A stack cold stress characteristic analysis method based on finite element analysis

Abstract

The application provides a kind of based on finite element analysis's electric pile cold stress characteristic analysis method, comprising: step S1, according to the physical structure modeling assembly of solid oxide electric pile forms full-size electric pile model;Step S2, the co-sintering process of porous electrode and thin layer electrolyte in full-size electric pile model is simulated by molecular dynamics, residual stress and first stress parameter generated in co-sintering process are obtained and first elastic stress and first inelastic stress are calculated;Step S3, the assembly stress and second stress parameter generated in the assembly process of each component are obtained and second elastic stress and second inelastic stress are calculated;Step S4, first elastic stress, first inelastic stress, second elastic stress and second inelastic stress are taken as electric pile cold stress characteristic analysis result.The beneficial effect is that the application can break through the limitation under complex stress coupling scene, while considering fusion multi-source stress and adapting to scale electric pile for accurate cold stress characteristic analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of stack reliability evaluation, in particular to a stack cold stress characteristic analysis method based on finite element analysis. BACKGROUND

[0002] As a key energy conversion device that can operate in both fuel cell (power generation) and electrolysis (hydrogen production) modes, the performance degradation and life loss of solid oxide stack during service are mainly regulated by multi-field coupled stress. Such stress runs through the whole life cycle of the stack, and the cold stress, as the initial internal stress state of the solid oxide stack at room temperature during assembly, has a basic influence on the stress evolution and structural stability in subsequent working conditions. Cold stress is mainly composed of two parts: one is the manufacturing residual stress, which is caused by the non-uniform shrinkage and stress redistribution due to the difference in thermal expansion coefficient (CTE) and elastic modulus (E) during the co-sintering process of thin electrolyte and porous electrode, and the dynamic evolution of material thermal physical parameters will exacerbate its distribution complexity; the other is the assembly stress, which is caused by the contact constraint between the components due to the bolt pre-tightening force, and its distribution characteristics are directly related to the geometric constraint and pre-tightening force.

[0003] The existing technology has obvious limitations in evaluating cold stress: first, it analyzes residual stress or assembly stress in isolation, ignoring the coupling effect of the two, which leads to deviation in stack failure risk evaluation; second, for complex geometric models of stacks with more than 30 units, the calculation complexity is extremely high due to the fine channel and fin structure of the single interconnector, making it difficult to balance accuracy and efficiency, limiting the quantitative research of multi-stress coupling mechanism; third, the small deformation theory is used to describe the large deformation (such as displacement gradient norm ‖∇u‖>0.1) in the sintering process, ignoring the geometric nonlinearity and dynamic changes of material properties, resulting in a stress prediction error of more than 15%.

[0004] Therefore, it is urgent to establish a cold stress characteristic comprehensive evaluation method that integrates multi-source stress and adapts to large-scale stacks to break through the technical bottleneck in complex stress coupling scenarios and improve evaluation accuracy and applicability. SUMMARY

[0005] The technical problem to be solved by the present application is how to break through the limitations in complex stress coupling scenarios, conduct accurate cold stress characteristic analysis while considering the integration of multi-source stress and adaptation to large-scale stacks, and improve evaluation accuracy and applicability. In order to overcome the defects of the above prior art (or related technology), the present application provides a stack cold stress characteristic analysis method based on finite element analysis.

[0006] The present application provides a stack cold stress characteristic analysis method based on finite element analysis, comprising:

[0007] Step S1, according to the physical structure of the solid oxide stack, a three-dimensional model of the solid oxide stack is established, and a plurality of component parts of the solid oxide stack are obtained, and each of the component parts is assembled to form a full-size stack model;

[0008] Step S2, the co-sintering process of the porous electrode and the thin-layer electrolyte in the full-size stack model is simulated by molecular dynamics, the residual stress and the first stress parameter generated in the co-sintering process are obtained, and based on the finite deformation theory and the second Piola-Kirchhoff stress tensor, the first elastic stress and the first inelastic stress of the full-size stack model are obtained according to the residual stress and the first stress parameter;

[0009] Step S3, the assembly stress and the second stress parameter generated in the assembly process of each of the component parts are obtained, and based on the small deformation theory and the linear elastic constitutive relation, the second elastic stress and the second inelastic stress of the full-size stack model are obtained according to the assembly stress and the second stress parameter;

[0010] Step S4, the first elastic stress, the first inelastic stress, the second elastic stress and the second inelastic stress are taken as the cold-state stress characteristic analysis result of the stack.

[0011] Compared with the prior art, the stack cold-state stress characteristic analysis method based on finite element analysis has the following advantages:

[0012] In the present application, the full-size stack model is constructed by step S1, the first elastic stress and the first inelastic stress under the residual stress are calculated by step S2, the second elastic stress and the second inelastic stress under the assembly stress are calculated by step S3, and the cold-state stress characteristic analysis result of the stack is integrated by step S4. In the above steps, the full-flow coupling model of residual stress and assembly stress, i.e. the full-size stack model, is established to provide a basic model for the co-sintering process and the assembly process, which breaks through the limitations in the complex stress coupling scenario and adapts to the large-scale stack to improve the applicability. Through the segmented application of the finite deformation theory and the small deformation theory, the stress evolution process of the solid oxide stack from manufacturing to assembly is accurately described, the multi-source stress of the first elastic stress, the first inelastic stress, the second elastic stress and the second inelastic stress is fused for precise cold-state stress characteristic analysis, and the evaluation accuracy is improved.

[0013] In a possible implementation, the step S2 obtains the instantaneous temperature in the co-sintering process, the real-time thermal expansion coefficient corresponding to different instantaneous temperatures, the reference temperature under no stress, the unit tensor, the intrinsic strain, the initial strain, the displacement gradient, the first elastic matrix and the deformation gradient matrix, and includes them into the first stress parameter.

[0014] In a possible implementation, in the step S2, the thermal deformation gradient is obtained according to the real-time thermal expansion coefficient, the instantaneous temperature, the reference temperature and the unit tensor, the intrinsic deformation gradient is obtained according to the initial strain and the unit tensor, the initial deformation gradient is obtained, and then the first elastic stress and the first inelastic stress are obtained according to the residual stress, the displacement gradient, the thermal deformation gradient, the intrinsic deformation gradient, the initial deformation gradient, the first elastic matrix and the deformation gradient matrix.

[0015] In a possible implementation, in the step S2, the first elastic stress is obtained according to the displacement gradient, the thermal deformation gradient, the intrinsic deformation gradient, the initial deformation gradient, the first elastic matrix and the deformation gradient matrix, and the first inelastic stress is obtained by subtracting the residual stress from the first elastic stress.

[0016] In a possible implementation, in the step S2, the thermal deformation gradient is obtained by the following calculation formula:

[0017] ;

[0018] ;

[0019] wherein,

[0020] represents the thermal deformation gradient;

[0021] represents the unit tensor;

[0022] represents thermal strain;

[0023] represents the real-time thermal expansion coefficient;

[0024] represents the instantaneous temperature of the sintering process;

[0025] represents the reference temperature.

[0026] In a possible implementation, in the step S2, the intrinsic deformation gradient and the initial deformation gradient are obtained by the following calculation formula:

[0027] ;

[0028] ;

[0029] wherein,

[0030] denotes the eigen-deformation gradient;

[0031] denotes the unit tensor;

[0032] denotes the eigen-strain;

[0033] denotes the initial deformation gradient;

[0034] denotes the initial strain.

[0035] In one possible implementation, the first elastic stress and the first inelastic stress are obtained in the step S2 by the following calculation formulas:

[0036]

[0037]

[0038]

[0039]

[0040] wherein,

[0041] denotes the residual stress;

[0042] denotes the first elastic stress;

[0043] denotes the first inelastic stress;

[0044] denotes the determinant of the deformation gradient matrix;

[0045] denotes the inverse matrix operation on the matrix;

[0046] denotes the inverse matrix operation on the matrix followed by the transpose matrix operation;

[0047] denotes the first elastic matrix;

[0048] denotes the elastic strain;

[0049] denotes the displacement deformation gradient;

[0050] denotes the unit tensor;​​​​

[0051] This represents the displacement gradient;

[0052] Indicates the elastic deformation gradient;

[0053] Indicates the gradient of inelastic deformation;

[0054] This represents the thermal deformation gradient;

[0055] This represents the intrinsic deformation gradient;

[0056] This represents the initial deformation gradient;

[0057] It represents elastic strain.

[0058] In one possible implementation, the second stress parameter includes the elastic modulus, Poisson's ratio, initial strain, and stack displacement of the materials of each component during the assembly process at room temperature. In step S3, a second elastic matrix is ​​obtained based on the elastic modulus and the Poisson's ratio; the total stack strain is obtained based on the stack displacement; the inelastic strain of the stack is obtained based on the initial strain; the elastic strain of the stack is obtained based on the total stack strain and the inelastic strain of the stack; the second elastic stress is obtained based on the elastic strain of the stack and the second elastic matrix; and the assembly stress is subtracted from the second elastic stress to obtain the second inelastic stress.

[0059] In one possible implementation, in step S3, the second elasticity matrix is ​​obtained using the following calculation formula:

[0060] ;

[0061] in,

[0062] This represents the second elasticity matrix;

[0063] This represents the elastic modulus;

[0064] This represents the Poisson's ratio.

[0065] In one possible implementation, in step S3, the second elastic stress and the second inelastic stress are obtained by the following calculation formula:

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] in,

[0072] This indicates the assembly stress;

[0073] This represents the second elastic stress;

[0074] This represents the second inelastic stress;

[0075] This represents the total strain of the fuel cell stack;

[0076] This indicates the displacement of the fuel cell stack;

[0077] This indicates that the matrix is ​​first inverted and then transposed.

[0078] This indicates the inelastic strain of the fuel cell stack;

[0079] This represents the initial strain;

[0080] This represents the elastic strain of the fuel cell stack;

[0081] This represents the second elasticity matrix. Attached Figure Description

[0082] Figure 1 This is a flowchart of the steps of the present invention;

[0083] Figure 2 This is a schematic diagram of the assembly process of the solid oxide fuel cell of the present invention;

[0084] Figure 3 This is a geometric schematic diagram of the solid oxide fuel cell stack of the present invention;

[0085] Figure 4 This is a schematic diagram of the mesh division of the solid oxide fuel cell of the present invention. Detailed Implementation

[0086] First, those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention. Those skilled in the art can make adjustments as needed to adapt to specific application scenarios.

[0087] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0088] See Figure 1 This invention discloses a method for analyzing the cold stress characteristics of a fuel cell stack based on finite element analysis, comprising:

[0089] Step S1: Based on the physical structure of the solid oxide fuel cell, a three-dimensional model is created to obtain multiple components of the solid oxide fuel cell, and the components are assembled to form a full-size fuel cell model.

[0090] Step S2: The co-sintering process of porous electrodes and thin-layer electrolyte in the full-size electric stack model is simulated by molecular dynamics to obtain the residual stress and first stress parameters generated during the co-sintering process. Based on the finite deformation theory and the second Piola-Kirchhoff stress tensor, the first elastic stress and the first inelastic stress of the full-size electric stack model are obtained according to the residual stress and the first stress parameters.

[0091] Step S3: Obtain the assembly stress and second stress parameters generated by each component during the assembly process, and based on the small deformation theory and linear elastic constitutive relation, obtain the second elastic stress and second inelastic stress of the full-size fuel cell model according to the assembly stress and second stress parameters.

[0092] Step S4: The first elastic stress, the first inelastic stress, the second elastic stress, and the second inelastic stress are taken as the results of the cold stress characteristic analysis of the fuel cell stack.

[0093] In this embodiment of the invention, in step S2, the co-sintering process of porous electrodes and thin electrolyte in the battery cell of the solid oxide stack is simulated by molecular dynamics to obtain the dynamic evolution law of thermal expansion coefficient, elastic modulus and micro shrinkage rate in length direction. These are used as inputs to the finite element simulation of battery cell sintering, and the shrinkage rate is correlated with intrinsic strain. The residual stress is obtained by combining geometric nonlinear theory analysis.

[0094] In this embodiment of the invention, the co-quantification of residual stress and assembly stress is achieved through multiphysics coupling modeling. The main technical solutions adopted include:

[0095] Full-scale fuel cell stack modeling: A 3D model is built based on the actual fuel cell stack geometry, including repeating elements, seals and bolt connection details;

[0096] Multi-stress coupling analysis: Integrating manufacturing residual stress (intrinsic strain obtained through molecular dynamics simulation) and assembly stress (bolt preload), the cold stress characteristics of the fuel cell stack, including the first elastic stress, the first inelastic stress, the second elastic stress, and the second inelastic stress, are calculated using finite deformation theory and linear elastic constitutive relations.

[0097] In this embodiment of the invention, considering that the assembly process of the solid oxide fuel cell is one of the important steps, including assembly alignment and bolt tightening, such as... Figure 2 As shown, it is worth noting that the battery will bulge and deform in the middle after sintering during the manufacturing process. Therefore, it needs to be flattened with a 2 kg pressure block before the solid oxide battery is assembled. The flattened battery (with the air electrode facing up) is placed on the lower electrode connector of the solid oxide battery and aligned with the reference position. Then, the lower sealant, metal frame, upper sealant and upper electrode connector are placed in sequence. Finally, the assembled solid oxide battery is bolted. The bolt tightening force used in this embodiment is 5844 Newtons.

[0098] In this embodiment of the invention, a full-size fuel cell stack model with three-dimensional modeling was developed, such as... Figure 3 As shown, the battery is embedded in the internal square cavity of the metal frame, and the electrode connectors and sealant are installed on both sides of the battery to form a repeating unit of the solid oxide fuel cell stack. It should be noted that the battery is surrounded by the metal frame, which provides edge support so that the pressure of other components does not act directly on the battery. These repeating units are assembled in series to form the solid oxide fuel cell stack, and then clamped between the top and bottom end plates by eight bolts to achieve a tight seal.

[0099] In this embodiment of the invention, the electrode connector of the solid oxide fuel cell stack is made of Crofer 22 APU, the end plate and frame are made of SUS 310 material, the sealing material is flexible sealing material Flexitallic 866, and the core component of the solid oxide fuel cell stack, the battery cell, includes a porous fuel electrode Ni-8YSZ and an air electrode La. 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3–δ –Gd 0.1 Ce 0.9 O 1.95 (LSCF–GDC) and a dense electrolyte layer 8YSZ.

[0100] In embodiments of the present invention, such as Figure 4As shown, different discretization schemes are implemented according to the geometric characteristics of each component of the solid oxide fuel cell. For the full-size fuel cell model, a structured hexahedral mesh is generated by using a parametric scanning algorithm in orthogonal geometric regions (such as air electrodes and electrode connectors). An unstructured triangular mesh method is applied to the four rounded transition regions of the fuel electrode and electrolyte layer. An adaptive tetrahedral mesh refinement technique is used for complex geometries including the metal frame and fasteners.

[0101] In this embodiment of the invention, the manufacturing process of the battery cells in the solid oxide stack mainly involves high-temperature sintering and subsequent flattening at room temperature. Specifically, the air electrode composite material is deposited on the electrolyte surface of the sintered half cell using screen printing technology (i.e., the first sintering step), and then sintering is performed to form a complete full cell structure (i.e., the second sintering step).

[0102] During the manufacturing process of solar cells in solid oxide fuel cells, although the absolute deformation occurs at the millimeter scale, the relative deformation becomes quite large due to the total thickness of the solar cell being 630 micrometers. For example, the deformation displacement caused by sintering can reach 8.04 millimeters, which is about 12.76 times the total thickness of the solar cell. Under such conditions, the Frobenius norm (‖∇u‖) of the displacement gradient tensor may exceed the threshold applicable to the small deformation theory (i.e., ‖∇u‖≪1).

[0103] In this case, geometric nonlinearity needs to be considered when |∇u|>0.1, which makes the Cauchy stress tensor-based approach more complex. σ The linear constitutive model cannot fully describe the nonlinear deformation behavior. Therefore, a finite deformation framework is adopted in this embodiment: the initial undeformed state is defined as the reference configuration, the kinematics is controlled by the total Lagrange formula, and the constitutive equation integrates the second Piola-Kirchhoff stress tensor.

[0104] In this embodiment of the invention, in step S2, the instantaneous temperature during the co-sintering process, the real-time thermal expansion coefficient corresponding to different instantaneous temperatures, the reference temperature under no stress, the unit tensor, the intrinsic strain, the initial strain, the displacement gradient, the first elastic matrix, and the deformation gradient matrix are obtained and included in the first stress parameter. In step S2, the thermal deformation gradient is obtained based on the real-time thermal expansion coefficient, the instantaneous temperature, the reference temperature, and the unit tensor; the intrinsic deformation gradient is obtained based on the intrinsic strain and the unit tensor; and the initial deformation gradient is obtained based on the initial strain and the unit tensor. Subsequently, the first elastic stress and the first inelastic stress are obtained based on the residual stress, the displacement gradient, the thermal deformation gradient, the intrinsic deformation gradient, the initial deformation gradient, the first elastic matrix, and the deformation gradient matrix.

[0105] In this embodiment of the invention, residual stress can be directly obtained using COMSOL finite element software based on loading conditions (such as temperature change), material constitutive relations (such as elastic modulus), and deformation gradient. The method for obtaining assembly stress is the same as that for residual stress, and will not be elaborated further. The expression for residual stress is as follows:

[0106] ;

[0107] in, This refers to the residual stress; This represents the first elastic stress; This represents the first inelastic stress;

[0108] The first elastic stress is calculated using the following formula:

[0109] ;

[0110] ;

[0111] ;

[0112] in, The determinant of the deformed gradient matrix is ​​represented by . This indicates an operation that first finds the inverse of a matrix; This indicates that the matrix is ​​first inverted and then transposed. This represents the first elasticity matrix; Indicates elastic strain; Indicates the displacement deformation gradient; Represents the unit tensor; This represents the displacement gradient; Indicates the elastic deformation gradient; Indicates the gradient of inelastic deformation; This represents the thermal deformation gradient; This represents the intrinsic deformation gradient; This represents the initial deformation gradient; Indicates elastic strain;

[0113] The intrinsic deformation gradient and the initial deformation gradient are calculated using the following formulas:

[0114] ;

[0115] ;

[0116] in, This represents the intrinsic deformation gradient; Represents the unit tensor; Indicates the intrinsic strain; This represents the initial deformation gradient; The initial strain refers to the strain remaining inside the half-cell after the first sintering process when evaluating the entire fuel cell stack sintering process. However, when simulating the entire fuel cell stack assembly process, the initial strain is the strain remaining inside the entire cell after the second sintering stage. Furthermore, it should be noted that... The strain represents the small deformation strain describing volume change, with its non-zero component appearing only on the diagonal. During the sintering process of the fuel cell stack, particle aggregation and neck formation lead to planar shrinkage of the sintered fuel cell stack. The shrinkage rate along the x-axis (i.e., the horizontal length direction) was emphasized and quantitatively evaluated using molecular dynamics (MD) methods to assess the shrinkage effect of particle clusters, which is further correlated with intrinsic strain.

[0117] The thermal deformation gradient is calculated using the following formula:

[0118] ;

[0119] ;

[0120] in, This represents the thermal deformation gradient; Represents the unit tensor; Indicates thermal strain; This represents the real-time coefficient of thermal expansion; This represents the instantaneous temperature during the sintering process; The reference temperature is indicated; the sintering process of the battery cell includes multiple stages such as heating, holding and cooling. The inherent temperature gradient formed in each stage will drive the sintered structure to undergo coordinated deformation under the corresponding thermal environment.

[0121] In this embodiment of the invention, during assembly, the flattened battery cells are tightly sealed to other components of the solid oxide fuel cell stack (such as the frame and sealant) via a bolt pre-tightening device. Due to the rigid constraint applied by the bolt pre-tightening force, the deformation of each component is limited to a small deformation range. Assuming that the mechanical behavior of all components within the solid oxide fuel cell stack conforms to the small deformation theory assumption, in this case, the Cauchy stress tensor... σ Effectively utilizes the true stress distribution in current solid oxide fuel cell configurations for description, i.e., a linearized Cauchy strain tensor. ε The linear elastic constitutive relation can reasonably describe the local stress response caused by the pre-tightening of solid oxide fuel cell assembly.

[0122] In this embodiment of the invention, the second stress parameter includes the elastic modulus, Poisson's ratio, initial strain, and stack displacement of the materials of each component during the assembly process at room temperature. In step S3, the second elastic matrix is ​​obtained based on the elastic modulus and Poisson's ratio, the total stack strain is obtained based on the stack displacement, the inelastic strain of the stack is obtained based on the initial strain, the elastic strain of the stack is obtained based on the total stack strain and the inelastic strain of the stack, and the second elastic stress and the second inelastic stress are obtained based on the elastic strain of the stack and the second elastic matrix.

[0123] In this embodiment of the invention, the second elastic stress and the second inelastic stress are calculated using the following formulas:

[0124] ;

[0125] ;

[0126] ;

[0127] ;

[0128] ;

[0129] in, This indicates the assembly stress; This represents the second elastic stress; This represents the second inelastic stress; This represents the total strain of the fuel cell stack; This indicates the displacement of the fuel cell stack; This indicates that the matrix is ​​first inverted and then transposed. This indicates the inelastic strain of the fuel cell stack; This represents the initial strain; This represents the elastic strain of the fuel cell stack; This represents the second elastic matrix; under room temperature conditions without a supply of reactive gas, the stack maintains thermal equilibrium due to the lack of electrochemical reaction, therefore the thermal expansion effect can be ignored;

[0130] The second elasticity matrix is ​​calculated using the following formula:

[0131] ;

[0132] in, This represents the second elasticity matrix; This represents the elastic modulus; The Poisson's ratio is represented; the material properties of each component in the solid oxide fuel cell are shown in Table 1 below:

[0133] Table 1. Material properties of each component in a solid oxide fuel cell.

[0134] ;

[0135] The second elasticity matrix can be obtained by substituting the corresponding values ​​of elastic modulus and Poisson's ratio in Table 1.

[0136] In the description of this invention, the references to "one embodiment," "some embodiments," "in this embodiment," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0137] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for analyzing the cold stress characteristics of a fuel cell stack based on finite element analysis, characterized in that, Includes the following steps: Step S1: Based on the physical structure of the solid oxide fuel cell, perform three-dimensional modeling to obtain multiple components of the solid oxide fuel cell, and assemble the components to form a full-size fuel cell model. Step S2: Simulate the co-sintering process of porous electrodes and thin-layer electrolyte in the full-size electric stack model using molecular dynamics simulation, obtain the residual stress and first stress parameter generated during the co-sintering process, and obtain the first elastic stress and first inelastic stress of the full-size electric stack model based on the finite deformation theory and the second Piola-Kirchhoff stress tensor, according to the residual stress and the first stress parameter. Step S3: Obtain the assembly stress and second stress parameters generated by each component during the assembly process, and based on the small deformation theory and the linear elastic constitutive relation, obtain the second elastic stress and second inelastic stress of the full-size fuel cell model according to the assembly stress and the second stress parameters. Step S4: The first elastic stress, the first inelastic stress, the second elastic stress, and the second inelastic stress are taken as the results of the cold stress characteristic analysis of the fuel cell stack. In step S2, the instantaneous temperature during the co-sintering process, the real-time thermal expansion coefficients corresponding to different instantaneous temperatures, the reference temperature under no stress, the unit tensor, the intrinsic strain, the initial strain, the displacement gradient, the first elastic matrix, and the deformation gradient matrix are obtained and included in the first stress parameter. The thermal deformation gradient is obtained based on the real-time thermal expansion coefficient, the instantaneous temperature, the reference temperature, and the unit tensor. The intrinsic deformation gradient is obtained based on the intrinsic strain and the unit tensor. The initial deformation gradient is obtained based on the initial strain and the unit tensor. Subsequently, the first elastic stress is obtained based on the displacement gradient, the thermal deformation gradient, the intrinsic deformation gradient, the initial deformation gradient, the first elastic matrix, and the deformation gradient matrix. The residual stress is subtracted from the first elastic stress to obtain the first inelastic stress. The second stress parameter includes the elastic modulus, Poisson's ratio, initial strain, and stack displacement of the materials of each component during the assembly process at room temperature. In step S3, a second elastic matrix is ​​obtained based on the elastic modulus and the Poisson's ratio; the total stack strain is obtained based on the stack displacement; the inelastic strain of the stack is obtained based on the initial strain; the elastic strain of the stack is obtained based on the total stack strain and the inelastic strain of the stack; the second elastic stress is obtained based on the elastic strain of the stack and the second elastic matrix; and the assembly stress is subtracted from the second elastic stress to obtain the second inelastic stress.

2. The method for analyzing the cold stress characteristics of a fuel cell stack based on finite element analysis according to claim 1, characterized in that, In step S2, the thermal deformation gradient is obtained using the following formula: ； ； in, This represents the thermal deformation gradient; Represents the unit tensor; Indicates thermal strain; This represents the real-time coefficient of thermal expansion; This represents the instantaneous temperature during the sintering process; This indicates the reference temperature.

3. The method for analyzing the cold stress characteristics of a fuel cell stack based on finite element analysis according to claim 1, characterized in that, In step S2, the intrinsic deformation gradient and the initial deformation gradient are obtained using the following formulas: ； ； in, This represents the intrinsic deformation gradient; Represents the unit tensor; Indicates the intrinsic strain; This represents the initial deformation gradient; This represents the initial strain.

4. The method for analyzing the cold stress characteristics of a fuel cell stack based on finite element analysis according to claim 1, characterized in that, In step S2, the first elastic stress and the first inelastic stress are obtained using the following calculation formulas: ； ； ； ； in, This refers to the residual stress; This represents the first elastic stress; This represents the first inelastic stress; The determinant of the deformed gradient matrix is ​​represented by . This indicates an operation that first finds the inverse of a matrix; This indicates that the matrix is ​​first inverted and then transposed. This represents the first elasticity matrix; Indicates elastic strain; Indicates the displacement deformation gradient; Represents the unit tensor; This represents the displacement gradient; Indicates the elastic deformation gradient; Indicates the gradient of inelastic deformation; This represents the thermal deformation gradient; This represents the intrinsic deformation gradient; This represents the initial deformation gradient; It represents elastic strain.

5. The method for analyzing the cold stress characteristics of a fuel cell stack based on finite element analysis according to claim 1, characterized in that, In step S3, the second elasticity matrix is ​​obtained using the following calculation formula: ； in, This represents the second elasticity matrix; This represents the elastic modulus; This represents the Poisson's ratio.

6. The method for analyzing the cold stress characteristics of a fuel cell stack based on finite element analysis according to claim 1, characterized in that, In step S3, the second elastic stress and the second inelastic stress are obtained using the following calculation formulas: ； ； ； ； ； in, This indicates the assembly stress; This represents the second elastic stress; This represents the second inelastic stress; This represents the total strain of the fuel cell stack; This indicates the displacement of the fuel cell stack; This indicates that the matrix is ​​first inverted and then transposed. This indicates the inelastic strain of the fuel cell stack; This represents the initial strain; This represents the elastic strain of the fuel cell stack; This represents the second elasticity matrix.

Images