Method, device, electronic equipment and system for solving mechanical response of degenerated fiber material

Abstract

The present application relates to a kind of degenerative fiber material mechanics response solving method, device, electronic equipment and system, belong to material mechanics technical field, wherein, the degenerative fiber material mechanics response solving method includes obtaining the reference configuration region of the object to be analyzed, based on the reference configuration region Establishment solving region, And the node discrete of solving region;Through shape function, the global displacement field of the node discrete solving region is constructed, and the deformation gradient is calculated;Based on the deformation gradient, the material free energy expression is established, and the random damage field of the object to be analyzed is constructed;Based on the material free energy expression and the random damage field, the degenerative fiber action mechanism is constructed, and the mechanical response analysis result of the object to be analyzed is calculated according to the degenerative fiber action mechanism.It is closer to the state of actual organization or material.Can reflect the characteristics of material gradually weak in degradation under multiple loadings or complex loading paths.

Description

Technical Field

[0001] This invention relates to the field of materials mechanics, and in particular to a method, apparatus, electronic device, and system for solving the mechanical response of degraded fiber materials. Background Technology

[0002] Fiber-reinforced superelastic materials are widely found in biological soft tissues, flexible composite materials, and engineering protective materials. These materials typically consist of a matrix and fibers with a specific orientation, exhibiting significant nonlinearity, large deformation, and anisotropy under external loads. Particularly in biological tissues such as blood vessel walls and the aorta, the orientation, load-bearing capacity, and local degradation state of the fibers directly affect the overall mechanical response of the material. Therefore, developing a mechanical analysis method that can simultaneously reflect the fiber reinforcement effect, material nonlinearity, and spatially random non-uniform degradation characteristics has always been an important research topic in this field.

[0003] However, the mechanical behavior of such materials is highly complex. On the one hand, fiber-reinforced hyperelastic materials often exhibit large deformation, directional dependence, and significant history dependence during stress. On the other hand, real materials often contain random damage, localized failure, and spatially inhomogeneous degradation, especially in diseased tissues. Traditional uniform parameter models typically only describe the overall average characteristics and are insufficient to reflect the local stiffness differences, stress concentrations, and deformation localization caused by varying degrees of damage at different locations within the material. Furthermore, at the solution level, due to the strong nonlinearity of constitutive relations, the complex fiber orientation distribution, and the spatial randomness of the damage field, stably and accurately solving the boundary value problem is also a practical challenge.

[0004] To address the aforementioned problems, existing methods typically handle them from two aspects: one is to use traditional hyperelastic or fiber-reinforced constitutive models to describe the mechanical contributions of the matrix and fibers; the other is to use numerical methods such as the finite element method to discretize and solve the boundary value problem. Some studies have considered fiber tension activation, orientation distribution, and degradation mechanisms, and some methods have attempted to describe the spatial fluctuations of material parameters through random fields. However, existing solutions still have some shortcomings: first, some models simplify the expression of fiber degradation, making it difficult to simultaneously account for random fiber damage, local degradation, and overall nonlinear response; second, although some methods introduce damage or random parameters, their integration with constitutive relations and the solution process is not tight enough, making it difficult to uniformly reflect the relationship between material composition, random damage, and mechanical solution; third, under complex nonlinear and random degradation conditions, existing solution methods still have room for improvement in terms of boundary condition application, numerical stability, and local response fidelity. Therefore, it is necessary to propose a Lagrangian energy solution method that considers random damage fields and constitutive characteristics of degraded fibers to more reasonably describe the true mechanical behavior of such materials. Summary of the Invention

[0005] In view of this, it is necessary to provide a method, apparatus, electronic device and system for solving the mechanical response of degraded fiber materials, so as to solve the problem that existing mechanical response analysis of fiber materials cannot take into account random damage and constitutive characteristics of degraded fibers.

[0006] To address the aforementioned problems, this invention provides a method for solving the mechanical response of degraded fiber materials. This method obtains a reference configuration region of the object to be analyzed, establishes a solution region based on the reference configuration region, and discretizes the solution region at its nodes. The global displacement field of the solution domain after node discretization is constructed using shape functions, and the deformation gradient is calculated. Based on the deformation gradient, an expression for the material free energy is established, and a stochastic damage field of the object to be analyzed is constructed. Based on the material free energy expression and the random damage field, a degradation fiber action mechanism is constructed, and the mechanical response analysis results of the object to be analyzed are calculated according to the degradation fiber action mechanism.

[0007] In some implementations, obtaining a reference configuration region of the object to be analyzed, establishing a solution region based on the reference configuration region, and discretizing the solution region by nodes include: Obtain the reference configuration region of the object to be analyzed; The geometric dimensions, boundary range, and load type are determined based on the configuration region; The solution domain is established based on the boundary conditions, the geometric dimensions, the boundary range, and the load type, and the solution domain is discretized at nodes.

[0008] In some implementations, the step of constructing the global displacement field of the solution region after node discretization using shape functions and calculating the deformation gradient includes: The nodal displacement degrees of freedom are interpolated to the solution domain after the nodes are discretized by using shape functions to obtain the global displacement field. The configuration tensor of the global displacement field is calculated, and the deformation gradient is determined based on the calculation results.

[0009] In some implementations, establishing a material free energy expression based on the deformation gradient, and constructing a stochastic damage field of the object to be analyzed, includes: The matrix energy term, right Cauchy-Green tensor, and volume change are determined based on the deformation gradient. A material free energy expression is established based on the matrix energy term, the right Cauchy-Green tensor, and the volume change. A random damage field of the object to be analyzed is constructed based on the fiber orientation of the object.

[0010] In some implementations, constructing the random damage field of the object to be analyzed based on the fiber orientation of the object includes: Obtain the fiber orientation information of the object to be analyzed; Calculate fiber strain invariants based on the fiber orientation information, and establish a fiber orientation weighting function based on the fiber orientation information; A random damage field is constructed based on the fiber strain invariant and the fiber orientation weighting function.

[0011] In some embodiments, the step of constructing a degradation fiber action mechanism based on the material free energy expression and the random damage field, and calculating the mechanical response analysis results of the object under analysis based on the degradation fiber action mechanism, includes: The local health coefficient of each material point of the object to be analyzed is calculated based on the random damage field and the material free energy expression. The fiber potential function is determined based on the local health coefficient, and the mechanism of degenerative fiber action is constructed based on the fiber potential function. The mechanical response analysis results of the object under analysis were calculated based on the mechanism of action of the degraded fibers.

[0012] In some embodiments, the calculation of the mechanical response analysis results of the object under analysis based on the degraded fiber mechanism includes: The total fiber energy and total system potential energy of the object under analysis are calculated based on the degraded fiber mechanism described above. Apply displacement boundary conditions to the total potential energy of the system and perform a minimization solution to obtain the minimum potential energy solution of the system. The mechanical response analysis results of the object to be analyzed are determined based on the total fiber energy and the minimum solution of the system potential energy. The mechanical response analysis results include the overall displacement distribution of the material, the internal strain and stress distribution of the material, the random damage factor field distribution, the stiffness degradation and stress concentration phenomena corresponding to the local damage area, and the mechanical response results under different random damage parameters, fiber orientation parameters and load conditions.

[0013] Secondly, embodiments of this application also provide a device for solving the mechanical response of degraded fiber materials, comprising: a solution domain module, a deformation gradient module, a random damage module, and a mechanical analysis module; the solution domain module is used to obtain a reference configuration region of the object to be analyzed, establish a solution domain based on the reference configuration region, and discretize the nodes of the solution domain; the deformation gradient module is used to construct the global displacement field of the node-discrete solution domain through shape functions, and calculate the deformation gradient; the random damage module is used to establish a material free energy expression based on the deformation gradient, and construct a random damage field of the object to be analyzed; the mechanical analysis module is used to construct the degraded fiber action mechanism based on the material free energy expression and the random damage field, and calculate the mechanical response analysis results of the object to be analyzed according to the degraded fiber action mechanism.

[0014] Thirdly, the present invention also provides an electronic device, including a memory and a processor, wherein, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the method for solving the mechanical response of degraded fiber materials as described in any of the above implementations.

[0015] Fourthly, the present invention also provides a mechanical response solution system for degraded fiber materials. The mechanical response solution system for degraded fiber materials includes an electronic device, a data acquisition device, and a result output device. The data acquisition device and the result output device are respectively connected to the electronic device. The data acquisition device is used to acquire material data of the object to be analyzed, and the result output device is used to output and display the mechanical response analysis results of the object to be analyzed.

[0016] Fifthly, the present invention also provides a computer-readable storage medium for storing a computer-readable program or instructions, which, when executed by a processor, can implement the steps in the method for solving the mechanical response of degraded fiber materials described in any of the above implementations.

[0017] The beneficial effects of this invention are as follows: The method for solving the mechanical response of degraded fiber materials provided by this invention first obtains the reference configuration region of the object to be analyzed, then establishes the solution region, calculates the deformation gradient, then constructs the material free energy expression and random damage field, and finally constructs the degraded fiber action mechanism for mechanical response analysis. The introduction of a random damage factor field to represent the difference in damage degree at different locations within the material allows for the simulation not only of overall degradation but also of phenomena such as localized damage, localized softening, and stress concentration, thus more closely resembling the state of actual tissues or materials. The fiber energy of the degraded fiber is calculated only when the fiber is under tension, describing the irreversible degradation process of the fiber and reflecting the characteristic of gradual weakening of the material under multiple loading or complex loading paths. Attached Figure Description

[0018] Figure 1 A flowchart illustrating the steps of a method for solving the mechanical response of degraded fiber materials according to an embodiment of this application; Figure 2 Elastic fiber direction vector for solving the mechanical response of degraded fiber materials provided in an embodiment of this application. N Schematic diagram; Figure 3 A schematic diagram of the structural boundary conditions for a method for solving the mechanical response of degraded fiber materials provided in an embodiment of this application; Figure 4 A schematic diagram illustrating the influence of the magnitude of the penalty term coefficient γ on the calculation results of the mechanical response solution method for degraded fiber materials provided in an embodiment of this application; Figure 5 A schematic diagram of the solution domain and boundary conditions for a method for solving the mechanical response of degraded fiber materials provided in an embodiment of this application; Figure 6 This is a schematic diagram of LEM method element selection for a method of solving the mechanical response of degraded fiber materials according to an embodiment of this application; Figure 7 A schematic diagram illustrating the influence of fiber orientation on stress distribution in a method for solving the mechanical response of degraded fiber materials provided in an embodiment of this application; Figure 8 A schematic diagram illustrating the influence of different random damage fields on stress distribution in a method for solving the mechanical response of degraded fiber materials provided in an embodiment of this application; Figure 9 A flowchart illustrating another step of the method for solving the mechanical response of degraded fiber materials according to an embodiment of this application; Figure 10 A schematic diagram of the weight distribution on the fiber elastic energy integral hemisphere for a method of solving the mechanical response of degraded fiber materials provided in an embodiment of this application; Figure 11A schematic diagram of the random damage factor field for a method of solving the mechanical response of degraded fiber materials provided in an embodiment of this application; Figure 12 A functional block diagram of a device for solving the mechanical response of degraded fiber materials provided in an embodiment of this application; Figure 13 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0019] 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 a part of the embodiments of the present invention, and not all of them. 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.

[0020] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0021] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0022] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0023] To address the above problems, this invention provides a method for solving the mechanical response of fiber-reinforced hyperelastic materials, with the following symbol definitions: X represents the initial configuration; x represents the modified configuration. Represents the deformation gradient; C=F T F represents the right Cauchy–Green tensor; E = 1 / 2 (C 1) Represents the Green-Lagrange strain tensor; J=detF 1. If J=1, it means the volume deformation is 0; v =J 1 represents volumetric strain; This indicates the distortion after removing the volumetric deformation portion; This represents the modified right Cauchy-Green tensor; Indicates the first invariant; These represent the azimuth and polar angle, respectively. Indicates fiber orientation; Indicates the fourth invariant; This represents the modified fourth invariant; Represents total energy; Represents volumetric deformation energy; It represents distortion energy.

[0024] This invention provides a method, apparatus, electronic device, and system for solving the mechanical response of degraded fiber materials, which are described below.

[0025] Figure 1 This is a schematic flowchart of an embodiment of the method for solving the mechanical response of degraded fiber materials provided by the present invention. The executing entity of the method for solving the mechanical response of degraded fiber materials can be a computer, a portable smart device, or a cloud server, etc., and this embodiment does not limit it in this way. Figure 1 As shown, the methods for solving the mechanical response of degraded fiber materials include: S101. Obtain the reference configuration region of the object to be analyzed, establish the solution region based on the reference configuration region, and discretize the nodes of the solution region.

[0026] It should be noted that this invention relates to the interdisciplinary fields of computational mechanics, continuum mechanics, intelligent scientific computing, and materials constitutive modeling. Specifically, it relates to the field of mechanical analysis and numerical solution technology for fiber-reinforced hyperelastic materials, and more specifically, to a Lagrange energy solution method considering random damage fields and degraded fiber constitutive models. More specifically, this invention relates to a method that decomposes the material free energy into isotropic hyperelastic energy terms for the matrix, volumetric energy terms, and anisotropic energy terms for multiple fiber families, and generates a continuous random damage field based on Gaussian processes to simulate random lesions and degradation of tissue fibers. Regarding the solver, the Lagrange energy method is employed. First, the solution space is discretized at nodes, and then shape functions are applied to interpolate the node displacements to the global domain, thereby enabling the calculation of deformation gradients and further calculation of global internal strain energy and external potential energy. This constitutive method and Lagrange energy solver can be applied to the mechanical analysis of fiber-reinforced soft materials, biological tissues, composite flexible structures, and other anisotropic large-deformation hyperelastic materials.

[0027] It should be understood that the complete description of the scheme in this embodiment is as follows: First, the free energy decomposition form of the hyperelastic material is performed. For the material to be analyzed, its total free energy function is constructed, and the total free energy is decomposed into the sum of the matrix volume energy term and the distortion energy term, that is: Ψ=Ψ iso +Ψ v in P iso The calculation considers the matrix portion P g and elastic fiber part P e : P iso =Ψ g +Ψ e

[0028] It should be understood that, considering elastic fiber materials with degradation characteristics, a strain energy function is constructed that takes into account collagen fiber dispersion while excluding the contribution of compressed fibers. The elastic energy of the elastic fiber is integrated within an integral hemisphere. The fiber integration process can be represented by the following hemispherical model:

[0029] in, S Indicates a hemisphere. R Indicates the main direction of the fiber. be Indicates that the fiber is in R The density of directions, be The larger the value, the more the fiber is in R Direction is focused. When be=0 Indicating that the weights are equal across the entire hemisphere, it is easy to derive:

[0030] Specifically, such as Figure 2 The diagram shows the direction vector of the elastic fiber. N Schematic diagram: When integrating the elastic energy, only the fibers located inside the inverted cone are considered, i.e., only the fibers located inside the inverted cone are considered. N 1. Not considering N 2. In direction N i The elastic properties of the fibers are expressed as follows:

[0031]

[0032]

[0033] in, P i Indicates direction N i The elastic properties of the fibers, c 1 and c 2 represents material parameters. x For damage parameters, x The meaning is as follows:

[0034] Therefore, it is possible to calculate the total elastic potential energy at a material point under given parameters.

[0035] Furthermore, the Cauchy stress tensor can be expressed as:

[0036] When using the classical finite element method solver, and when using the Newton-Raphson nonlinear solver, it is usually necessary to manually derive the material tangent matrix.

[0037] This allows us to construct the material tangent matrix. However, in our method, there is no need to explicitly calculate the stress tensor and tangent matrix, as the problem is transformed into an optimization problem. The objective is to minimize the overall state energy. P It includes internal elasticity. P in Work done by external loads P ext .

[0038] The third step is to generate a random damage factor field based on a Gaussian process: In order to more realistically characterize the randomness and spatial non-uniformity of damage distribution inside biological tissues, fiber-reinforced soft materials or diseased tissues, a random damage factor field is further introduced based on the above embodiments, and a spatially correlated random field is generated by a random Gaussian process to simulate the random damage, local degradation and spatial discrete damage characteristics inside the tissue.

[0039] Establish a random factor field: Let the material reference configuration region be Oh d ,in d Representing dimensions (d=2 or 3) In the region Oh Define a random factor variable field. ζX It follows a Gaussian process, that is:

[0040] in, m(X) This represents the mean. k(X,X') This represents the covariance function, used to characterize the statistical relationship between different spatial locations. The covariance function is a squared exponential kernel function.

[0041] in, Represents the variance of a random field. l c Spatial correlation length is used to control the smoothness of the factor distribution and local clustering characteristics. When l c When the value is small, the random distribution changes rapidly, indicating stronger local dispersion of damage within the tissue; when... l c When the value is large, the damage field distribution is relatively smooth, indicating that the tissue degradation has stronger spatial continuity.

[0042] Random field generation based on Cholesky decomposition: The covariance kernel function of the random field is generated according to the above formula. K Then proceed with Cholesky: K=LL T Random variables are generated using independent normal distributions. r~N(0, I) Thus, a random field is obtained: ζ=Lr Normalization mapping of the random damage factor field: Since the health coefficient or damage factor should usually be limited to a predetermined range, such as [0~1], it is necessary to normalize the Gaussian random field. g(X) Further mapping to a bounded random damage factor field ξ(X) This invention employs a Sigmoid mapping:

[0043] in, α Steepness coefficient, β This is the offset parameter. Adjust it... α and β It can control the concentration range of the health coefficient distribution and the proportion of damage.

[0044] Finally, the Lagrangian Energy Method (LEM) is defined as follows: An energy functional is established under a Lagrangian reference configuration, and all integrals, fiber orientation definitions, and deformation tensor calculations are based on the initial configuration. XIn essence, this is the Total Lagrangian framework. The LEM uses displacement representation based on nodal degrees of freedom under the reference configuration, while the DEM represents the displacement field as a continuous function of spatial position. Therefore, its field representation is closer to the spatial (Eulerian-like) description.

[0045] Advantages of this embodiment: For the aforementioned degraded fiber hyperelastic material, given the material parameters, fiber orientation distribution, degradation factor, and boundary conditions, the material's mechanical response can be characterized by a total potential energy functional. The total potential energy is typically written as: P=P in P ex in, P in Indicates internal strain energy. P ex This represents the work done by external forces. For the above-described stochastic degenerate fiber hyperelastic model, the internal energy can be denoted as:

[0046] in, F For deformation gradient, x For the overall health coefficient, N In the direction of the fiber.

[0047] Specifically, the Lagrange energy method is implemented as follows: First, discretize the solution space under the reference configuration: Material Area Oh The mesh is divided into a regular mesh or a finite element mesh, with each element node carrying a displacement degree of freedom. Let the node be a displacement vector: u={u1, u2,…,un} in n This represents the total number of discrete degrees of freedom.

[0048] Extend the nodal displacements to the shape functions. Oh Approximate continuous displacement field on:

[0049] in, N a (X) For shape functions, u a For nodal displacement. The deformation gradient can be denoted as:

[0050] Substituting into the above model, the total energy over the entire domain is obtained. Combining body force and boundary traction, the external potential is calculated as follows:

[0051] in, f b For volume forces, t For boundary traction force, C t These are force boundary conditions.

[0052] Finally, the neural network output is established as the displacement corresponding to the degree of freedom: a fully connected network consisting of multiple hidden layers and an output layer is constructed. The network does not receive spatial coordinate input, but instead uses a fixed constant vector as its initial input, and outputs the displacement degrees of freedom of all nodes. If the total number of discrete grid nodes is... N For a two-dimensional problem, the dimension of the network output is... 2N For three-dimensional problems, the network output dimension is... 3N The network consists of an input layer, multiple hidden layers, and an output layer. The hidden layers use the hyperbolic tangent activation function, and the network parameters are initialized with zero bias and normally distributed weights.

[0053] It should be understood that the advantages of using a constitutive model are: 1. Random damage factors can be used to describe non-uniform damage within tissues. This invention introduces a random damage factor field to represent the differences in damage levels at different locations within a material. Therefore, it can simulate not only overall degradation but also localized damage, localized softening, and stress concentration, thus more closely resembling the state of actual tissues or materials.

[0054] 2. More in line with the actual stress characteristics of fiber-reinforced materials. This invention describes the material's free energy by dividing it into three parts: matrix, volume, and fiber. This allows for a clearer distinction between the effects of different components on the overall mechanical response, which is more reasonable than treating the material as a whole.

[0055] 3. It can more realistically reflect the fiber degradation and damage process. This invention calculates fiber energy only when the fiber is under tension and combines historical variables to describe the irreversible degradation process of the fiber, which can reflect the characteristic of the material gradually weakening under multiple loading or complex loading paths.

[0056] In practical implementation, the advantages of using the LEM method are: boundary conditions are easier to apply and more accurate. LEM directly uses the nodal displacement degrees of freedom as the solution variables, and displacement boundary conditions can be directly applied to the nodes. This is more direct than the indirect application of boundary conditions through penalty functions in DEM, and it is also easier to ensure that the boundary conditions are satisfied accurately.

[0057] Specifically, to illustrate the advantages of the LEM method, we introduce, for example... Figure 3The example shown illustrates this, where one end uses a consolidation constraint and the other end uses a displacement constraint. The DEM method applies boundary conditions by adding a penalty term to the loss function. For example, the following loss function:

[0058] in, P in P ext For potential energy minimization, For boundary penalties, among which C For displacement boundary, For the displacement on the boundary, This is the displacement predicted by the deep neural network. At this point, the calculation result is affected by... c The effect of size, specifically as follows: Figure 4 As shown. In the LEM method, displacement constraints are precisely applied to the boundary Γ, without the need to introduce a displacement boundary penalty term into the loss function (potential energy function).

[0059] It should be noted that this embodiment proposes a Lagrangian energy solution method that considers random damage fields and degraded fiber constitutive models, which is used to solve the displacement field, strain field and stress field of fiber-reinforced hyperelastic materials under external loads.

[0060] In some embodiments, step S101 includes: obtaining a reference configuration region of the object to be analyzed; determining the geometric dimensions, boundary range, and load type based on the configuration region; establishing a solution region based on the boundary conditions, the geometric dimensions, the boundary range, and the load type, and discretizing the solution region at nodes.

[0061] It should be understood that, firstly, a reference configuration region of the object to be analyzed is obtained. This involves establishing a reference configuration region for the material based on the object being analyzed, and determining its geometric dimensions, boundary extent, and load type. For a two-dimensional problem, a two-dimensional solution domain is established; for a three-dimensional problem, a three-dimensional solution domain is established. Boundary conditions are then set, including displacement boundary conditions and external force boundary conditions. Displacement boundary conditions are used to constrain displacement components on specified boundaries, while external force boundary conditions are used to describe surface loads or body forces. For example... Figure 5 As shown, one section uses consolidation constraints, and the other section uses displacement boundary constraints.

[0062] In practical implementation, the solution domain is discretized at nodes: the solution domain under the reference configuration is discretized, a finite number of nodes are arranged within the domain, and mesh elements are formed according to the node connection relationships. For example... Figure 5 As shown, if the total number of nodes is NIn this three-dimensional problem, the total displacement degrees of freedom are 3N. The displacement degrees of freedom of each node serve as the basic unknowns for subsequent solutions.

[0063] S102. Construct the global displacement field of the solution region after node discretization using shape functions, and calculate the deformation gradient.

[0064] It should be noted that after obtaining the solution domain and discretizing the nodes, the global displacement field is established through shape functions, and then the deformation gradient is calculated for subsequent establishment of the material free energy expression.

[0065] In some embodiments, step S102 includes: interpolating the nodal displacement degrees of freedom to the solution region after the nodes are discretized by using shape functions to obtain a global displacement field; performing configuration tensor calculation on the global displacement field, and determining the deformation gradient based on the calculation results.

[0066] It should be understood that after discretizing the nodes, shape functions are used to interpolate the nodal displacement degrees of freedom across the entire solution domain, resulting in a continuous displacement field. The displacement field can be expressed as:

[0067] in, X For reference, the position coordinates in the configuration, N a (X) For the first a The shape function corresponding to each node u a Let be the displacement vector of this node. Through the above interpolation, the displacement at any position within the entire solution domain can be recovered from the discrete node displacements.

[0068] In specific implementations, such as Figure 6 As shown, the LEM method uses triangular elements for two-dimensional problems and tetrahedral elements for three-dimensional problems. Figure 6 As shown, under three-dimensional conditions, the unit configuration tensor can be obtained. D Let the coordinates of the four nodes of the tetrahedral element in the reference configuration be as follows: X 1 ,X 2 ,X 3 ,X 4. Typically, the fourth node is chosen as the base point; therefore, the reference configuration tensor can be written as:

[0069] Arranging each edge vector column-wise results in a 3×3 matrix. Expanded, it is denoted as:

[0070] Similarly, the coordinates of the four nodes in the current configuration are... x 1, x 2,x 3, x 4. The current configuration tensor is then...

[0071] The current configuration expansion is denoted as:

[0072] Therefore, the gradient deformation is calculated as follows: F=D'D 1 S103. Based on the deformation gradient, establish the material free energy expression and construct the random damage field of the object to be analyzed.

[0073] It should be noted that after obtaining the deformation gradient, the material free energy expression and random damage field are established, so that random damage can be considered for subsequent mechanical analysis.

[0074] S104. Construct the degradation fiber action mechanism based on the material free energy expression and the random damage field, and calculate the mechanical response analysis results of the object to be analyzed according to the degradation fiber action mechanism.

[0075] It should be understood that the participation range of degenerated fibers is controlled by a random health coefficient field, and then the mechanical response parameters such as different fiber energy and system potential energy are calculated in detail.

[0076] In some embodiments, step S104 includes: calculating the local health coefficient at each material point of the object to be analyzed based on the random damage field and the material free energy expression; determining the fiber potential function based on the local health coefficient, and constructing the degraded fiber action mechanism based on the fiber potential function; and calculating the mechanical response analysis results of the object to be analyzed based on the degraded fiber action mechanism.

[0077] In the specific implementation, at each material point, based on the local health coefficient... ξ(X) Define the inverted cone polar angle threshold:

[0078] For each discrete fiber direction N i The fiber energy term is included in the calculation only if the following condition is met in this direction: 1. The fibers in this direction are under tension, that is... ; 2. This direction is within the effective inverted cone range, i.e. . Therefore, the fiber energy in a single fiber direction can be written as:

[0079] In one implementation, the fiber potential function can be expressed as:

[0080] in, c 1 and c 2 represents the material parameters.

[0081] In some embodiments, calculating the mechanical response analysis results of the object to be analyzed based on the degradation fiber action mechanism includes: calculating the total fiber energy and total system potential energy of the object to be analyzed based on the degradation fiber action mechanism; applying displacement boundary conditions to the total system potential energy and performing a minimization solution to obtain the minimum solution of the system potential energy; determining the mechanical response analysis results of the object to be analyzed based on the total fiber energy and the minimum solution of the system potential energy, wherein the mechanical response analysis results include the overall displacement distribution of the material, the internal strain and stress distribution of the material, the random damage factor field distribution, the stiffness degradation and stress concentration phenomena corresponding to the local damage area, and the mechanical response results under different random damage parameters, fiber orientation parameters, and load conditions.

[0082] In the specific implementation, the total fiber energy is calculated by weighted summation over all discrete fiber directions within the hemisphere to obtain the total fiber energy at the material point.

[0083] Subsequently, the volume energy, matrix energy, and fiber energy are added together to obtain the total free energy at this point in the material: Ψ=Ψ vol +Ψ g +Ψ e It should be noted that the total potential energy of the system is calculated as follows: Integrating the free energy over the solution domain yields the global internal strain energy:

[0084] Simultaneously, the external potential energy is calculated based on the external load:

[0085] in, f b For physical strength, t For boundary traction force.

[0086] Therefore, the total potential energy of the system can be expressed as:

[0087] It should be understood that applying displacement boundary conditions: For a given displacement boundary, the LEM method can directly constrain the corresponding nodal degrees of freedom to a specified value, thereby applying displacement boundary conditions. The LEM method allows for accurate application of displacement boundary conditions, improving solution stability. Unconstrained nodal degrees of freedom are treated as unknowns in the total potential energy minimization process.

[0088] In the specific implementation, the total potential energy is minimized: all unconstrained nodal displacement degrees of freedom are treated as unknowns, and the solution is performed with the goal of minimizing the total potential energy, i.e.:

[0089] During the solution process, an iterative optimization method can be used to continuously update the nodal displacements, gradually reducing the total potential energy of the system until the preset convergence condition is met. When the change in total potential energy, the increment of nodal displacements, or the residual reaches a given threshold, the iteration stops, and the final displacement solution is obtained.

[0090] Finally, the analysis results are output: After obtaining the nodal displacement solutions, the global displacement field, strain field, and stress field can be further recovered, and the following results are output (e.g. Figure 7 as well as Figure 8 The LEM and DEM simulation results for fiber tension show the influence of fiber direction on stress distribution. When the fiber direction is completely perpendicular to the tensile direction, the deformation is larger; the smaller the angle between the fiber direction and the tensile direction, the smaller the deformation. The influence of different random damage fields ξ(X) on stress distribution is also shown, with smaller stress at locations of greater damage. The following are the components: 1. Overall material displacement distribution; 2. Internal strain and stress distribution of the material; 3. Random damage factor field distribution; 4. Stiffness degradation and stress concentration phenomena corresponding to local damage areas; 5. Mechanical response results under different random damage parameters, fiber direction parameters, and load conditions.

[0091] Compared with existing technologies, the mechanical response solution method for degraded fiber materials provided in this embodiment first obtains the reference configuration region of the object to be analyzed, then establishes the solution region, calculates the deformation gradient, constructs the material free energy expression and random damage field, and finally constructs the degraded fiber action mechanism for mechanical response analysis. By introducing a random damage factor field to represent the differences in damage degree at different locations within the material, it can simulate not only overall degradation but also localized damage, localized softening, and stress concentration, thus more closely resembling the state of actual tissues or materials. It calculates the fiber energy of the degraded fiber only when the fiber is under tension, describing the irreversible degradation process of the fiber and reflecting the characteristic of the material gradually weakening under multiple loading or complex loading paths.

[0092] Please refer to Figure 9 , Figure 9This is a flowchart illustrating the steps of an embodiment of the method for solving the mechanical response of degraded fiber materials according to this application. Depending on different requirements, the order of the steps in this flowchart can be changed, and some steps can be omitted. This method for solving the mechanical response of degraded fiber materials can be applied to the aforementioned apparatus for solving the mechanical response of degraded fiber materials, but is not limited thereto, and the embodiments of this application do not limit this application.

[0093] This embodiment is a further improvement on the aforementioned embodiment. The main improvement is that in this embodiment, the material free energy is described in three parts: matrix, volume and fiber. This can more clearly distinguish the role of different components in the overall mechanical response, which is more reasonable than treating the material as a whole.

[0094] The specific process of this embodiment is as follows: Figure 9 As shown, it includes the following steps: S901. Determine the matrix energy term, right Cauchy-Green tensor, and volume change based on the deformation gradient.

[0095] It should be noted that after obtaining the deformation gradient, the right Cauchy-Green tensor is then calculated: C=F T F And the change in volume: J=det(F) To account for the isovolute deformation portion, a modified deformation gradient and a modified right Cauchy-Green tensor can be constructed for subsequent hyperelastic energy calculations.

[0096] S902. Establish the material free energy expression based on the matrix energy term, the right Cauchy-Green tensor, and the volume change.

[0097] It should be understood that this invention adopts the free energy decomposition form of fiber-reinforced hyperelastic materials, expressing the total free energy of the material as the sum of the matrix energy term, the volume energy term, and the fiber energy term, that is: Ψ=Ψ vol +Ψ g +Ψ e in, P vol This is the volumetric energy term, used to constrain changes in material volume; P g This is the matrix energy term, used to describe the isotropic hyperelastic response of the matrix; P e This is the fiber energy term, used to describe the fiber reinforcement effect.

[0098] In one implementation, the volumetric energy term can be expressed as:

[0099] in, K This refers to the bulk modulus or volumetric deformation penalty parameter.

[0100] The matrix energy term can be expressed as:

[0101] in, m Shear modulus To correct the first-order invariants.

[0102] S903. Construct a random damage field of the object to be analyzed based on the fiber orientation of the object to be analyzed.

[0103] It should be noted that a random damage field needs to be constructed at the end.

[0104] In some embodiments, step S903 includes: obtaining fiber orientation information of the object to be analyzed; calculating fiber strain invariants based on the fiber orientation information, and establishing a fiber orientation weighting function based on the fiber orientation information; and constructing a random damage field based on the fiber strain invariants and the fiber orientation weighting function.

[0105] It should be understood that defining fiber orientation and calculating fiber strain invariants: to characterize the directional effect of fiber-reinforced materials, the principal fiber orientation is predefined in the material. R Multiple discrete fiber directions are arranged within the hemispherical integral region. N i For each integration direction, calculate the fiber strain invariant:

[0106] It is used to reflect the tensile state in the corresponding fiber direction.

[0107] In the specific implementation, a fiber orientation weighting function is established: to describe the distribution characteristics of fibers near the main direction, a corresponding weight is assigned to each discrete fiber orientation. The weighting function can be expressed as:

[0108] in, b e This is a fiber distribution parameter used to adjust the degree to which fibers are concentrated along the main direction. When b e When the fiber is larger, it is more concentrated near the main direction; when b e =0At that time, the weights in all directions are equal. Energy calculation is performed by integration on the hemispherical surface, as follows: Figure 10 As shown.

[0109] It should be noted that a random damage field is constructed: to simulate random damage and spatial non-uniform degradation within tissue, this invention introduces a random damage factor field. A Gaussian random process is defined within the reference configuration region to generate a continuous random field, such as... Figure 11 As shown.

[0110] Based on the same idea as the method for solving the mechanical response of degraded fiber materials in the above embodiments, this application also provides a device for solving the mechanical response of degraded fiber materials. This device can be used to execute the above-described method for solving the mechanical response of degraded fiber materials. For ease of explanation, the structural schematic diagram of the embodiment of the device for solving the mechanical response of degraded fiber materials only shows the parts related to the embodiments of this application. Those skilled in the art will understand that the illustrated structure does not constitute a limitation on the device, and it may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0111] like Figure 12 As shown, the mechanical response solving device 1200 for degraded fiber materials includes a solution domain module 1201, a deformation gradient module 1202, a random damage module 1203, and a mechanical analysis module 1204. In some embodiments, the above modules can be programmable software instructions stored in memory and executable by a processor. It is understood that in other embodiments, the above modules can also be program instructions or firmware embedded in a processor.

[0112] The solution region module 1201 is used to obtain the reference configuration region of the object to be analyzed, establish a solution region based on the reference configuration region, and discretize the nodes of the solution region. The deformation gradient module 1202 is used to construct the global displacement field of the solution region after node discretization through shape functions, and to calculate the deformation gradient. The random damage module 1203 is used to establish a material free energy expression based on the deformation gradient and construct a random damage field of the object to be analyzed. The mechanical analysis module 1204 is used to construct the degradation fiber action mechanism based on the material free energy expression and the random damage field, and to calculate the mechanical response analysis results of the object to be analyzed according to the degradation fiber action mechanism.

[0113] Please refer to Figure 13 , Figure 13This is a schematic diagram of an embodiment of the electronic device of this application. In this embodiment of the invention, the electronic device 1300 includes a processor 1301, a memory 1302, and a display 1303. Figure 13 Only some components of the electronic device 1300 are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0114] In some embodiments, processor 1301 may be a central processing unit (CPU), microprocessor or other data processing chip, used to run program code stored in memory 1302 or process data, such as the mechanical response solution method for degraded fiber materials in this invention.

[0115] In some embodiments, processor 1301 may be a single server or a group of servers. The server group may be centralized or distributed. In some embodiments, processor 1301 may be local or remote. In some embodiments, processor 1301 may be implemented on a cloud platform. In one embodiment, the cloud platform may include a private cloud, public cloud, hybrid cloud, community cloud, distributed cloud, inter-cloud, multi-cloud, or any combination thereof.

[0116] In some embodiments, memory 1302 may be an internal storage unit of electronic device 1300, such as a hard disk or memory of electronic device 1300. In other embodiments, memory 1302 may also be an external storage device of electronic device 1300, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on electronic device 1300.

[0117] Furthermore, the memory 1302 may include both internal storage units of the electronic device 1300 and external storage devices. The memory 1302 is used to store application software and various types of data installed on the electronic device 1300.

[0118] In some embodiments, display 1303 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. Display 1303 is used to display information from electronic device 1300 and to display visual user applications. Components 1301-1303 of electronic device 1300 communicate with each other via a system bus.

[0119] In one embodiment, when the processor 1301 executes the mechanical response solution program for degraded fiber materials in the memory 1302, the following steps can be implemented: Obtain the reference configuration region of the object to be analyzed, establish the solution region based on the reference configuration region, and discretize the nodes of the solution region; The global displacement field of the solution domain after node discretization is constructed using shape functions, and the deformation gradient is calculated. Based on the deformation gradient, an expression for the material free energy is established, and a stochastic damage field of the object to be analyzed is constructed. Based on the material free energy expression and the random damage field, a degradation fiber action mechanism is constructed, and the mechanical response analysis results of the object to be analyzed are calculated according to the degradation fiber action mechanism.

[0120] It should be understood that when the processor 1301 executes the mechanical response solution program for degraded fiber materials in the memory 1302, in addition to the functions mentioned above, it can also perform other functions, as can be found in the description of the corresponding method embodiments above.

[0121] Furthermore, the embodiments of the present invention do not specifically limit the type of the electronic device 1300 mentioned. The electronic device 1300 can be a mobile phone, tablet computer, personal digital assistant (PDA), wearable device, laptop computer, or other portable electronic device. Exemplary embodiments of portable electronic devices include, but are not limited to, portable electronic devices running iOS, Android, Microsoft, or other operating systems. The aforementioned portable electronic device can also be other portable electronic devices, such as a laptop computer with a touch-sensitive surface (e.g., a touch panel). It should also be understood that in some other embodiments of the present invention, the electronic device 1300 may not be a portable electronic device, but rather a desktop computer with a touch-sensitive surface (e.g., a touch panel).

[0122] Accordingly, this application also provides a computer-readable storage medium for storing computer-readable programs or instructions. When the programs or instructions are executed by a processor, they can implement the steps or functions in the methods for solving the mechanical response of degraded fiber materials provided in the above-described method embodiments.

[0123] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.), and the computer program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0124] The above provides a detailed description of the method, apparatus, electronic device, and system for solving the mechanical response of degraded fiber materials provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for solving the mechanical response of degraded fiber materials, characterized in that, include: Obtain the reference configuration region of the object to be analyzed, establish the solution region based on the reference configuration region, and discretize the nodes of the solution region; The global displacement field of the solution domain after node discretization is constructed using shape functions, and the deformation gradient is calculated. Based on the deformation gradient, an expression for the material free energy is established, and a stochastic damage field of the object to be analyzed is constructed. Based on the material free energy expression and the random damage field, a degradation fiber action mechanism is constructed, and the mechanical response analysis results of the object to be analyzed are calculated according to the degradation fiber action mechanism.

2. The method for solving the mechanical response of degraded fiber materials according to claim 1, characterized in that, The process of obtaining the reference configuration region of the object to be analyzed, establishing the solution region based on the reference configuration region, and discretizing the nodes of the solution region includes: Obtain the reference configuration region of the object to be analyzed; The geometric dimensions, boundary range, and load type are determined based on the configuration region; The solution domain is established based on the boundary conditions, the geometric dimensions, the boundary range, and the load type, and the solution domain is discretized at nodes.

3. The method for solving the mechanical response of degraded fiber materials according to claim 1, characterized in that, The process of constructing the global displacement field of the solution region after node discretization using shape functions and calculating the deformation gradient includes: The nodal displacement degrees of freedom are interpolated to the solution domain after the nodes are discretized by using shape functions to obtain the global displacement field. The configuration tensor of the global displacement field is calculated, and the deformation gradient is determined based on the calculation results.

4. The method for solving the mechanical response of degraded fiber materials according to claim 1, characterized in that, The process of establishing a material free energy expression based on the deformation gradient and constructing a stochastic damage field for the object to be analyzed includes: The matrix energy term, right Cauchy-Green tensor, and volume change are determined based on the deformation gradient. A material free energy expression is established based on the matrix energy term, the right Cauchy-Green tensor, and the volume change. A random damage field of the object to be analyzed is constructed based on the fiber orientation of the object.

5. The method for solving the mechanical response of degraded fiber materials according to claim 4, characterized in that, The construction of the random damage field of the object to be analyzed based on the fiber orientation of the object to be analyzed includes: Obtain the fiber orientation information of the object to be analyzed; Calculate fiber strain invariants based on the fiber orientation information, and establish a fiber orientation weighting function based on the fiber orientation information; A random damage field is constructed based on the fiber strain invariant and the fiber orientation weighting function.

6. The method for solving the mechanical response of degraded fiber materials according to claim 1, characterized in that, The process of constructing a degradation fiber action mechanism based on the material free energy expression and the random damage field, and calculating the mechanical response analysis results of the object under analysis based on the degradation fiber action mechanism, includes: The local health coefficient of each material point of the object to be analyzed is calculated based on the random damage field and the material free energy expression. The fiber potential function is determined based on the local health coefficient, and the mechanism of degenerative fiber action is constructed based on the fiber potential function. The mechanical response analysis results of the object under analysis were calculated based on the mechanism of action of the degraded fibers.

7. The method for solving the mechanical response of degraded fiber materials according to claim 6, characterized in that, The mechanical response analysis results of the object under analysis calculated based on the mechanism of action of the degraded fibers include: The total fiber energy and total system potential energy of the object under analysis are calculated based on the degraded fiber mechanism described above. Apply displacement boundary conditions to the total potential energy of the system and perform a minimization solution to obtain the minimum potential energy solution of the system. The mechanical response analysis results of the object to be analyzed are determined based on the total fiber energy and the minimum solution of the system potential energy. The mechanical response analysis results include the overall displacement distribution of the material, the internal strain and stress distribution of the material, the random damage factor field distribution, the stiffness degradation and stress concentration phenomena corresponding to the local damage area, and the mechanical response results under different random damage parameters, fiber orientation parameters and load conditions.

8. A device for solving the mechanical response of degraded fiber materials, characterized in that, include: The module includes a solution domain module, a deformation gradient module, a random damage module, and a mechanical analysis module. The solution domain module is used to obtain the reference configuration domain of the object to be analyzed, establish the solution domain based on the reference configuration domain, and discretize the nodes of the solution domain. The deformation gradient module is used to construct the global displacement field of the solution region after node discretization through shape functions, and to calculate the deformation gradient. The random damage module is used to establish the material free energy expression based on the deformation gradient and to construct the random damage field of the object to be analyzed. The mechanical analysis module is used to construct the degradation fiber action mechanism based on the material free energy expression and the random damage field, and to calculate the mechanical response analysis results of the object to be analyzed according to the degradation fiber action mechanism.

9. An electronic device, the electronic device comprising a processor and a memory, characterized in that, The memory is used to store instructions, and the processor is used to call the instructions in the memory to cause the electronic device to execute the mechanical response solution method for degraded fiber materials as described in any one of claims 1 to 7.

10. A system for solving the mechanical response of degraded fiber materials, characterized in that, The mechanical response solution system for degraded fiber materials includes an electronic device, a data acquisition device, and a result output device. The data acquisition device and the result output device are respectively connected to the electronic device. The data acquisition device is used to acquire material data of the object to be analyzed, and the result output device is used to output and display the mechanical response analysis results of the object to be analyzed.

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