A method for calculating nonlinear mechanical properties of braided composite materials

Abstract

The present invention discloses a method for calculating the nonlinear mechanical properties of a braided composite material structure, which belongs to the field of simulation calculation methods, and includes: constructing an RVE unit cell model corresponding to the braided composite material structure; obtaining periodic boundary conditions, and correcting the periodic boundary conditions based on the principle of linear superposition to obtain physical consistency boundary conditions; obtaining the average strain energy expression of the beam structure unit cell and the modified Hill conditions, and combining the RVE unit cell model, periodic boundary conditions, and physical consistency boundary conditions to calculate the equivalent section flexibility matrix; and calculating the nonlinear mechanical properties of the braided composite material structure based on the equivalent section flexibility matrix and the RVE unit cell model. The present invention solves the problems of low calculation efficiency caused by excessive structural complexity of large-scale complex braided composite material components in multi-scale simulation processes and insufficient accuracy of stress and strain fields at details caused by internal shear forces after using typical periodic boundary conditions.

Description

Technical Field

[0001] The invention belongs to the field of simulation calculation methods, and in particular relates to a calculation method for nonlinear mechanical properties of a braided composite material structure. Background Art

[0002] Braided composite structures have been widely used in aerospace, aviation, shipbuilding, automobile manufacturing, engineering machinery and other fields. The use of simulation methods to predict the structural properties of braided composite materials is a common technical means in the field of design and manufacturing, which can effectively reduce costs and optimize design solutions. Among them, large-scale composite structures have nonlinear deformation characteristics under load. The efficient analysis of large-scale composite structures is a key issue in the mechanical analysis of heterogeneous structures. The key issue in the mechanical response analysis of large-scale structures with complex geometric topology and complex material systems is to balance the analysis efficiency and simulation accuracy. The use of high-fidelity reduced-order models is an effective technical approach. For such multi-scale structural analysis problems, the complex structure can be reduced to a low-order beam structure model by performing a reasonable homogenization analysis on the structure to improve the computational efficiency. At the same time, it is necessary to retain the detailed information of the structure, maintain the ability to restore the accurate stress and strain field, and ensure the accuracy of the analysis.

[0003] Structural homogenization methods are widely used in topological optimization of microstructure units. The theory of topological optimization design of microstructure units of composite materials was first proposed in the mid-1990s and has now become one of the frontiers in the field of materials research. A lot of basic research has also been done on topological optimization in China. At present, research on multiscale homogenization theory is mainly focused on the problem of optimizing the design of composite material structures. It is widely used in the macro-micro multiscale computational analysis methods of composite materials, and the optimization design of composite microstructures with macroscopic mechanical properties as the goal.

[0004] However, these methods usually use periodic boundary conditions for homogenization analysis without considering the deformation state of the actual shear-containing structure, resulting in insufficient accuracy of the stress-strain field at the structural details, and the calculation results of the equivalent section stiffness are inconsistent with the actual physics. Therefore, there are still certain problems that need to be solved in practical applications. The present invention proposes a method for constructing a simplified beam model of a three-dimensional shear-containing structure unit cell to solve the problems existing in traditional structural homogenization methods, thereby accurately solving the equivalent section properties of the structural unit cell and accurately retaining the stress and strain fields in the structural unit cell, serving the accurate and efficient mechanical response analysis of large-scale complex composite structures. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a method for calculating the nonlinear mechanical properties of a braided composite material structure to solve the above problems existing in the prior art.

[0006] To achieve the above object, the present invention provides a method for calculating the nonlinear mechanical properties of a braided composite material structure, comprising:

[0007] Construct the RVE unit cell model corresponding to the braided composite material structure;

[0008] Obtain conventional periodic boundary conditions, modify them based on the linear superposition principle, and obtain physically consistent boundary conditions;

[0009] The average strain energy expression and modified Hill condition of the beam structure unit cell are obtained, and the equivalent section flexibility matrix is ​​calculated based on the RVE unit cell model, conventional periodic boundary conditions, physical consistency boundary conditions, average strain energy expression and modified Hill condition;

[0010] The nonlinear mechanical properties of braided composite structures are calculated based on the equivalent section flexibility matrix and the RVE unit cell model.

[0011] Optionally, the process of constructing an RVE unit cell model corresponding to a braided composite material structure includes:

[0012] The definition of displacement field and displacement disturbance field of a beam structure unit cell with generalized strain as a constant is obtained, and the displacement field expression of the Timoshenko beam is obtained based on the displacement field definition of the beam structure unit cell. The periodic boundary conditions are obtained, and based on the displacement field expression of the Timoshenko beam and the conventional periodic boundary conditions, the displacement field relationship on the positive and negative end faces of the beam structure unit cell is derived.

[0013] Optionally, the application object of the reduced-order model is a woven composite material structure having a beam structure.

[0014] Optionally, the process of obtaining physically consistent boundary conditions includes:

[0015] According to the equilibrium equation of the beam model, the relationship between the gradient of the bending moment and the shear force is obtained. The influence of the constant shear force on the bending moment of the adjacent unit cells is considered, and the superposition of the adjacent unit cells and the unit cells under pure bending moment is taken as the load and deformation of the unit cell under constant shear force. The conventional periodic boundary conditions are modified in combination with the principle of linear superposition to obtain physically consistent boundary conditions.

[0016] Optionally, the physical consistency boundary condition is expressed as follows:

[0017]

[0018] In the formula, It is expressed as the positive end surface displacement disturbance field, is the negative end surface displacement disturbance field, is the negative end surface force field, is the tensor permutation symbol, indicating the positive or negative direction, and is defined as

[0019]

[0020] in, is the subscript indicating the direction, is the concentrated force at both ends of the beam Concentration of direction, is the characteristic length of the unit cell, is the positive end surface force field, Expressed as a beam model unit cell at unit moment The displacement disturbance field generated by It represents the surface force field on the boundary surface.

[0021] Optionally, define the initial average strain energy expression of the beam structure unit cell, and obtain the average strain energy expression of the beam structure unit cell according to the macroscopic stress characteristics of the beam structure unit cell and the initial average strain energy expression; consider the linear change of the bending moment under the action of shear force, obtain the generalized force distribution expression, and combine the average strain energy expression of the beam structure unit cell to obtain the modified Hill condition.

[0022] Optionally, the equivalent section flexibility matrix comprises a section coefficient, a marking coefficient, and a physical consistency boundary condition coefficient.

[0023] Optionally, the process of calculating and obtaining the equivalent section flexibility matrix includes: using the conventional periodic boundary conditions, loading unit-sized tension, bending moment and torsional moment on the periodic unit cell respectively, and calculating the generalized strain of each loading, and obtaining the section coefficient by associating the generalized stress with the generalized strain; using the physical consistency boundary conditions, applying a shear load to the beam structure unit cell, and calculating the marking coefficient based on the average strain energy and the modified Hill condition; calculating the physical consistency boundary condition coefficient based on the modified Hill condition to obtain the equivalent section flexibility matrix.

[0024] Compared with the prior art, the present invention has the following advantages and technical effects:

[0025] The present invention proposes a method for establishing a beam structure reduced-order model based on a homogenization method, and corrects the typical periodicity through physical consistency boundary conditions to eliminate the detail distortion of the stress-strain field caused by shear force. It mainly solves the problem of low computational efficiency caused by excessive structural complexity of large-scale complex woven composite components in multi-scale simulation and insufficient accuracy of the stress-strain field in the details caused by the shear force inside the structure after using typical periodic boundary conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0027] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0028] Figure 2 A homogenization process of a beam structure according to an embodiment of the present invention;

[0029] Figure 3 The homogenization process of the plate-shell structure according to the embodiment of the present invention;

[0030] Figure 4 The figure is a calculation flow of equivalent cross-sectional properties according to an embodiment of the present invention. DETAILED DESCRIPTION

[0031] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0032] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0033] Embodiment 1

[0034] like Figure 1 As shown, this embodiment provides a method for calculating the nonlinear mechanical properties of a braided composite material structure, comprising:

[0035] (1) Homogenization method of beam structure

[0036] The purpose of the structural homogenization method is to use the beam model to describe the mechanical response of a three-dimensional periodic complex structure unit cell. Therefore, for a periodic beam structure unit cell, it is necessary to calculate the equivalent section stiffness / flexibility matrix and then establish the relationship between the generalized strain and generalized stress in the unit cell model, such as Figure 2 , 3 As shown. The following takes the beam structure unit cell as an example to introduce its homogenization process.

[0037] The definition of displacement field and displacement disturbance field of a beam structure unit cell with generalized strain as a constant is obtained, and the displacement field expression of the Timoshenko beam is obtained based on the displacement field definition of the beam structure unit cell. The periodic boundary conditions are obtained, and based on the displacement field expression of the Timoshenko beam and the conventional periodic boundary conditions, the displacement field relationship on the positive and negative end faces of the beam structure unit cell is derived.

[0038] Specifically, for a beam structure unit cell with a generalized strain constant, the displacement field can be expressed as:

[0039]

[0040] (1)

[0041] in, is the displacement in three directions, is the three-dimensional coordinate position of the unit, are the bending curvatures in three directions respectively.

[0042] Similar to the material homogenization process, in addition to the displacement given in the above formula, a displacement disturbance field is further assumed in the unit cell:

[0043] (2)

[0044] in, is expressed as a displacement field, is the displacement field corresponding to constant cross-sectional strain, Expressed as a displacement disturbance field.

[0045] The periodic boundary conditions (conventional periodic boundary conditions) commonly used in structural homogenization analysis require that the disturbance fields on the positive and negative end faces of the unit cell are equal and the sum of the surface force fields is 0, that is:

[0046] (3)

[0047] In the formula, It is expressed as the positive end surface displacement disturbance field, is the negative end surface displacement disturbance field, is the negative end surface force field, is the positive end surface force field.

[0048] For the Euler beam, the periodic boundary condition can be further expressed as:

[0049] (4)

[0050] in, represents the displacement field of the positive end surface, represents the negative end displacement field, is the three-dimensional coordinate position of the unit, are the curvatures in three directions, is the unit characteristic length.

[0051] When shear deformation is considered, similar equations can be derived using Timoshenko's theory. The displacement field in the unit cell corresponding to constant generalized shear strain (the displacement field expression of Timoshenko beam) is:

[0052] (5)

[0053] in, is the displacement in three directions, is the three-dimensional coordinate position of the unit, are the curvatures in three directions, is the shear strain in the i direction.

[0054] On the two end faces of the beam structure unit cell, the relationship between the displacement fields can be expressed as:

[0055] (6)

[0056] in, It is expressed as a displacement field, with the positive and negative superscripts referring to the positive and negative end faces. is the three-dimensional coordinate position of the unit, are the curvatures in three directions, is the unit characteristic length, It is expressed as the positive end surface displacement disturbance field, is the negative end surface displacement disturbance field, is the shear strain in the i direction.

[0057] (2) Corrected boundary conditions and calculation of equivalent section properties

[0058] According to the equilibrium equation of the beam model, the relationship between the gradient of the bending moment and the shear force is obtained. The influence of the constant shear force on the bending moment of the adjacent unit cells is considered, and the superposition of the adjacent unit cells and the unit cells under pure bending moment is taken as the load and deformation of the unit cell under constant shear force. The conventional periodic boundary conditions are modified in combination with the principle of linear superposition to obtain physically consistent boundary conditions.

[0059] Taking the beam structure as an example, in a periodic unit cell, the existence of shear force causes the bending moment in the unit cell to no longer be a constant, but to change linearly. According to the equilibrium equation of the beam model, the bending moment Gradient and shear The relationship between them satisfies:

[0060] (7)

[0061] Therefore, unlike the tension, bending moment and torque in the Euler beam, the action of constant shear will cause a difference in the bending moment of two adjacent unit cells in the beam structure, namely:

[0062] (8)

[0063] This further shows that the load and deformation of a unit cell under constant shear force can be regarded as the superposition of its adjacent unit cells and the unit cell under pure bending moment. According to the linear superposition principle, the boundary conditions are appropriately modified to obtain the physically consistent boundary condition (PCBC).

[0064] (9)

[0065] in, It is expressed as the positive end surface displacement disturbance field, is the negative end surface displacement disturbance field, is the negative end surface force field, is the tensor permutation symbol, which is defined as

[0066]

[0067] Indicates the positive or negative direction, where is the subscript indicating the direction, is the concentrated force at both ends of the beam Concentration of direction, is the characteristic length of the unit cell, is the positive end surface force field, Expressed as a beam model unit cell at unit moment The displacement disturbance field generated by It represents the surface force field on the boundary surface.

[0068] Therefore, the physical consistency boundary condition can be expressed as:

[0069] (10)

[0070] The process of calculating and obtaining the equivalent section flexibility matrix includes: using the conventional periodic boundary conditions, loading unit-sized tension, bending moment and torsional moment on the periodic unit cell respectively, and calculating the generalized strain of each loading, and obtaining the section coefficient by associating the generalized stress with the generalized strain; using the physical consistency boundary conditions, applying shear load to the beam structure unit cell, and calculating the marking coefficient based on the average strain energy and the modified Hill condition; calculating the physical consistency boundary condition coefficient based on the modified Hill condition to obtain the equivalent section flexibility matrix.

[0071] In the traditional procedure of material homogenization, after solving the deformation and stress distribution of the RVE under different loading cases, the equivalent mechanical properties of the homogenized material can be calculated by relating the macroscopic stress to the strain or relating it to the strain energy according to the Hill conditions. For the homogenization process of the beam structure, we use a similar method to calculate the equivalent cross-sectional properties.

[0072] For the Euler beam and Timoshenko beam models, the initial average strain energy is expressed as:

[0073] (11)

[0074] For the Euler beam, since the macroscopic stress is constant in the unit cell of the beam model, the average strain energy can be expressed as , and then the equivalent section flexibility matrix can be solved. The section properties can also be expressed by the generalized constitutive relation get, is the generalized strain vector.

[0075] However, for the Timoshenko beam with shear force, the macroscopic stress is no longer a constant due to the shear force. Therefore, the linear variation of the bending moment needs to be considered in the beam model unit cell. The generalized force distribution in the unit cell can be expressed as , where the matrix A is defined as:

[0076] (12)

[0077] Therefore, the average strain energy of the beam structure unit cell is expressed as:

[0078] (13)

[0079] The above formula is the modified Hill condition for the beam model considering shear action. It can be seen that due to the linear change of the bending moment in the unit cell, the equivalent section flexibility matrix Corrected to .

[0080] When considering shear effects, taking a periodic beam structure as an example, the calculation of the equivalent cross-sectional properties is divided into the following three steps:

[0081] First, periodic boundary conditions are used to load unit forces, bending moments, and torsional moments on the periodic unit cell. The generalized strains are calculated for each of the four cases, and then the 16 section coefficients are calculated by relating the generalized stresses to the generalized strains, as Figure 4 In the second step, shear loads are applied to the beam structure unit cell using physically consistent boundary conditions, and the dark-colored coefficients are calculated using the mean strain energy and the modified Hill condition. Finally, in the third step, the physically consistent condition coefficients are calculated using the modified Hill condition. After these three steps, the complete equivalent section flexibility matrix of the unit cell can be obtained.

[0082] According to the equivalent section properties of the beam structure unit cell, the Timoshenko beam element can be used to simulate the mechanical behavior of the beam structure under given load and constraint conditions. The detailed microscopic stress / strain distribution of the unit cell can be further obtained through a simple "heterogeneous step": since the mechanical response of the unit cell under the unit internal force in six directions has been solved in the homogenization step, the detailed stress / strain distribution of the unit cell under the given six generalized stress components can be directly obtained by linear superposition, such as Figure 4 Specifically, the “heterogeneous step” uses the mechanical response results of the reduced-order model as input to restore the detailed stress of key components. The specific method is to directly linearly superimpose the stress and strain obtained by the solution.

[0083] Specifically, the application object of the reduced-order model is a braided composite material structure with a beam structure, and can also be used for a braided composite material structure with a plate structure. The process is as follows Figure 3 shown.

[0084] Specifically, the modified physically consistent boundary conditions are universal and automatically degenerate into typical periodic boundary conditions when the shear force is zero.

[0085] Based on the multi-scale theory of physical consistency, a complete, feasible, easy-to-operate and computationally efficient composite structure reduction analysis tool has been developed for beam / plate-shell structures. The tool is based on the existing finite element analysis software Abaqus. By processing and calculating the RVE finite element mesh model, a new unit suitable for the mechanical analysis of the macro model of large-scale composite components is submitted to the finite element software.

[0086] The beam / plate-shell structure multi-scale analysis software includes two main modules: one is the homogenization module, which is an interactive interface module responsible for the basic information processing and equivalent stiffness calculation of RVE; the other is the heterogenization module, which takes the mechanical response results of the reduced-order model as input to restore the detailed stress of key components.

[0087] The homogenization module serves as an interactive interface for processing basic information of RVE. Its function is to read the unit cell model of the complex structure given by the user, and obtain the unilateral stress and strain field consistent with the real physics under tension, bending, shear and torsion conditions by applying physically consistent boundary conditions on the boundary plane of RVE. The equivalent structural stiffness matrix is ​​solved using strain energy through simulation results.

[0088] The function of the heterogeneous module is to combine the force analysis results of the unit cell under various working conditions obtained by the homogenization module, and the generalized force results of the unit cell obtained by the reduced-order model simulation analysis. By superimposing working conditions, the detailed stress field of the unit cell under actual loading conditions is obtained. It is mainly used in the mechanical response analysis of key components in macroscopic large-scale models.

[0089] This embodiment aims at the computational analysis problem of woven composite material structures with nonlinear characteristics in the deformation process. An RVE model of a complex structure is established through homogenization analysis, and the problem that the shear-containing structure is not compatible with typical periodic boundary conditions is corrected, thereby establishing a reduced-order model of the macroscopic structure, achieving high-fidelity and high-efficiency multi-scale computational analysis of the mechanical properties of nonlinear woven composite material structures.

[0090] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for calculating the nonlinear mechanical properties of a braided composite material structure, characterized in that: The following steps are involved: Construct the RVE unit cell model corresponding to the braided composite material structure; Obtain conventional periodic boundary conditions, modify them based on the linear superposition principle, and obtain physically consistent boundary conditions; The process of obtaining physically consistent boundary conditions involves: According to the equilibrium equation of the beam model, the relationship between the gradient of the bending moment and the shear force is obtained. The influence of the constant shear force on the bending moment of the adjacent unit cells is considered. The superposition of the adjacent unit cells and the unit cells under pure bending moment is taken as the load and deformation of the unit cells under constant shear force. The conventional periodic boundary conditions are modified in combination with the linear superposition principle to obtain the physically consistent boundary conditions. The physical consistency boundary condition is expressed as follows: In the formula, It is expressed as the positive end surface displacement disturbance field, is the negative end surface displacement disturbance field, is the negative end surface force field, is the tensor permutation symbol, indicating the positive or negative direction, and is defined as in, is the subscript indicating the direction, is the concentrated force at both ends of the beam Concentration of direction, is the characteristic length of the unit cell, is the positive end surface force field, Expressed as a beam model unit cell at unit moment The displacement disturbance field generated by It represents the surface force field on the boundary surface; The average strain energy expression and modified Hill condition of the beam structure unit cell are obtained, and the equivalent section flexibility matrix is ​​calculated based on the RVE unit cell model, conventional periodic boundary conditions, physical consistency boundary conditions, average strain energy expression and modified Hill condition; Calculate the nonlinear mechanical properties of braided composite structures based on the equivalent section flexibility matrix and RVE unit cell model; The reduced-order model is applied to woven composite structures with beam structures.

2. The method for calculating the nonlinear mechanical properties of a braided composite material structure according to claim 1, characterized in that: The process of constructing the RVE unit cell model corresponding to the woven composite structure includes: The definition of displacement field and displacement disturbance field of a beam structure unit cell with generalized strain as a constant is obtained, and the displacement field expression of the Timoshenko beam is obtained based on the displacement field definition of the beam structure unit cell. The periodic boundary conditions are obtained, and based on the displacement field expression of the Timoshenko beam and the conventional periodic boundary conditions, the displacement field relationship on the positive and negative end faces of the beam structure unit cell is derived.

3. The method for calculating the nonlinear mechanical properties of a braided composite material structure according to claim 1, characterized in that: The initial average strain energy expression of the beam structure unit cell is defined, and the average strain energy expression of the beam structure unit cell is obtained according to the macroscopic stress characteristics of the beam structure unit cell and the initial average strain energy expression. The linear change of the bending moment under the action of shear force is considered to obtain the generalized force distribution expression, and the modified Hill condition is obtained by combining the average strain energy expression of the beam structure unit cell.

4. The method for calculating the nonlinear mechanical properties of a braided composite material structure according to claim 1, characterized in that: The equivalent section flexibility matrix comprises a section coefficient, a marking coefficient, and a physical consistency boundary condition coefficient.

5. The method for calculating the nonlinear mechanical properties of a braided composite material structure according to claim 4, characterized in that: The process of calculating and obtaining the equivalent section flexibility matrix includes: using the conventional periodic boundary conditions, loading unit-sized tension, bending moment and torsional moment on the periodic unit cell respectively, and calculating the generalized strain of each loading, and obtaining the section coefficient by associating the generalized stress with the generalized strain; using the physical consistency boundary conditions, applying shear load to the beam structure unit cell, and calculating the marking coefficient based on the average strain energy and the modified Hill condition; calculating the physical consistency boundary condition coefficient based on the modified Hill condition to obtain the equivalent section flexibility matrix.

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