Multi-layer structure design method of flexible electronic material

Abstract

The invention relates to the technical field of design of flexible electronic materials, and discloses a multilayer structure design method of a flexible electronic material, which comprises the following steps of: constructing and optimizing a comprehensive objective function by performing nonlinear mechanical modeling and thermal-mechanical coupling analysis on each layer of material of a multilayer structure; optimal design parameters are solved by using a variational method and an optimal control theory, then nonlinear finite element analysis is performed to verify material performance, and finally effectiveness of optimization design is verified through mechanical and thermal performance experiments; the invention further provides a multilayer structure design system of the flexible electronic material. The multilayer structure design system comprises a mathematical modeling module, an optimization design module, a finite element analysis module, a simulation module and an experimental verification module. According to the method, a nonlinear stress-strain relation and a thermal-mechanical coupling modeling technology are adopted, so that the mechanical and thermal properties of the material under large deformation and different temperature conditions are accurately predicted, and the failure risk in a complex working environment is avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of the design of flexible electronic materials, and specifically to a design method for the multi-layer structure of flexible electronic materials. Background Art

[0002] With the continuous progress of technology, the application of flexible electronic materials in various fields such as wearable devices, intelligent sensors, flexible displays, and biomedical devices has gradually increased. Such materials have high flexibility, bendability, and thinness, and exhibit unique advantages in scenarios where traditional rigid electronic materials are not applicable. However, in practical applications, flexible electronic materials face a series of technical challenges, especially the complexity in the design of multi-layer structures and the optimization of material properties.

[0003] The design of the multi-layer structure of flexible electronic materials mainly relies on traditional linear mechanical models and empirical formulas. The existing design methods in the prior art mostly focus on the optimization of single performance, such as only paying attention to mechanical properties or thermal properties. However, the multi-layer flexible electronic materials in practical applications not only need to meet mechanical stability, but also need to effectively manage thermal stress. Due to the difference in the coefficient of thermal expansion between different material layers, thermal stress often generates in the multi-layer structure, thereby affecting the stability and service life of the material. The prior art fails to fully consider the thermo-mechanical coupling effect at this point, often resulting in inaccurate designs or inability to cope with the complex conditions in the actual working environment; moreover, the existing optimization design methods mostly rely on simple empirical formulas or theories based on linear assumptions, and cannot accurately predict the true performance of the material under large deformations or complex loads. The traditional mechanical modeling methods do not consider the non-linear behavior of the material, while the thermodynamic modeling ignores the interaction between thermal stress and mechanical properties. For example, many existing design schemes have material failure or fatigue problems in the area where thermal stress accumulates, and these problems have not been effectively solved in the traditional design methods; furthermore, the existing technology usually adopts the method of repeated experiments and empirical adjustment during the optimization design, which is not only inefficient, but also increases the design cycle and cost. In some cases, excessive reliance on experimental tests also makes the optimization results not universal, restricting the wide application of flexible electronic materials in actual production. Therefore, those skilled in the art have proposed a design method for the multi-layer structure of flexible electronic materials to solve the above problems. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention provides a design method for the multi-layer structure of flexible electronic materials, which solves the problems that the existing technology lacks effective thermo-mechanical coupling analysis and non-linear optimization design methods, resulting in unstable performance and failure of multi-layer flexible electronic materials under complex working conditions.

[0005] To achieve the above object, the present invention is implemented through the following technical solutions: A method for designing a multi-layer structure of flexible electronic materials, comprising the following steps:

[0006] Perform mechanical modeling on each layer of the multi-layer structure, and the mechanical modeling uses a non-linear stress-strain relationship to describe the mechanical behavior of the material;

[0007] Establish a thermo-mechanical coupling model, and the thermo-mechanical coupling model describes the influence of temperature on the mechanical properties of the material by combining the thermal expansion coefficient and temperature change of the material;

[0008] Construct a comprehensive objective function, the objective function includes mechanical energy and thermal energy, and optimize the objective function;

[0009] Use the variational method and optimal control theory to solve the objective function to obtain the optimal design parameters of each layer of material;

[0010] Perform non-linear finite element analysis on the multi-layer structure to verify the mechanical properties and thermal properties of the material;

[0011] Verify the effectiveness of the optimized design through experiments, and the verification content includes mechanical property testing and thermal property testing.

[0012] Preferably, the non-linear stress-strain relationship is the Mooney-Rivlin model, and the model includes a stress-strain relationship describing the elasticity of the material and a stress-strain relationship describing the non-linear effect of the material.

[0013] Preferably, the thermo-mechanical coupling model takes into account the thermal stress caused by temperature change, and the thermal stress is jointly determined by the elastic modulus, thermal expansion coefficient and temperature change amount of the material, thereby affecting the mechanical properties of the multi-layer structure.

[0014] Preferably, the objective function includes the following two parts:

[0015] The first part is mechanical energy, expressed as the relationship between stress and strain;

[0016] The second part is thermal energy, expressed as the relationship between thermal conductivity and temperature gradient.

[0017] Preferably, the following constraint conditions are included in the optimization process:

[0018] Material thickness constraint, ensuring that the thickness of each layer of material is within the specified range;

[0019] Elastic modulus constraint, ensuring that the elastic modulus of each layer of material is within the specified range;

[0020] Non-linear deformation constraint, ensuring that the material does not undergo excessive non-linear deformation.

[0021] Preferably, the variational method obtains the optimal relationship between the control variable and the response variable by calculating the derivative of the objective function, thereby obtaining the optimal design parameters.

[0022] Preferably, the nonlinear finite element analysis includes the following steps:

[0023] Divide the multi-layer material into finite element meshes;

[0024] Calculate the stress and strain of each element according to the stress-strain relationship of the material;

[0025] Summarize the stress distribution of each element to obtain the mechanical properties of the overall material.

[0026] Preferably, the thermal-mechanical coupling simulation includes the following steps:

[0027] Set the initial conditions and define the physical properties of each layer of material;

[0028] Set the boundary conditions and simulate the temperature gradient and external loading conditions;

[0029] Solve the heat conduction equation and the mechanical equation simultaneously to obtain the results of thermal-mechanical coupling.

[0030] Preferably, the experimental verification includes the following steps:

[0031] Use a scanning electron microscope (SEM) to test the bending strength and tensile strength of the material;

[0032] Conduct a thermal conductivity test to measure the thermal conductivity and thermal stability of the material;

[0033] Compare the experimental results with the simulation results to verify the accuracy of the optimized design.

[0034] There is also provided a multi-layer structure design system for flexible electronic materials, including:

[0035] A mathematical modeling module for constructing the mechanical and thermal models of each layer of material;

[0036] An optimization design module for solving the optimal design parameters according to the objective function;

[0037] A finite element analysis module for performing nonlinear large deformation analysis on the optimized multi-layer structure;

[0038] A simulation module for performing thermal-mechanical coupling simulation to verify the optimized design;

[0039] An experimental verification module for verifying the effectiveness of the optimized design through mechanical property and thermal property experiments. The present invention provides a multi-layer structure design method for flexible electronic materials. It has the following beneficial effects:

[0040] 1. The present invention adopts non-linear stress-strain relationships and thermo-mechanical coupling modeling techniques, achieving accurate prediction of the mechanical and thermal properties of materials under large deformations and different temperature conditions. Compared with the linear material models commonly used in the prior art, the present invention can more realistically simulate the actual performance of flexible electronic materials, avoiding the risk of failure in complex working environments and solving the problem of the neglect of large deformations and thermal stresses by traditional models.

[0041] 2. The present invention introduces the variational method and optimal control theory for objective function optimization, achieving the purpose of optimizing design parameters in multiple physical scenarios. Compared with the optimization methods that solely rely on experience and repeated experiments in the prior art, the present invention significantly improves the design efficiency and accuracy through the accurate solution of mathematical models, reduces the need for manual adjustment, and ensures the feasibility of design parameters in practical applications.

[0042] 3. The present invention accurately solves for multi-layer structures through non-linear finite element analysis, achieving a comprehensive assessment of the material performance under complex loads and thermal stresses. Compared with traditional linear analysis methods, this technology can more accurately simulate the stress distribution and deformation of multi-layer structures, solving the limitations of previous methods in effectively handling thermo-mechanical coupling effects and non-linear deformations.

[0043] 4. The present invention combines experimental verification of mechanical and thermal properties, effectively ensuring the reliability of the optimized design in practical applications. Compared with designs that only rely on simulation results in the prior art, the present invention verifies the accuracy and feasibility of the design through actual experimental tests, avoiding design failures caused by insufficient experimental verification, and improving the stability and durability of materials in various working environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic flow chart of the method of the present invention;

[0045] Figure 2 is a schematic diagram of the system architecture of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0047] Please refer to the attached Figure 1 , the embodiments of the present invention provide a method for designing a multi-layer structure of flexible electronic materials, including the following steps:

[0048] S1. Perform mechanical modeling on each layer of the multi-layer structure. The mechanical modeling uses a non-linear stress-strain relationship to describe the mechanical behavior of the material.

[0049] Specifically, first, during the design process of the multi-layer structure of flexible electronic materials, mechanical modeling is one of the most crucial basic steps. Through mechanical modeling, a theoretical basis can be provided for subsequent optimization design and thermo-mechanical coupling analysis. Mechanical modeling can accurately describe the deformation behavior of the material under external loads. Especially in a multi-layer structure, it can accurately predict the stress and strain distributions of each layer to ensure the stability and reliability of the final design. The focus of this step is to establish the stress-strain relationship of each layer of material and perform accurate modeling in combination with non-linear material behavior.

[0050] In this embodiment, the mechanical modeling adopts a non-linear stress-strain relationship to accurately describe the mechanical response of flexible electronic materials under large deformations. Since the deformation of flexible electronic materials is relatively complex, the traditional linear elastic theory cannot fully reflect the behavior of the material under actual loads. Especially when the material is in a large deformation state, the non-linear stress-strain relationship can more accurately reflect its true mechanical properties.

[0051] As an option, in this embodiment, the Mooney-Rivlin model is adopted to describe the non-linear stress-strain relationship. The Mooney-Rivlin model is a theoretical model widely used in rubber and other large deformation materials. This model takes into account the elastic part and the plastic part of the material and can provide more accurate stress predictions during large deformations.

[0052] Specifically, the expression of the Mooney-Rivlin model is:

[0053]

[0054] where: σ i represents the stress of the i-th layer of material; ∈ i represents the strain of the i-th layer of material; C 1 and C 2 are the linear and non-linear stress-strain coefficients of the i-th layer of material, respectively.

[0055] In a possible implementation, the values of C 1 and C 2 can be obtained through experimental measurement or fitting from the stress-strain curve of the material. Usually, specific experimental tests are required to determine the specific parameters of each layer of material. These parameters are crucial for accurately predicting the mechanical properties of the material.

[0056] In general, the behavior of non-linear materials usually leads to large strains in the material under the action of external forces, especially during the process of tension or compression. Therefore, in mechanical modeling, it is necessary to comprehensively consider the strain-stress relationship of the material and its corresponding non-linear characteristics. By closely connecting the stress and strain of each layer of the material through a formula relationship, the model can be made more accurate when dealing with large deformations and complex loading conditions.

[0057] In practical applications, each layer of the material may exhibit different mechanical behaviors due to its different physical properties, such as elastic modulus, thickness, and material type. We adopted a layered modeling method, that is, each layer of the multi-layer flexible material is modeled separately, taking into account the contributions of physical parameters such as the thickness and elastic modulus of each layer to the overall mechanical properties. By independently modeling each layer of the material, it can be ensured that the coupling effects between the layers are fully considered, and the stress distribution of the entire multi-layer structure under the action of external forces can be accurately calculated.

[0058] In another possible implementation, if the material exhibits obvious plastic properties, or if the hardening behavior of the material needs to be further considered, a hyperbolic stress-strain relationship can also be introduced, or a tension-compression non-linear model can be used. These models provide a more flexible description method for more complex material behaviors, especially when dealing with more complex loading conditions.

[0059] Specifically, in this embodiment, when calculating the stress distribution of each layer, the interaction between the inner and outer layer materials is considered. This interaction not only affects the local deformation of each layer but also determines the overall stability of the entire structure. To ensure effective stress transfer between different layer materials in the multi-layer structure, the interface performance between layers also needs to be fully considered in mechanical modeling, which includes interface bonding strength and possible slip phenomena.

[0060] In this embodiment, we also added the ability to adapt to different external loading methods. Whether it is uniform pressure, point load, or other types of complex loads, it can be accurately described by adjusting the boundary conditions in the model. For each layer of the material, its actual mechanical properties are calculated based on its strain response under the load.

[0061] In some embodiments, mechanical modeling can also be extended to three-dimensional modeling, especially in scenarios where different geometric shapes and loading methods need to be considered. In this case, the three-dimensional finite element analysis (FEM) method is used to model and simulate the entire multi-layer structure to ensure the integrity and reliability of the material in practical applications.

[0062] Generally speaking, through accurate mechanical modeling, we can ensure that the performance of the material in actual use meets the design requirements, providing strong theoretical support for subsequent optimization design.

[0063] S2. Establish a thermo-mechanical coupling model, which describes the influence of temperature on the mechanical properties of materials by combining the coefficient of thermal expansion and temperature change of the materials.

[0064] Specifically, in the aforementioned step S1, we have completed the mechanical modeling of each layer of materials, accurately describing the stress and strain distributions of the materials under external forces. Next, in step S2, we will focus on thermo-mechanical coupling modeling. The core purpose of this step is to consider the behavior of materials under different temperature conditions, especially the influence of thermal expansion on the mechanical properties of materials. Multilayer flexible materials usually work in different temperature environments, and thermal stress is generated due to the difference in the coefficients of thermal expansion of different materials, which may lead to structural failure. Therefore, thermo-mechanical coupling modeling can provide a more accurate prediction of the thermodynamic behavior for the overall material design and effectively avoid damage caused by excessive thermal stress.

[0065] In this embodiment, the thermo-mechanical coupling model takes into account the thermal expansion effect of the materials and the influence of temperature change on the stress and deformation of the materials. Thermal expansion is a physical phenomenon in which the size of a material changes during temperature change. In a multilayer structure, the coefficients of thermal expansion between material layers may be different, so thermal stress will be generated between layers, affecting the stability of the overall structure. To accurately describe this process, we introduce a thermal stress model and combine the elastic modulus of the materials to calculate the thermal stress generated in each layer of materials due to temperature change.

[0066] As an option, in this embodiment, we adopt the following thermal stress formula to describe the thermal stress of each layer of materials:

[0067] T i =E i α i ΔT;

[0068] Where: T i represents the thermal stress of the i-th layer of materials; E i represents the elastic modulus of the i-th layer of materials; α i represents the coefficient of thermal expansion of the i-th layer of materials; ΔT represents the temperature change.

[0069] Specifically, this formula indicates that thermal stress is not only related to the elastic modulus of the materials but also related to the coefficient of thermal expansion of the materials and the amplitude of temperature change. For a multilayer structure, temperature change will cause stress accumulation between layers of materials. If the difference in the coefficients of thermal expansion between layers of materials is large, it may lead to large thermal stress, affecting the stability of the overall structure. Therefore, in the design process, these factors must be fully considered to ensure that the thermal stress does not exceed the load-bearing capacity of the materials.

[0070] If the multi-layer structure contains different types of materials or the temperature of the materials varies greatly, an appropriate temperature range can be selected according to the actual situation to further calculate the thermal stress. In some applications, especially in electronic devices, the coefficient of thermal expansion and temperature change of the materials may be dynamic. Therefore, a time factor needs to be added to the thermo-mechanical coupling model to more accurately predict the change of thermal stress.

[0071] In some embodiments, if the multi-layer structure operates under extreme temperature conditions, more complex thermo-mechanical coupling effects may need to be considered. In this case, a more refined heat conduction model can be used to calculate the heat exchange process between different material layers. In addition, if the working environment of the multi-layer structure involves high temperature or high pressure conditions, a heat flow equation can also be introduced to supplement the calculation of thermal stress. In such cases, the distribution of the temperature field and the calculation of heat flow play a crucial role in the stability and performance of the entire material system.

[0072] Generally, the thermo-mechanical coupling model not only considers a single thermal stress, but also needs to comprehensively consider the influence of temperature change on the overall thermal stability and mechanical properties of the material. Temperature change may affect mechanical properties such as the elastic modulus and yield strength of the material. Therefore, these changes need to be fully considered in the modeling process. To ensure the stability of the structure, the thermo-mechanical coupling model in this embodiment has fully considered the influence of temperature on the physical properties of the material and can accurately predict the performance of the material under different temperature conditions.

[0073] Specifically, in the design of multi-layer materials, the thermal stress of each layer of material is the result of the combined action of the stress caused by temperature change and the elastic response. Therefore, in this embodiment, by comprehensively analyzing the thermal stress and mechanical stress, the thermodynamic behavior of the material can be comprehensively evaluated at the design stage. This enables us to take effective measures to reduce the negative impact of thermal stress during the optimization design process, such as reasonably selecting the material combination and optimizing the interlayer structure.

[0074] S3. Construct a comprehensive objective function that includes mechanical energy and thermal energy, and optimize this objective function;

[0075] Specifically, in the aforementioned steps S1 and S2, we have respectively completed mechanical modeling and thermo-mechanical coupling modeling, which respectively describe the mechanical behavior of each layer of material and the thermal stress caused by thermal expansion. On this basis, step S3 will start to construct a comprehensive objective function and conduct an optimization design. By optimizing the objective function, the comprehensive performance of the material can be improved, ensuring that it can meet both mechanical stability and the thermal stress problem caused by temperature change in multiple rounds of design. The construction and optimization design of the objective function are the key steps to achieve high-efficiency and multi-functional flexible electronic materials.

[0076] In this embodiment, the construction of the objective function depends on two main parts: mechanical energy and thermal energy. Mechanical energy is mainly related to the strain and stress of the material under external load, while thermal energy is related to the thermal expansion coefficient, thermal conductivity of the material, and the influence of temperature change. Considering these two parts of energy comprehensively, we obtain a comprehensive objective function that includes mechanical and thermal properties, and optimize the material design by minimizing this objective function.

[0077] As an option, the objective function can be divided into two main components:

[0078] The first part is mechanical energy, which reflects the stress-strain action of external forces on the material;

[0079] The second part is thermal energy, which describes the thermal stress caused by temperature change and the heat conduction effect of the material.

[0080] Specifically, the part of mechanical energy can be expressed by the relationship between stress and strain, which usually reflects the degree of deformation of the material. In the calculation, mechanical energy is usually described by the following formula:

[0081]

[0082] Where: J 1 is the mechanical energy; σ i is the stress of the i-th layer of material; ∈ i is the strain of the i-th layer of material; V i is the volume of the i-th layer; n represents the total number of material layers; dV represents the infinitesimal change of the volume element in the integral.

[0083] The calculation of mechanical energy not only depends on the stress-strain relationship of the material, but also takes into account the nonlinear behavior of the material, especially in the case of large deformation. Therefore, in this embodiment, a nonlinear material model (such as the Mooney-Rivlin model) is considered to accurately predict the mechanical response of the material, and the energy of each layer of material is obtained by integral solution.

[0084] The thermal energy part reflects the thermal stress caused by temperature change and the influence of thermal conductivity on the overall heat transfer. The thermal energy part can be described by the relationship between heat flux and temperature gradient, and can be expressed by the following formula in specific calculations:

[0085]

[0086] Where: J 2 is the thermal energy; κ i is the thermal conductivity of the i-th layer of material; represents the temperature change; n represents the total number of material layers; dV represents the infinitesimal change of the volume element in the integral.

[0087] In some embodiments, the temperature gradient reflects the rate of change of temperature in the material. There may be different thermal conductivities between different material layers, resulting in different heat transfer efficiencies. Therefore, when calculating the thermal energy, the differences in the thermal conductivities of each layer of material must be taken into account. To further improve the simulation accuracy, detailed modeling considering the heat flow direction can be added in some special cases, especially in complex three-dimensional structures.

[0088] Generally, the design of the objective function should consider the interaction between mechanics and thermotics simultaneously. Mechanics and thermotics are coupled with each other, which means that their performance optimizations cannot be carried out independently. Temperature changes may affect the elastic modulus of the material, thus affecting the stress-strain relationship. Similarly, external forces will also affect the coefficient of thermal expansion of the material. Therefore, the optimization of the objective function should not only meet the mechanical stability but also ensure the reliability of the thermal performance to avoid failure caused by excessive thermal stress.

[0089] In a possible implementation, the objective function can also introduce constraint conditions. In addition to optimizing the mechanical energy and thermal energy, the constraint conditions include restrictions on physical properties such as the thickness, elastic modulus, and coefficient of thermal expansion of the material. The introduction of these constraint conditions can ensure the practical feasibility of the design. For example, if the material thickness is too thin, it may lead to insufficient mechanical strength, while if it is too thick, it will affect the flexibility of the material. Therefore, the thickness of each layer of material needs to be restricted.

[0090] As another option, the constraint conditions in the objective function can also include the maximum value of thermal stress. Since temperature changes can cause excessive thermal stress, which may cause irreversible damage to the multi-layer structure, setting an upper limit on thermal stress is an important part of the optimization process. By restricting the magnitude of thermal stress, it can be ensured that the material will not fail due to temperature changes during operation.

[0091] Generally speaking, in the optimization process, by constructing a comprehensive objective function and introducing constraint conditions, the optimizations of mechanical and thermal performances can be comprehensively considered, and the design parameters of each layer of material can be optimized using a mathematical model, ultimately achieving the best balance between mechanical stability and thermal management effects.

[0092] S4. Solve the objective function using the variational method and optimal control theory to obtain the optimal design parameters of each layer of material;

[0093] Specifically, in step S3, we have constructed the comprehensive objective function and described the mechanical energy and thermal energy in detail. The construction of the objective function provides us with the mathematical basis for the optimization design. In step S4, we will use the variational method and the optimal control theory to solve this objective function, so as to obtain the optimal design parameters. By solving the objective function, we can obtain the optimal design scheme that meets the requirements of mechanical stability and thermal management. The implementation of this step can ensure the best performance of the design in multiple physical scenarios, and has strong feasibility and accuracy.

[0094] In this embodiment, during the optimization process of the objective function, the variational method is used to solve the optimal relationship between the control variables and the response variables. As a mathematical method widely used in optimization problems, the variational method obtains the optimal solution of the objective function by taking the derivative of the objective function. In specific operations, first, the control variables in the objective function (such as the thickness, elastic modulus, thermal expansion coefficient, etc. of each layer of material) need to be set, and then the relationship of the corresponding response variables (such as stress, strain, thermal stress, etc.) is solved.

[0095] As an option, in this embodiment, the optimization problem is solved through the derivative formula of the variational method. The core of the solution process is to obtain the optimal conditions for the control variables by taking the variation of the objective function. By calculating the derivative of the objective function, we can obtain the influence degree of each design parameter (such as the thickness, elastic modulus, etc. of each layer) on the objective function. This method can effectively find the optimal design parameters, so that the entire multi-layer structure reaches the optimal state both mechanically and thermally.

[0096] Specifically, the optimization problem of the objective function J can be completed by solving the following variational equation:

[0097]

[0098] where: J is the objective function, including the energy of both mechanical and thermal parts; h i is the design parameter of the i-th layer, such as the thickness, elastic modulus or thermal expansion coefficient of the material, etc.; represents the partial derivative of the objective function with respect to the design parameter of the i-th layer.

[0099] The solution steps of the variational method usually involve multiple iterative processes. In each iteration, by continuously adjusting the design parameters, it gradually approaches the optimal solution. Due to the complexity of the multi-layer material system, the design parameters of each layer of material may affect each other. Therefore, the coupling effect between layers needs to be fully considered during the optimization process. In actual solution, numerical calculation methods such as the gradient descent method or the Lagrange multiplier method can be used to obtain the optimal solution of each control variable.

[0100] In some embodiments, if the complexity of the multi-layer material system is high or there are many design parameters, computer-aided design (CAD) software can be used in combination with optimization algorithms to assist in the solution. These software can quickly perform large-scale parameter optimization in an automated manner, thereby improving the solution efficiency.

[0101] Generally, the application of the optimal control theory can further optimize the design by setting reasonable constraint conditions. The constraint conditions may include the maximum strain of the material, the maximum thermal stress, the maximum thickness, etc. Through reasonable constraint conditions, the practical feasibility and safety of the design can be ensured, and at the same time, structural failures caused by unreasonable designs can be avoided.

[0102] In another possible implementation, sensitivity analysis can be introduced to analyze the influence of each design parameter on the objective function. This helps to identify which design parameters have a greater impact on the final result, so that these key parameters can be concentrated for optimization, improving the design efficiency. Through sensitivity analysis, the design parameters can be better adjusted to obtain the material structure with the optimal performance.

[0103] As an option, the variational method and the optimal control theory can be combined with the multi-objective optimization method for solution. Multi-objective optimization not only considers a single optimization objective, but also takes multiple optimization objectives (such as mechanical stability, thermal management effect, etc.) into account simultaneously. Through multi-objective optimization, an optimal solution that balances various performances can be obtained, ensuring that in practical applications, the material structure can take into account multiple performance requirements.

[0104] Specifically, when applying the variational method for optimization and solution, it may be necessary to perform numerical approximation on the objective function, especially when the nonlinear behavior of the material and the thermo-mechanical coupling effect are relatively complex. These nonlinear factors usually need to be processed by numerical simulation methods to ensure the accuracy of the solution results. In numerical simulation, the finite element analysis method (FEM) can be used to simulate the mechanical response of the material under different working conditions, thereby providing data support for the solution of the variational method.

[0105] S5. Perform non-linear finite element analysis on the multi-layer structure to verify the mechanical properties and thermal properties of the material;

[0106] Specifically, in the aforementioned step S4, we solved the objective function through variational methods and optimal control theory to obtain the optimal design parameters for each layer of material. These design parameters provide the basis for the next step of nonlinear finite element analysis. The goal of step S5 is to verify whether the design obtained through the optimization method can operate stably under actual conditions. Specifically, the nonlinear finite element analysis will evaluate the mechanical behavior of the optimized design in the multi-layer structure and check the response of the material under different load and temperature conditions. Through this analysis step, we can comprehensively understand the mechanical properties of the material, ensure the reliability of the design, and provide a basis for further optimization and experimental verification.

[0107] In this embodiment, we use finite element analysis (FEM) to simulate the deformation behavior of multi-layer materials. In a multi-layer structure, the physical properties (such as thickness, elastic modulus, coefficient of thermal expansion, etc.) of each layer may be different, resulting in different deformation characteristics when responding to external loads. Finite element analysis divides the overall structure into small elements, calculates the stress and strain of each element under a given load, and finally obtains the mechanical properties of the entire structure.

[0108] As an option, for each layer of material, the finite element analysis can be carried out through the following steps:

[0109] Mesh generation: First, each layer of material is divided into a finite number of small elements. The division accuracy of the mesh directly affects the accuracy of the analysis. In a multi-layer structure, considering the thickness and mechanical property differences of each layer of material, the mesh should be divided as finely as possible to improve the calculation accuracy. The shape and size of each element should be adjusted according to the geometric characteristics of the material.

[0110] Material property input: Input the physical properties of each layer of material, such as elastic modulus, density, thickness, etc. In this embodiment, we particularly focus on the nonlinear behavior and thermo-mechanical coupling effect of each layer of material. Therefore, it is necessary to provide the stress-strain curves of each layer of material under different temperatures and loads.

[0111] Loading condition setting: Set the external load conditions, which may include uniform pressure, point load, thermal load, etc. In practical applications, the load may have strong nonlinear characteristics. Especially in flexible electronic materials, the deformation and stress under external forces often show nonlinear behavior. Therefore, it is necessary to simulate these complex situations through nonlinear finite element analysis.

[0112] Solution and analysis: Solve the stress, strain, displacement, etc. of the system through finite element software. Specifically, we solve the stress field through numerical methods and analyze the deformation behavior of the material under different conditions. During this process, the nonlinear characteristics and thermo-mechanical coupling effect of the material will directly affect the final result. Therefore, the software needs to be able to handle these complex factors to ensure the accuracy of the solution results.

[0113] In general, the results of non-linear finite element analysis include stress distribution, deformation, relative displacement of each layer of material, etc. These results can help designers understand the performance of multi-layer structures under actual load and temperature conditions, and determine whether there are problems such as excessive deformation, failure risk or thermal stress concentration.

[0114] To further enhance the analysis accuracy, dynamic analysis methods can be used to simulate the response of materials under dynamic loads. For example, for flexible electronic devices, it may be necessary to consider stress changes under dynamic loads such as vibration and shock, and then analyze the stability and durability of the materials.

[0115] Specifically, in multi-layer structures, the coupling effect between different layers is very important. For example, differences in thermal expansion coefficients may cause thermal stresses between layers, and these thermal stresses will interact with each other and cause non-linear deformation of the materials. Therefore, both thermal stress and mechanical stress of the materials need to be considered in finite element analysis to obtain a comprehensive design evaluation.

[0116] During the process of non-linear finite element analysis, contact mechanics analysis can also be considered. In multi-layer structures, the contact characteristics between different layers may affect the mechanical response of the overall structure. Especially at the contact interface between materials, there may be phenomena such as friction and slip. These factors will cause the response of the structure under load to be different from the expected value. Therefore, the analysis of contact mechanics is crucial for understanding the actual performance of materials under load.

[0117] In some embodiments, if the analysis results show that the stress of a certain layer of material is too large or the deformation is uneven, further adjustments can be made according to the finite element analysis results. For example, parameters such as the thickness and elastic modulus of the material can be changed, or a new material layer can be introduced into the multi-layer structure to optimize the overall structure performance.

[0118] In general, the stress and deformation data obtained through non-linear finite element analysis can be used as the basis for further optimization. Based on these data, improvements can be made to the coupling effect between material layers, and the design scheme can be adjusted to ensure that the material can withstand the required load and maintain good performance in actual applications.

[0119] To further ensure the practical feasibility of the design, thermodynamic analysis can be combined to further verify the multi-layer structure. By comprehensively considering the thermal behavior and mechanical response of the material, the performance of the material under extreme conditions can be predicted more accurately. For example, in high-temperature or high-pressure environments, the performance of the material may change significantly, and thermodynamic analysis can help us evaluate the risks under these extreme conditions.

[0120] S6. Verify the effectiveness of the optimized design through experiments. The verification content includes mechanical property tests and thermal property tests.

[0121] Specifically, in the above steps S1 to S5, we have completed the mechanical modeling, thermo-mechanical coupling modeling, construction and optimization of the objective function, and nonlinear finite element analysis of the multi-layer flexible electronic material. These steps provide a theoretical and simulation basis to predict the performance of the material under different load and temperature conditions. Then, step S6 focuses on experimentally verifying the practical feasibility of the optimized design to ensure that the material meets the expected performance requirements in the real environment. Experimental verification is the last step to ensure the effectiveness of the multi-layer structure design. It not only verifies the accuracy of the simulation and optimization but also provides practical data support for further applications.

[0122] In this embodiment, the experimental verification mainly includes two aspects: mechanical property testing and thermal property testing. First, in the mechanical property testing, high-precision equipment such as a scanning electron microscope (SEM) is used to test important mechanical indexes such as the bending strength, tensile strength, and compressive strength of the material. Through these experiments, the stress and deformation of the material under external loads can be verified, and the stability of the material in actual use can be confirmed.

[0123] When testing the mechanical properties, we will simulate different working environmental conditions, such as different temperatures, different humidities, and different load conditions. For the tests at different temperatures, the material may exhibit different mechanical responses. Especially in flexible electronic materials, temperature changes may lead to changes in thermal stress. Therefore, in the experiment, these influencing factors need to be comprehensively considered to ensure the comprehensiveness of the test results.

[0124] Specifically, during the mechanical property testing process, a tensile testing machine and a compression testing machine are first needed to conduct tensile and compression tests on the material. For the tensile test, the material will experience changes in the stress-strain relationship during the tensile process, which can provide us with important indexes such as the yield strength, ultimate strength, and elongation rate of the material. In the compression test, we can test the stress distribution and the maximum bearing capacity of the material under the compression load, thereby providing a basis for design optimization.

[0125] When conducting the mechanical property testing, dynamic mechanical analysis (DMA) can also be combined to measure the mechanical properties of the material at different frequencies, temperatures, and humidities, further revealing the mechanical stability and adaptability of the material.

[0126] The connection between the mechanical property testing and the optimized design is crucial. By comparing with the simulation results, the accuracy of the model assumptions and the reliability of the optimization scheme in actual applications can be verified. For example, if the test results show that the maximum stress of the material is lower than the expected design value, it indicates that some key factors (such as interfacial friction, etc.) have not been considered in the optimization scheme and need to be further corrected.

[0127] In terms of thermal performance testing, we first measure key thermal properties such as the thermal conductivity, coefficient of thermal expansion, and thermal stability of the material. By comprehensively evaluating the thermal performance of the material, important feedback can be provided for optimizing the design. Especially in the design of multi-layer structures, the impact of thermal stress on the overall stability cannot be ignored. The thermal conductivity of the material directly affects the conduction and distribution of thermal stress, while the coefficient of thermal expansion affects the strain effect of temperature changes on the material.

[0128] In thermal performance testing, we use high-precision measurement methods such as the laser flash method to obtain the thermal conductivity of the material. In addition, dilatometers and thermal analyzers can help us measure the coefficient of thermal expansion of the material to further understand the thermal stress interaction between different layer materials.

[0129] Specifically, in thermal performance testing, we expose the material to different temperature gradients to simulate the temperature fluctuations that the material may experience during actual use. By measuring the relationship between the temperature change of the material and the thermal stress, we can further understand how the thermal expansion difference affects the overall thermal stability of the material. If the test results show that the thermal stress exceeds the allowable range of the material, then the design of the material needs to be adjusted. Especially at the contact interface of the multi-layer structure, it may be necessary to add a buffer layer or optimize the thickness distribution of the material to reduce the impact of thermal stress on the structural stability.

[0130] In some embodiments, when conducting thermal performance testing, we can also consider the adaptability of the material in different environments. For example, some flexible electronic devices may be exposed to high temperatures or extremely cold environments, and these environmental conditions need to be simulated in the experiment to ensure the reliability of the material in various extreme environments.

[0131] The combined use of mechanical performance and thermal performance testing can comprehensively verify the design of multi-layer flexible electronic materials. Based on these tests, we can compare the actual performance of the material with the simulation results to verify whether the optimized design can meet the requirements in actual applications.

[0132] The results of experimental verification can also be used for further feedback and correction of the optimization process. If the test results indicate that there are deficiencies in the design, such as excessive thermal stress or insufficient mechanical strength, then the design parameters (such as thickness, elastic modulus, etc.) can be modified or the material combination can be adjusted for optimization, so as to achieve further performance improvement.

[0133] The multi-layer structure design system of the flexible electronic material described below can be correspondingly referred to the multi-layer structure design method of the flexible electronic material described above.

[0134] Please refer to the attached Figure 2 , the multi-layer structure design system of the flexible electronic material, including:

[0135] A mathematical modeling module for constructing mechanical and thermal models of each layer of material;

[0136] An optimization design module for solving optimal design parameters according to the objective function;

[0137] A finite element analysis module for performing non-linear large deformation analysis on the optimized multi-layer structure;

[0138] A simulation module for performing thermal-mechanical coupling simulation to verify the optimized design;

[0139] An experimental verification module for verifying the effectiveness of the optimized design through mechanical property and thermal property experiments.

[0140] Specifically, the mathematical modeling module is responsible for constructing the mechanical and thermal models of each layer of material. This module first establishes an accurate mechanical model based on the physical properties of each layer of material (such as elastic modulus, coefficient of thermal expansion, specific heat capacity, etc.), and combines the thermal-mechanical coupling effect to establish a mathematical model describing the thermal stress of the material. The module uses a non-linear material model (such as the Mooney-Rivlin model) to model the stress-strain relationship of the material to adapt to the calculation of large deformations and complex loading conditions.

[0141] The optimization design module is used to solve the optimal design parameters according to the constructed objective function. The objective function combines two parts of mechanical energy and thermal energy, comprehensively considering the mechanical stability and thermal performance of the multi-layer structure. By using the variational method and the optimal control theory, this module can solve the optimal thickness, elastic modulus, coefficient of thermal expansion and other design parameters of each layer of material.

[0142] The finite element analysis module performs non-linear large deformation analysis on the optimized multi-layer structure. This module decomposes the multi-layer structure into several small elements, and evaluates the mechanical properties of the entire multi-layer structure by solving the stress and strain of each element under the action of external loads. This module supports complex geometric shapes and the coupling effect between different material layers, and can simulate the response of the multi-layer structure under actual working conditions, including but not limited to deformations in the forms of bending, stretching and compression.

[0143] The simulation module is used to perform thermal-mechanical coupling simulation to verify the thermal stability and mechanical properties of the optimized design. This module combines the heat conduction equation and the mechanical equation to simulate the thermal stress and mechanical stress distribution of the material under different temperature gradients. Through thermal-mechanical coupling simulation, the module can analyze the behavior of the multi-layer structure under different temperature and load conditions, predict possible regions of thermal stress concentration, and evaluate the mutual influence between the thermal expansion and mechanical response of the material.

[0144] The experimental verification module is used to verify the effectiveness of the optimized design through mechanical property and thermal property experiments. This module is responsible for performing standardized mechanical experiments such as tensile, compression, and bending tests, measuring key indicators such as the mechanical strength, elastic modulus, and plastic behavior of the material. At the same time, the thermal property test evaluates the thermal stability of the material under different environmental conditions by measuring parameters such as the thermal conductivity and coefficient of thermal expansion of the material. The experimental data will be compared with the simulation results to verify whether the optimized design achieves the expected effect.

[0145] The system of this embodiment can be used to execute the above method embodiment, and its principle and technical effect are similar, so they will not be elaborated here.

[0146] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for designing a multilayer structure of a flexible electronic material, characterized in that: The following steps are involved: Performing mechanical modeling on each layer of the multilayer structure, wherein the mechanical modeling uses a nonlinear stress-strain relationship to describe the mechanical behavior of the material; Establishing a thermo-mechanical coupling model, wherein the thermo-mechanical coupling model describes the effect of temperature on the mechanical properties of a material by combining the thermal expansion coefficient of the material with the temperature change; Constructing a comprehensive objective function, wherein the objective function includes mechanical energy and thermal energy, and optimizing the objective function; The objective function is solved by using the calculus of variations and optimal control theory to obtain the optimal design parameters of each layer of material; Performing nonlinear finite element analysis on the multilayer structure to verify the mechanical and thermal properties of the material; The effectiveness of the optimized design is verified through experiments, including mechanical property tests and thermal property tests.

2. The method for designing a multilayer structure of a flexible electronic material according to claim 1, characterized in that: The nonlinear stress-strain relationship is a Mooney-Rivlin model, which includes a stress-strain relationship describing the elasticity of the material and a stress-strain relationship describing the nonlinear effect of the material.

3. The method for designing a multilayer structure of a flexible electronic material according to claim 1, characterized in that: The thermal-mechanical coupling model takes into account the thermal stress caused by temperature changes, which is determined by the elastic modulus, thermal expansion coefficient and temperature change of the material, thereby affecting the mechanical properties of the multilayer structure.

4. The method for designing a multilayer structure of a flexible electronic material according to claim 1, characterized in that: The objective function consists of the following two parts: The first part is the mechanical energy, expressed as the relationship between stress and strain; The second part is the thermal energy, expressed as the relationship between thermal conductivity and temperature gradient.

5. The method for designing a multilayer structure of a flexible electronic material according to claim 1, characterized in that: The optimization process includes the following constraints: Material thickness constraints to ensure that the thickness of each layer of material is within the specified range; Elastic modulus constraint to ensure that the elastic modulus of each layer of material is within the specified range; Nonlinear deformation constraints ensure that the material does not undergo excessive nonlinear deformation.

6. The method for designing a multilayer structure of a flexible electronic material according to claim 1, characterized in that: The variational method obtains the optimal relationship between the control variable and the response variable by calculating the derivative of the objective function, thereby obtaining the optimal design parameters.

7. The method for designing a multilayer structure of a flexible electronic material according to claim 1, characterized in that: The nonlinear finite element analysis comprises the following steps: Divide the multi-layer material into a finite element mesh; Calculate the stress and strain of each unit according to the stress-strain relationship of the material; Summarize the stress distribution of each unit to obtain the mechanical properties of the overall material.

8. The method for designing a multilayer structure of a flexible electronic material according to claim 1, characterized in that: The thermal-mechanical coupling simulation includes the following steps: Set initial conditions and define the physical properties of each layer of material; Set boundary conditions to simulate temperature gradients and external loading conditions; The heat conduction equation and the mechanical equation are solved simultaneously to obtain the result of thermal-mechanical coupling.

9. The method for designing a multilayer structure of a flexible electronic material according to claim 1, characterized in that: The experimental verification comprises the following steps: The flexural strength and tensile strength of the material were tested using a scanning electron microscope (SEM); Conduct thermal conductivity tests to measure the thermal conductivity and thermal stability of materials; The experimental results are compared with the simulation results to verify the accuracy of the optimized design.

10. A multilayer structure design system for flexible electronic materials, applied to the multilayer structure design method for flexible electronic materials according to any one of claims 1 to 9, characterized in that: include: Mathematical modeling module, used to build mechanical and thermal models of each layer of material; Optimization design module, used to solve the optimal design parameters according to the objective function; Finite element analysis module, used to perform nonlinear large deformation analysis on optimized multi-layer structures; Simulation module, used to perform thermal-mechanical coupling simulation and verify the optimized design; The experimental verification module is used to verify the effectiveness of the optimized design through mechanical and thermal performance experiments.

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