterns without relying on manually defined, complex numerical solution formats based on partial differential equations, as is the case with traditional methods.

[0083] An architecture based on graph convolutional networks (GCN).

[0084] GCN is a basic GNN architecture whose core operation involves aggregating and updating the neighbor information of each node. In this invention, a multi-layer GCN network is constructed. Its input is an initial mechanical graph, whose node features can be initialized as the node's spatial coordinates (x, y, z) and a one-hot encoding indicating whether it is a load application point or a constraint point. After L layers of graph convolution operations, the node representation in each layer is fused with information from its L-hop neighbors. Finally, the network's output layer is a fully connected layer that embeds the high-dimensional nodes output from the last GCN layer, mapping them to a low-dimensional material physics parameter vector p=(E, v). The advantage of this architecture is its high computational efficiency, making it suitable for processing graphs with relatively regular connection relationships.

[0085] An architecture based on Graph Attention Network (GAT).

[0086] GAT is an improvement on GCN. When aggregating neighbor node information, GAT uses a self-attention mechanism to assign different attention weights to different neighbor nodes. This means the model can autonomously and dynamically learn which neighbor nodes are more important for the material property decisions of the current node in mechanical analysis. For example, in regions of stress concentration, the model may give higher weights to neighbor nodes from the main force transmission path. This architecture is particularly effective for handling components with complex stress distributions and irregular geometric boundaries because it can capture the key features of the local mechanical environment more precisely, potentially leading to better material property field solutions.

[0087] 1.2 Detailed Design of the Loss Function

[0088] As described in Example 1, the loss function L_total = L_target + L_phy is the core of PINN training. This section provides a further detailed explanation of its mathematical construction.

[0089] The concretization of the target performance constraint L_target:

[0090] This item is a set of mathematical expressions for multiple user-defined engineering constraints. For example:

[0091] Displacement constraint: If it is required that the displacement norm ||u(x)|| of all points in a certain region Ω_d within the design domain must not exceed d_max, then the corresponding loss term can be expressed as:

[0092] L_displacement = ∫_{x∈Ω_d} ReLU(||u(x)||^2 - d_{max}^2) dx

[0093] Here, ReLU(z) = max(0, z) is an activation function that indicates that a penalty is only incurred when the displacement exceeds the limit. u(x) is the displacement field simultaneously predicted by the PINN network.

[0094] Stress constraint: If the von Mises equivalent stress σ_vm(x) within the region Ω_s is required not to exceed the material's allowable stress σ_safe, then the corresponding loss term can be expressed as:

[0095] L_stress = ∫_{x∈Ω_s} ReLU(σ_{vm}(x) - σ_{safe}) dx

[0096] The equivalent stress σ_vm(x) can be calculated from the displacement field u(x) predicted by the network and the predicted material property p(x) through the constitutive relation of elasticity.

[0097] L_target is the weighted sum of all constraints similar to those described above.

[0098] The concretization of the physical law constraint term L_phy:

[0099] This term ensures that the model's predictions follow the laws of physics. For a three-dimensional linear elastic static problem, the residual field R(x) of the Navier-Cauchy equations is defined as:

[0100]

[0101] Where σ is the stress tensor and F is the body force (such as gravity) acting on point x. It is the divergence operator. The relationship between the stress tensor σ and the displacement field u and material properties p (including Young's modulus E and Poisson's ratio v) is determined by Hooke's Law.

[0102] Therefore, the physical constraint loss term is the residual field over the entire design domain Ω (including the boundary). The square of the L2 norm of ), i.e.:

[0103] L_phy = ∫_{x∈Ω} ||R(x)||^2 dx

[0104] During training, this integral is approximated by randomly sampling tens of thousands of configuration points within the design domain and calculating the mean square value of the residuals at these points.

[0105] 1.3 Training Process

[0106] Data Sampling: Since the model is unsupervised or self-supervised, its training does not depend on labeled data. In each training iteration, the system samples data from the interior of the design domain Ω, as well as from the boundaries where Dirichlet and Neumann boundary conditions are defined. A batch of configuration points were randomly sampled.

[0107] Optimizer: The Adam optimizer can be selected because it exhibits good convergence and stability when handling large-scale stochastic optimization problems in deep learning models. In a preferred embodiment, a learning rate decay strategy can be employed, for example, using a large learning rate (e.g., 1e-3) for rapid exploration in the early stages of training, and gradually reducing the learning rate (e.g., decreasing it to 1e-5) as training progresses to achieve finer convergence. In some cases, second-order optimization algorithms such as L-BFGS can also be used to obtain higher solution accuracy in the later stages of training.

[0108] Exemplary Hyperparameters: To enable those skilled in the art to reproduce this, a set of exemplary hyperparameter configurations is provided: Number of GNN layers: 8; Number of hidden units per layer: 256; Activation function: tanh; Optimizer: Adam; Initial learning rate: 0.001; Number of training iterations: 50,000; Loss function weights: The weight of L_target is set to 1.0, and the weight of L_phy is set to 0.01. These parameters can be adjusted according to the complexity of the specific problem.

[0109] For example, Figure 4 The internal workings of the causal mechanical graph inversion engine (203) and model generation module (204) are illustrated in more detail. The entire process is divided into two stages. Stage 1: Causal inference based on PINN. The initial mechanical graph G is fed into a graph neural network (GNN) as input. The GNN is used to predict physical fields (such as displacement field and stress field) and compares them with the loss function L, which is composed of the target performance and physical laws. The loss function L = L_target + L_phy (PDE) is adjusted by backpropagating gradients to adjust the network weights. This closed-loop iterative process continues until the loss function converges, at which point the GNN outputs the optimal material physical property field P. Stage 2: Configuration generation based on C-VAE. The property field P output in the previous stage, together with the random vector sampled from the latent space Z, is fed into the C-VAE decoder. The decoder performs decoding and generation operations, and finally outputs a specific gradient three-dimensional digital model M. This two-stage architecture clearly demonstrates how the present invention decouples and connects the two tasks of solving physical laws and generating geometric shapes.

[0110] II. Detailed Implementation of Model Generation Module (204)

[0111] The task of the model generation module (204) is to implement step S3, which transforms the abstract material property field into a concrete three-dimensional geometric model. This section provides a detailed description of the architecture, training, and alternatives of the preferred implementation method, C-VAE.

[0112] C-VAE Model Architecture

[0113] Encoder Architecture: During the pre-training phase, the encoder learns to compress the 3D model into its latent space. A typical architecture is a 3D convolutional neural network (3D CNN). The input is an N × N × N 3D voxel grid (e.g., 128 × 128 × 128), where each voxel has a value of 1 (indicating the presence of material) or 0 (indicating the absence of material). The network consists of stacked layers of 3D convolutional layers, batch normalization layers, and activation functions (such as LeakyReLU), progressively decreasing the spatial resolution and increasing the number of channels. Finally, through fully connected layers, it outputs two vectors: the mean vector μ of the latent space distribution and the logarithmic variance term log(σ), representing the variance-related term. Here, the variance control parameter σ is interpreted independently using probabilistic notation.

[0114] Decoder Architecture: The decoder performs the opposite operation to the encoder. Its typical architecture is a 3D Transposed Convolutional Neural Network (3D Transposed CNN). Its input consists of two parts: a latent vector z sampled from the normal distribution N(μ, σ²) generated by the encoder; and an optimal material physical property field P, conditionally output by the PINN module. The property field P can be reshaped to the same spatial dimension as the latent vector z (e.g., as a flattened vector or a tensor with a specific spatial resolution), and then concatenated with z along the channel dimension. This concatenated vector serves as the input to the decoder, passing through a series of 3D transposed convolutional layers, batch normalization layers, and activation function layers, progressively increasing the spatial resolution and reducing the number of channels. The final output is an N × N × N 3D probability map of the same size as the input raster, where each voxel's value is between 0 and 1, representing the probability of material presence at that location.

[0115] Training process

[0116] Dataset Preparation: Training C-VAE requires a large number of "geometric model-property field" data pairs. Hundreds of thousands of 3D models with different internal structures and functionally graded material distributions can be created through parametric modeling or procedural generation. Subsequently, a series of typical load conditions are applied to each model, and forward simulations are performed using high-precision finite element analysis (FEA) software to calculate the stress and strain fields under its internal steady-state, thereby deriving an equivalent material physical property field. For example, a large number of training samples with diverse topological and geometric features can be procedurally generated by systematically changing one or more sets of design parameters, such as the fitting depth of the mortise and tenon structure, the radius of curvature of key chamfers, and the thickness function of the gradient material transition zone.

[0117] Loss function: The loss function L_CVAE of C-VAE consists of two parts: L_CVAE = L_reconstruction + β × L_KL.

[0118] Reconstruction loss L_reconstruction: This measures the consistency between the 3D model output by the decoder and the original input model. It typically uses the binary cross-entropy loss function.

[0119] KL divergence loss (L_KL): Used for regularization, it measures the difference between the latent space distribution of the encoder output and a standard normal prior. This makes the latent space more regular, which is beneficial for subsequent generation.

[0120] β is an adjustable hyperparameter used to balance the reconstruction quality and the strength of latent space regularization.

[0121] Example hyperparameters: latent space dimension: 256; optimizer: Adam; learning rate: 0.0002; batch size: 64; training epochs: 500; β value: 1.0.

[0122] The collaborative work of the causal mechanics graph inversion engine module (PINN implementation) and the model generation module (C-VAE implementation) described in this embodiment of the invention enables a smooth transformation from abstract physical requirements to concrete manufacturable models, achieving technical effects that are difficult to achieve with a single model alone.

[0123] First, the PINN module focuses on finding a theoretically optimal distribution of material properties within an abstract mathematical and physical space, unconstrained by specific geometric shapes. This avoids the problem of getting trapped in local optima due to mesh dependence or poor initial shape, which is common in traditional topology optimization. Subsequently, the C-VAE module acts as a geometry engineer, responsible for translating this physically optimal but shape-determined blueprint into a concrete, geometrically reasonable three-dimensional entity in a way that conforms to manufacturing constraints (such as continuity and smoothness).

[0124] Secondly, if an end-to-end generative model were to directly generate a 3D model based on performance metrics, its search space would be enormous, and training would be extremely difficult. This invention, by introducing PINN as an intermediate stage, significantly compresses the search space of subsequent generative models. C-VAE no longer needs to learn complex physical laws, but only needs to focus on how to elegantly construct a geometric model based on a given material property field. This decoupling makes C-VAE training more stable, and the generated model is superior in details (such as the smoothness of gradient transition regions).

[0125] In summary, the cascading collaboration of the two modules forms a complete, efficient, and robust logical chain from target definition to physical deduction and then to geometric generation. This is the key to the present invention's ability to generate high-performance, manufacturable gradient material components under complex constraints.

[0126] Finally, this invention is not limited to combinations of PINN and C-VAE. To further illustrate the broad applicability of this invention, several alternative technical implementation paths are provided below.

[0127] Alternative causal inference engines: Deep reinforcement learning (DRL) based methods.

[0128] The design process for optimal material distribution can be modeled as a Markov decision process. An agent, within a discretized design domain, progressively selects a material type (or mixing ratio) as its action for each micro-element (voxel). The state represents the partially constructed component geometry and material distribution. After each complete component design, the system runs a rapid FEA simulation, awarding a reward based on the degree to which the simulation results match the user-defined target performance parameters. Through millions of trials and learning iterations (e.g., using algorithms like PPO or SAC), the agent eventually learns to directly generate the optimal material distribution strategy given a performance objective. The advantage of this method is its vast exploration space, potentially uncovering counterintuitive metamaterial structures; however, its disadvantage is its extremely high computational cost.

[0129] Example 3

[0130] This embodiment provides a specific implementation of a multi-material mortise and tenon biomimetic configuration and additive manufacturing device based on causal mechanical graph inversion for performing the aforementioned method. (Refer to...) Figure 2 The system functional architecture diagram shown indicates that this device consists of a series of hardware devices and software modules deployed on them, aiming to realize an automated and intelligent process from design intent to physical entity.

[0131] I. Hardware Components of the Device

[0132] The hardware foundation of the device of this invention mainly includes a high-performance computing unit and a multi-material additive manufacturing unit.

[0133] High-performance computing unit: This is the core of the device's computation. Physically, it can be an engineering workstation equipped with a high-end graphics processing unit (GPU), a distributed computing cluster consisting of multiple servers, or a virtual computing resource deployed on a cloud platform. To efficiently perform the deep learning model training and large-scale numerical calculations involved in this invention, this unit is preferably equipped with one or more Tensor Core GPUs with at least 24GB of dedicated video memory, such as the NVIDIA RTX 4090, A100, or H100 series. This computing unit also needs to be equipped with a large-capacity random access memory (RAM, e.g., ≥128GB) and a high-speed solid-state drive (SSD) to support efficient reading, writing, and processing of massive amounts of data.

[0134] Multi-material additive manufacturing unit (207): This is the physical execution end of the device, i.e., the equipment used to manufacture the final physical component. In this embodiment, an industrial-grade additive manufacturing device supporting the co-printing of at least two materials can be used. Optional equipment types include:

[0135] Fused Deposition Modeling (FDM) equipment: Equipped with two or more independently temperature-controlled extrusion nozzles, one for printing rigid materials (such as carbon fiber reinforced polymers) and the other for printing flexible materials (such as thermoplastic polyurethane, TPU). The equipment's main firmware must support precise control of the instantaneous extrusion rate ratio of different nozzles during the printing process via specific G-code instructions (such as M163 / M164) to achieve gradient mixing of materials or alternating printing of microstructures.

[0136] PolyJet or MultiJet-Printing equipment: capable of simultaneously spraying multiple photosensitive resins with different properties and selectively curing them with ultraviolet light, naturally supporting the creation of components with complex gradient material properties at the voxel level.

[0137] Directional Energy Deposition (DED) equipment: suitable for metallic materials, it can dynamically change the alloy composition of the metal powder supplied to the molten pool during the printing process through multiple powder feeding nozzles or coaxial powder feeding devices, thereby manufacturing functionally graded material components based on metals.

[0138] Online monitoring and feedback hardware: As a further enhancement to the device's functionality, an online monitoring sensor suite can be integrated into the multi-material additive manufacturing unit. For example, a high-resolution industrial camera and a line laser profilometer can be installed near the printhead of the FDM equipment to acquire the geometry and surface topography of the layer being printed in real time. An infrared thermal imager can also be integrated to monitor the temperature field distribution in the printing area. These sensors are connected to a high-performance computing unit via a data acquisition card, forming a closed-loop feedback path in the hardware.

[0139] II. Software Modules of the Device and Their Functional Implementation

[0140] The software system deployed on the high-performance computing unit constitutes the intelligent core of the device of the present invention. It contains a series of functional modules that work together to realize the method of the present invention.

[0141] 1. Target Input Module (201)

[0142] This module serves as the front-end interface for user interaction with the device. Its core function is to receive and structure the user's design requirements, namely, to obtain the target mechanical performance parameters that the target component needs to meet under preset working conditions, and to convert them into digital information that can be processed by subsequent modules.

[0143] In terms of software implementation, this module can be implemented as a graphical user interface (GUI) application. This GUI application includes a 3D model browser, an attribute editing panel, and a parameter input interface.

[0144] 3D Model Browser: Allows users to import standard format CAD files (such as .STEP, .IGES) to define initial geometric constraints. Users can intuitively examine the model in the browser through operations such as rotation, translation, and scaling.

[0145] Attribute editing panel: Provides interactive 3D annotation tools. Users can define specific geometric surfaces, edges, or volumes as different functional areas, such as "bearing surfaces", "constraint surfaces", and "flexible hinge areas" by clicking or selecting with the mouse on the model.

[0146] Parameter input interface: Provides a structured input form that allows users to input precise, quantified target mechanical performance indicators for the entire component or a specified functional area.

[0147] For example, when designing a beam structure subjected to bending moment, the user first imports the external dimensional constraint model of the beam. Next, in the properties panel, one end surface of the beam is defined as the "fixed constraint surface," and the other end surface is defined as the "load application surface." Then, in the parameter input interface, a load condition of "normal force = 1000N" is entered for the "load application surface," and a global performance constraint of "maximum deformation < 0.5mm" is set for the entire component. All these inputs are organized into a project file in XML or JSON format by the module in the background.

[0148] 2. Preprocessing and map construction module (202)

[0149] The main function of this module is to transform the user-input geometric model and constraints based on continuous medium description into a discretized graph structure data suitable for graph neural network processing, namely the initial mechanical spectrum.

[0150] This module can be composed of a series of algorithm programs at the software level.

[0151] Geometric discretization elements: Call an open-source or commercial geometry processing library (such as OpenCASCADE, CGAL, or Abaqus mesher) to perform high-quality voxelization or finite element meshing on the geometric model provided by the target input module (e.g., generating millions of tetrahedral or hexahedral elements).

[0152] Graph Construction Unit: This program traverses all discretized units (or unit nodes) and abstracts them as nodes in a graph. Edges of the graph are constructed based on the adjacency relationships between units. The unit also encodes geometric and physical information as features of nodes and edges.

[0153] For example, for the aforementioned beam structure, the geometric discretization element might divide it into 1 million tetrahedral elements. The graph building element would then create a graph containing 1 million nodes, each node representing a tetrahedral element. The initial eigenvector of each node could include its centroid coordinates (x, y, z) and a Boolean value indicating whether it belongs to a "fixed constraint surface" or a "load application surface." Edges between nodes indicate that the tetrahedra are physically adjacent. Finally, the module outputs a graph data file containing the node eigenvalue matrix and the edge connectivity adjacency matrix.

[0154] 3. Causal dynamics graph inversion engine module (203)

[0155] This module is the intelligent computing core of the device, used to perform inverse calculations from target mechanical properties to the optimal material physical property field. It receives the initial mechanical spectrum and solves for the optimal solution using an embedded AI model constrained by physical laws.

[0156] In terms of software, this module is a software package that embeds a specific artificial intelligence model.

[0157] Reverse Engineering Unit: The core of this unit is a Physical Information Neural Network (PINN) implemented using a deep learning framework (such as PyTorch or TensorFlow). The network's architecture (such as GCN or GAT) and loss function (including L_target and L_phy) are predefined in code. This unit is designed as an executable background service or a standalone computation program. Upon receiving the atlas file, it automatically loads the model, initializes the weights, and initiates a parallelized training task on one or more GPUs. During training, it periodically records changes in the loss function and automatically terminates training after meeting convergence conditions (e.g., the loss value does not decrease significantly for several consecutive iterations, or the preset maximum number of iterations is reached).

[0158] Example Explanation: For the beam structure example, the PINN model of the inverse inference unit begins training. Its loss function, L_target, includes a penalty for the subsurface displacement applied to the load at the beam ends, and a penalty for the maximum overall deformation of the beam. The L_phy term is the mean square value of the residuals of the Navier-Cauchy equations at all sampling points inside the beam. After approximately 50,000 iterations, the loss function converges. At this point, the output layer of the PINN model is a stable, high-dimensional node embedding matrix. Through a final mapping layer, this matrix is ​​decoded into an optimal material physical property field covering all 1 million nodes. For example, regions near the fixed ends and the upper surface are assigned high Young's moduli, while the center and lower surface regions of the beam are assigned lower Young's moduli, forming a material distribution that meets the bending resistance requirements.

[0159] 4. Model Generation Module (204)

[0160] The function of this module is to transform the abstract attribute field, which is composed of discrete node attributes, output by the inversion engine into a geometrically continuous, smooth, and understandable three-dimensional digital model that can be understood by additive manufacturing equipment.

[0161] At the heart of this module is a pre-trained deep generative model, such as the decoder part of a Conditional Variational Autoencoder (C-VAE).

[0162] Model Loading and Forward Propagation Unit: This program first loads the pre-trained C-VAE decoder model weights from disk. Then, it feeds the material property field array output by the inversion engine as conditional input into the decoder network for a forward propagation calculation.

[0163] Geometric Reconstruction Unit: This unit receives the 3D voxel probability map output from the decoder and applies an isosurface extraction algorithm (such as Marching Cubes) to generate a smooth triangular mesh surface model. Simultaneously, it interpolates and stores the material property values ​​of each voxel as the properties of the vertices of the triangular mesh model.

[0164] For example, continuing with the beam structure example, the C-VAE decoder, based on the input optimized Young's modulus field, not only generates the external geometry of the beam, but more importantly, it generates the gradient transition of the material internally. The output .3MF file contains not only the coordinates of the beam's triangular mesh vertices, but also associates a material ID and weight value with each vertex, accurately describing the continuous change from high modulus to low modulus.

[0165] 5. Instruction Generation Module (205)

[0166] This module is the final link between virtual design and physical manufacturing. Its function is to compile a three-dimensional digital model containing gradient material information into highly customized integrated manufacturing instructions that can drive multi-material additive manufacturing equipment to accurately reproduce the design.

[0167] This module can be viewed as a highly customized slicer in software.

[0168] Path planning unit: Using standard slicing algorithms (such as Contour-Parallel or Zig-zag), it generates layer-by-layer two-dimensional scanning paths for the print head and combines them into a three-dimensional motion trajectory.

[0169] Process parameter collaborative optimization unit: This is the core of this module. During the generation of G-code, the G-code generator executes an embedded "real-time query-calculation" logic when determining each path micro-segment (corresponding to a G1 instruction).

[0170] For example, in the .3MF file of a beam model, when the instruction generation module processes a layer, the program queries the corresponding material composition for each point (x, y) on the printhead path, such as (70% rigid material, 30% flexible material). The co-optimization unit then dynamically calculates the extrusion rates of the two extruders A and B at this moment, based on a preset control strategy (which can be a function or a lookup table), as E_A = 0.7 * E_base and E_B = 0.3 * E_base, respectively, and may fine-tune the printing speed of the current segment, F = F_base * 0.9. In the final generated G-code file, the E value following the G1 instruction changes in real time, rather than being a fixed value, achieving accurate reproduction of the material distribution.

[0171] 6. Online monitoring and feedback unit

[0172] This unit, as an optional enhancement module, is designed to incorporate real-time information from the manufacturing process to dynamically modify design or manufacturing instructions, thereby achieving closed-loop control.

[0173] This unit consists of a background data acquisition and processing daemon.

[0174] Data acquisition interface: Continuously receive image or point cloud data streams from online monitoring hardware via the SDK provided by the hardware manufacturer or a standard industrial camera interface (such as GenICam).

[0175] State analysis algorithm: Computer vision algorithms (such as edge detection and template matching) are used to analyze the image and calculate the deviation between the actual geometric size of the current printing layer and the theoretical slice contour.

[0176] Correction signal generator: When the detected deviation exceeds the preset tolerance threshold (e.g., >0.05mm), this unit generates a correction signal.

[0177] For example, during the beam printing process, the camera in the online monitoring unit detects that, due to material shrinkage, the actual width of a certain layer is 0.1 mm smaller than the theoretical value. The correction signal generator immediately sends an instruction to the instruction generation module, requesting that the extrusion rate compensation coefficient of subsequent printed layers be increased by 2%. Alternatively, if the deviation is too large, the signal can trigger the inversion engine module to quickly perform a local recalculation based on the current "imperfect" geometry as a new constraint, and generate a new set of subsequent printing instructions that can compensate for the error.

[0178] In summary, the device described in this embodiment, through the organic integration and collaborative work of the above-mentioned hardware and software modules, constitutes a complete and powerful system that can fully and automatically execute the advanced design and manufacturing method based on causal inversion proposed in this invention.

[0179] Example 4

[0180] This embodiment provides a complete application process for applying the method and apparatus described in this invention to a specific and demanding industrial scenario. This scenario involves designing and manufacturing a battery compartment "push-in-lock" tenon-and-mortise snap-fit ​​assembly for a high-performance unmanned aerial vehicle (UAV) that combines high reliability, lightweight design, and long lifespan.

[0181] In high-performance UAV applications, the battery compartment's securing and quick-replacement structure is a critical component. Its design must meet several mutually restrictive and stringent requirements: it must withstand severe vibrations and high G-forces during flight to ensure secure battery mounting; during ground maintenance, the assembly and disassembly process must be smooth and require minimal manpower, with insertion and extraction forces within specific ranges; simultaneously, as an aircraft component, lightweight design is a core requirement. Traditional single-material or simple dual-material injection-molded / printed snap-fit ​​systems often suffer fatigue fractures due to stress concentration at the root of the movable latch, or experience a decrease in locking force after long-term use due to material creep, making it difficult to simultaneously meet all the above requirements. This embodiment will describe in detail how to use the device and method of the present invention to creatively design and manufacture a high-performance multi-material gradient tenon-and-mortise snap-fit ​​assembly from scratch.

[0182] I. Hardware and Software Environment Configuration

[0183] The hardware and software environment configuration used in this embodiment constitutes a specific instance of the device described in Embodiment 3.

[0184] Hardware platform:

[0185] Computing unit: A Dell Precision 7920 tower workstation, configured with an Intel Xeon Gold 6248R processor (24 cores), 256GB DDR4 ECC memory, and an NVIDIA RTX A6000 professional graphics card (48GB GDDR6 video memory).

[0186] Additive Manufacturing Unit: A customized Ultimaker S5 Pro Bundle 3D printer. This printer features dual extrusion printheads (Print Core AA and BB), a material station, and a pre-air filter, enabling stable printing of engineering plastics. Its firmware has been modified to allow precise, real-time control of the dual printhead extrusion rates via G-code commands M163 (set blend weights) and M164 (save blend ratios).

[0187] Performance testing equipment: One Instron 5967 bi-column material testing machine for precise tensile, compressive and cyclic fatigue testing.

[0188] Software platform:

[0189] Operating system: Ubuntu 22.04 LTS.

[0190] Core software: The complete set of software modules described in this invention is deployed, wherein the construction and training of the deep learning model is based on the PyTorch 2.0 framework; the geometry processing and mesh generation call the Gmsh open source library; and the FEniCS project library is used for physics simulation verification (for generating training data and comparative verification).

[0191] Material system:

[0192] Material A (rigid matrix): Printhead AA is loaded with PolyMide™ PA6-CF, a carbon fiber reinforced nylon 6, characterized by extremely high specific strength, specific modulus and heat resistance (Young's modulus E_A ≈ 8.5 GPa, density ρ_A ≈ 1.24 g / cm³).

[0193] Material B (Flexibility / Toughness Transition): Printhead BB is loaded with PolyFlex™ TPU95, a thermoplastic polyurethane with a Shore hardness of 95A, characterized by excellent flexibility, tear resistance and abrasion resistance (Young's modulus E_B ≈ 0.1GPa, density ρ_B ≈ 1.20 g / cm³).

[0194] II. Generative Design and Manufacturing Process

[0195] Step 1: Define the design task through the target input module (201)

[0196] The design engineer launches the GUI software of this invention and performs the following operations:

[0197] 1. Import geometric constraints: Import simplified 3D models of the drone fuselage and battery. These two models define the design domain in space where the snap-fit ​​assembly can exist, as well as the installation interfaces that must be matched with it.

[0198] 2. Define Functions and Performance Metrics: Engineers input a set of clear, quantifiable performance metrics through an interactive interface, which serve as the ultimate goal (i.e., the "effect") of this "causal inversion":

[0199] Structural performance in locked state:

[0200] When subjected to an inertial overload of 15G (g=9.8m / s²) in the XYZ directions, the displacement strain of the battery relative to the frame is less than 0.1%.

[0201] Under simulated random vibration testing (frequency range 20-2000Hz, power spectral density 0.1 g² / Hz), after continuous loading for 2 hours, the structure must not exhibit any visible cracks or irreversible plastic deformation.

[0202] Dynamic plug-in / plug-out performance:

[0203] The peak force F_insert_max when the operator pushes the battery in and locks it should be less than 30 Newtons.

[0204] The initial peak force F_release_min required to unlock and remove the battery should be greater than 25 Newtons.

[0205] The insertion / removal cycle life N must be greater than 10,000 cycles, and the attenuation rate of the pull-out force F_release should be less than 10% after the cycle test is completed.

[0206] Lightweight design constraints:

[0207] The total weight W of the final product of the snap-fit ​​assembly shall not exceed 15 grams.

[0208] Step 2: Model abstraction through the preprocessing and graph construction module (202)

[0209] After receiving the above input, the system automatically starts the background preprocessing and map construction module:

[0210] 1. Geometric Discretization: This module calls the Gmsh library to divide the defined design domain into approximately 2.5 million high-quality tetrahedral elements with an average element size of 0.2 mm.

[0211] 2. Graph Construction: Based on these tetrahedral units, the module constructs an initial mechanical graph containing approximately 2.5 million nodes and over 15 million edges. The initial feature vector of each node contains its spatial coordinates and attributes inherited from the GUI annotations (e.g., the feature vector of a node labeled "contact surface" has a corresponding dimension of 1).

[0212] Step 3: Perform core calculations using the causal dynamics graph inversion engine (203).

[0213] The constructed mechanics map is fed into the core inversion engine module. The PINN unit (using the GAT architecture) in the engine begins to perform the reverse engineering task on the RTX A6000 GPU.

[0214] Loss function configuration: Its loss function L_total includes L_target penalty terms corresponding to all the aforementioned performance metrics, as well as an L_phy physical constraint term based on the Navier-Cauchy equation. The weight constraint is implemented by adding a penalty term related to the total volume and density distribution to the loss function.

[0215] Training process: The Adam optimizer was used for training, and a total of 80,000 iterations were performed. The entire computation process took approximately 6.2 hours. In the final stage of training, the total loss function value converged to a very small stable value.

[0216] Output: The engine ultimately outputs an optimal material physical property field covering all 2.5 million nodes. This field is a huge floating-point array, where each element corresponds to the ideal Young's modulus E and Poisson's ratio v for a node. Analysis of this field reveals that on the main load-bearing path that needs to withstand high stress, the E value is close to 8.5 GPa (PA6-CF); at the bending root of the latch, the E value shows a smooth transition from 8.5 GPa to 0.1 GPa (TPU95); and on the surface in direct contact with the battery casing, there is a pure flexible layer with an E value of approximately 0.1 GPa.

[0217] Step 4: Generate a 3D model using the model generation module (204).

[0218] The material property field output by the inversion engine is sent to the model generation module.

[0219] Decoding Generation: This module loads a pre-trained C-VAE decoder model. Conditioned by this property field, the decoder generates a refined voxelized gradient material model with a resolution of 1024x1024x512 in just about 15 minutes.

[0220] Model Conversion and Output: Subsequently, a post-processing program applies the Marching Cubes algorithm to convert the voxel model into a triangular mesh model and encodes gradient material information into each vertex. The final output is a 3D model file in .3MF format, approximately 310MB. Figure 5As shown, the rendering specifically illustrates the macroscopic component subdivisions and details of the transition between the latch and the actual component, focusing on the reshaping and cutting of the connection. Due to the significant advantages of the generated structural distribution and transition physical layer driven by this inverse mathematical decoding technology, the final solid component exhibits clearly defined functional characteristics at the material level, presenting integrated modules. In the above application, the cross-sectional representation of the structural entity will generally explicitly express the following areas constituting the solid part. The figure clearly shows the material distribution of three different functional areas: Reference numeral 302 indicates the rigid main frame of the latch, which is made of pure PA6-CF material to provide high strength and stiffness, ensuring structural stability under overload. Reference numeral 303 indicates the flexible contact surface, which is made of pure TPU95 material and is located on the surface in direct contact with the battery casing, used to buffer vibration and resist wear caused by long-term insertion and removal. Most importantly, reference numeral 301 indicates the gradient flexible transition area, located in stress concentration areas such as the bending root of the latch. Within this region, the material transitions smoothly and continuously from pure PA6-CF to pure TPU95. This biomimetic design effectively mitigates stress concentration, which is key to improving the fatigue life of components and the overall structural toughness.

[0221] Step 5: Generate manufacturing instructions through the instruction generation module (205).

[0222] The .3MF file is loaded into the custom instruction generation module of this invention.

[0223] Path planning and collaborative optimization: The module slices the model with a layer height of 0.1mm and plans the printing path for the dual printheads. In the loop that generates G-code, when determining the extrusion amount of each micro-segment, the program queries the material ratio in the model corresponding to the center point (x,y,z) of that micro-segment and dynamically calculates the mixing weight k value in M163 S0 P(k) S1 P(1-k), and then activates the ratio using the M164 instruction.

[0224] Final output: Ultimately, the module generated a custom G-code file of approximately 98MB containing millions of lines of code.

[0225] Step 6: Physical manufacturing and post-processing via additive manufacturing unit (207)

[0226] The generated G-code file was uploaded to the modified Ultimaker S5 printer. After the operator confirmed that both PA6-CF and TPU95 materials were correctly loaded, the printing job was started. The total printing time was approximately 9 hours. After printing, the finished product was removed, and the necessary support structures were removed to obtain the final physical entity of the snap-fit ​​assembly.

[0227] III. Result Validation and Performance Comparison

[0228] To verify the technical effect of the embodiments of the present invention, two other conventional methods were used to design and manufacture the same snap-fit ​​assembly as a control group:

[0229] Control group A: Commercial topology optimization software was used to optimize the design of pure PA6-CF material with the goal of minimizing weight.

[0230] Control group B: Manually designed by engineers using two materials, PA6-CF and TPU, but spliced ​​together in CAD software through simple Boolean operations, resulting in an abrupt and discontinuous interface between the two materials.

[0231] Three groups of samples (five samples per group, average value) were mounted on the Instron material testing machine and tested to the exact same performance parameters set in step 1. The detailed test results are summarized in the table below:

[0232] Performance indicators Control group A (pure PA6-CF) Control group B (simple splicing) Embodiments of the present invention Performance improvement rate (relative to the best control group) Total weight (g) 12.5 (Constraints satisfied) 14.8 (Constraints satisfied) 13.2 (Constraints satisfied) - Maximum displacement (mm) under 15G overload 0.08 0.25 (exceeding the standard) 0.06 25.0% (Better than A) Random vibration test (2 hours) The tongue broke at the base in the 35th minute. Delamination occurred at the material interface at the 70th minute. No visible damage was detected during testing. N / A (Pass / Fail) Maximum insertion force (N) 45.2 (Too tight, exceeding the standard) 28.5 29.1 - (Satisfies constraints) Initial unlocking force (N) 42.1 23.3 (too low, exceeds the standard) 27.3 - (Satisfies constraints) Unlocking force (N) after 10,000 insertions and removals 24.8 (Approaching expiration) 11.9 (Severely worn) 25.2 1.6% (better than A) Attenuation rate after 10,000 insertions and removals 41.3% (exceeding the standard) 48.9% (exceeding the standard) 7.7% 81.4% (better than A)

[0233] Experimental data clearly demonstrates that only the snap-fit ​​assembly created using the method and apparatus of this invention is the sole solution capable of simultaneously meeting all preset, stringent, and contradictory design specifications. Control group A, while exhibiting good rigidity, failed vibration and fatigue tests due to its brittle material and suffered from poor insertion and removal feel. Control group B attempted to combine the advantages of both materials, but the abrupt material interface became a structural weakness, leading to earlier failure in vibration and fatigue tests.

[0234] In summary, this invention provides a multi-material configuration and additive manufacturing method based on a causal inversion mechanism, along with corresponding systems and devices. The core technical solution of this invention lies in establishing a novel design and manufacturing logic: this logic uses the preset functions and performance indicators of the end product as the input and solution target for calculation. Through an artificial intelligence model embedded with objective physical laws (specifically manifested as partial differential equations in solid mechanics) as strong constraints, it performs reverse deduction to directly solve for the optimal material spatial distribution scheme necessary to achieve the preset target. Furthermore, this solution also includes a complete technical path that transforms this abstract material distribution scheme into a concrete three-dimensional digital geometric model with continuous gradient characteristics, and finally compiles and generates integrated and coordinated fine-grained processing instructions that can be directly executed by multi-material additive manufacturing equipment.

[0235] Compared with the prior art, the main improvements and technical effects of this invention are reflected in the following aspects:

[0236] First, this invention changes the traditional design and verification model. Existing technologies typically employ a "forward" approach, where designers first propose a specific geometric and material scheme, and then verify its performance through simulation or experimentation. This process relies on the designer's prior knowledge and often requires multiple iterations. This invention, however, adopts a reverse approach, directly generating design solutions from performance requirements. This reduces reliance on the designer's prior experience and enables the discovery of a global solution that satisfies multiple complex constraints within a unified, automated process, improving the efficiency of the design process and the optimality of the results.

[0237] Second, this invention provides a technical approach to deeply integrate first principles of physics with data-driven artificial intelligence models. In existing technologies, physical simulation and artificial intelligence models are often used as separate tools. This invention, by incorporating the residuals of physical partial differential equations as an intrinsic component of the neural network loss function, ensures that the entire learning and inference process of the AI ​​model is strictly constrained by physical laws. This mechanism guarantees the physical authenticity and self-consistency of its output results, avoiding the unreasonable degenerate resolution (degenerate divergence error) that may occur in purely data-driven models, which violates the objective laws of force transmission equilibrium.

[0238] Third, this invention establishes a closer link between digital design and physical manufacturing. Existing technologies typically output a static geometric file, relatively independent of downstream manufacturing process parameters. This invention, however, simultaneously generates a geometric model and collaboratively and dynamically optimizes additive manufacturing process parameters that precisely match the microscopic material distribution of that model, integrating both into a unified manufacturing command. This integrated design-manufacturing approach increases the likelihood and success rate of accurately and faithfully converting complex gradient material digital models into physical entities.

[0239] Therefore, the technical solution of the present invention has effectively improved the existing technology in multiple aspects such as design paradigm, application of physical laws and design-manufacturing integration, and solved the long-standing performance and reliability problems in the field of multi-material additive manufacturing caused by the disconnect between design and manufacturing reality.

[0240] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A multi-material mortise and tenon biomimetic configuration and additive manufacturing method based on causal mechanical spectrum inversion, characterized in that, Includes the following steps: Obtain the target mechanical performance parameters of the target component under preset working conditions; Based on the target mechanical performance parameters, an artificial intelligence model with embedded solid mechanics partial differential equations as physical constraints is used to perform reverse calculations to obtain the optimal material physical property field in the target component design domain corresponding to achieving the target mechanical performance parameters. Based on the optimal material physical property field, a three-dimensional digital model with a continuous gradient material distribution is generated; as well as The three-dimensional digital model is analyzed, and additive manufacturing process parameters are collaboratively optimized based on the continuous gradient material distribution to generate integrated manufacturing instructions for driving multi-material additive manufacturing equipment.

2. The method according to claim 1, characterized in that, The step of obtaining the target mechanical performance parameters, before performing reverse calculations using an artificial intelligence model, further includes: The design domain of the target component is discretized, and its geometric constraints and key functional nodes are abstracted into an initial mechanical graph containing nodes and edges. Wherein, the node represents a material element, and the edge represents the force transmission relationship between the material elements; The inverse calculation is performed on the initial mechanical graph to obtain the optimal material physical property field, which assigns a set of optimal material physical parameters to each node and edge of the graph.

3. The method according to claim 1, characterized in that, The artificial intelligence model is a hybrid deep learning model that includes two stages: causal inference and configuration generation. The specific steps for performing inverse calculations and generating a 3D digital model include: In the causal deduction stage, a physical information neural network is used, with the target mechanical performance parameters as the optimization objective in its loss function. In the calculation stage involving the elastic displacement field distribution, the residuals of the embedded solid mechanics partial differential equations are used as the physical constraint penalty term in the loss function. Through backpropagation training, the optimal material physical property field is deduced in reverse. During the configuration generation stage, the optimal material physical property field is used as the conditional input of the conditional variational autoencoder. The decoder of the conditional variational autoencoder decodes and reconstructs the three-dimensional digital model with continuous gradient material distribution in the latent space.

4. The method according to claim 3, characterized in that, In the loss function of the physical information neural network, the solid mechanics partial differential equation serving as the physical constraint is the Navier-Cauchy equation. The objective of the loss function is to adjust the network weights through backpropagation algorithm, under the premise of satisfying the user-defined target mechanical performance parameters, so that the displacement field predicted by the network can make the residual of the Navier-Cauchy equation approach zero, thereby ensuring that the optimal material physical property field obtained by the solution satisfies physical reality.

5. The method according to claim 3, characterized in that, The conditional variational autoencoder is pre-trained with a dataset containing functionally graded material structures and their corresponding physical property fields, and learns the mapping relationship from physical property fields to three-dimensional geometric configurations. The three-dimensional digital model is a voxel model, which reproduces the continuous gradient material distribution required by the optimal material physical property field at the voxel level, and automatically generates a soft transition zone that smoothly transitions from rigid materials to flexible materials when the region requiring stress relief is predicted.

6. The method according to claim 1, characterized in that, The steps for collaboratively optimizing additive manufacturing process parameters specifically include: Based on the spatial positional variations of material components in the aforementioned three-dimensional digital model, a three-dimensional motion path is planned for the printhead of the multi-material additive manufacturing equipment; and At each node of the motion path, based on the gradient material composition information of that node, at least one of the following process parameters is adjusted synchronously and dynamically: the instantaneous extrusion rate ratio of two or more materials, the printing nozzle temperature, the printing platform temperature, the layer height, or the print head movement speed, so as to ensure that the microscopic material properties of the final manufactured physical entity are highly consistent with the three-dimensional digital model.

7. A multi-material mortise and tenon biomimetic configuration and additive manufacturing device based on causal mechanical spectrum inversion, characterized in that, include: The target input module is configured to acquire the target mechanical performance parameters of the target component under preset working conditions; The causal mechanical graph inversion engine module is configured to perform inverse calculations based on the target mechanical performance parameters, using an artificial intelligence model with embedded solid mechanics partial differential equations as physical constraints, to obtain the optimal material physical property field in the target component design domain corresponding to achieving the target mechanical performance parameters. The model generation module is configured to generate a three-dimensional digital model with a continuous gradient material distribution based on the optimal material physical property field. as well as The instruction generation module is configured to parse the three-dimensional digital model and, based on the continuous gradient material distribution, collaboratively optimize the additive manufacturing process parameters to generate integrated manufacturing instructions for driving multi-material additive manufacturing equipment.

8. The apparatus according to claim 7, characterized in that, Also includes: The preprocessing and graph construction module is configured to abstract the design domain of the target component into an initial mechanical graph containing nodes and edges before the causal mechanical graph inversion engine module performs inverse calculations, wherein the nodes represent the discrete micro-elements of the target component region and the edges represent the spatial physical connections between the micro-elements. The causal mechanical graph inversion engine module is further configured to perform inverse calculations on the initial mechanical graph, assigning a set of optimal material physical parameters to each node and edge of the graph to form the optimal material physical property field.

9. The apparatus according to claim 7, characterized in that, The artificial intelligence model embedded within the causal dynamics graph inversion engine module is a hybrid deep learning model. The engine module specifically includes: A reverse inference unit based on a physical information neural network is configured to use the target mechanical performance parameters as the optimization objective and the residuals of the solid mechanics partial differential equations as part of the loss function for training, thereby inversely inferring the optimal material physical property field; and The configuration generation unit based on the conditional variational autoencoder is configured to use the optimal material physical property field as a condition to reconstruct the three-dimensional digital model with a continuous gradient material distribution in the latent space through a decoder.

10. The apparatus according to claim 7, characterized in that, The instruction generation module is further configured as follows: Based on the changes in the material gradient in the three-dimensional digital model, the additive manufacturing process parameters are dynamically and synchronously optimized, and a time-series instruction containing refined process control parameters is generated. This allows the device to output not only a static geometric model, but also a complete integrated solution encompassing macroscopic geometry, microscopic material distribution, and manufacturing process control.

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