A Composite Material Modeling Method Based on Meshless Method

Abstract

The present invention relates to a composite material modeling method based on the meshless method, which comprises the following steps: obtaining the CAD data of the composite material; sorting out the CAD data of the composite material to form standard data; based on the standard data, performing meshless modeling for the matrix and 1D element modeling for the fiber respectively; performing co-node processing on the matrix model and the fiber model to generate a co-node model, that is, obtaining the composite material model. Compared with the prior art, the present invention separately models the matrix and the fiber. Among them, the matrix part adopts meshless modeling, and the fiber part adopts 1D element modeling. Finally, the co-node processing is performed on the matrix model and the fiber 1D element model, which can improve the modeling accuracy while ensuring the integrity of the CAD data and truly simulate the coupled mechanical properties between the matrix and the fiber in the composite material.

Description

Technical Field

[0001] The present invention relates to the technical field of composite material modeling and simulation, and in particular to a composite material modeling method based on the meshless method. Background Art

[0002] Composite materials are multiphase materials, usually composed of two or more material components with different properties. Due to their designability, in general, composite materials can not only retain the advantages of the performance of each component material, but also obtain comprehensive mechanical properties that cannot be achieved by a single component material through the complementarity and correlation of the mechanical properties of each component. Carbon fiber reinforced matrix composite materials are one of the most advanced and widely used composite materials today. They have the characteristics of high specific strength, high specific modulus, excellent fatigue resistance, strong corrosion resistance and designability. Fiber reinforced composite plates have been widely used in the aerospace field. The damage form and damage size after high-speed impact have a great impact on the remaining strength of the structure. Studying them has important academic value and engineering application background. In response to the needs of composite materials in engineering use, existing research mainly uses the finite element analysis method for modeling and simulation research.

[0003] However, when using the finite element method to model and simulate composite material components, it is necessary to mesh the CAD data. It is very difficult to maintain the original CAD structural features during meshing, and even some features are directly simplified, which is likely to cause subsequent calculation errors.

[0004] During the calculation process of the finite element method, problems such as rapid re-meshing of the mesh and mesh distortion and deformation are usually faced, which will seriously affect the calculation efficiency and solution accuracy. If there are any discontinuities in the mesh or the mesh quality requirements are not met during the mesh reshaping process, it will lead to the correctness of subsequent calculations, and even cause the calculation to interrupt and the result cannot be obtained. And due to the limitation of the inherent mesh, it becomes relatively difficult to solve engineering problems such as dynamic crack propagation, material failure and failure involved in high-speed impact.

[0005] In addition, when using the finite element method to model composite materials, approximate modeling methods are mostly used, that is, the matrix and fibers are regarded as a type of anisotropic material for modeling and simulation. In reality, composite materials are composed of resin (matrix) and fibers. It is difficult for the simple finite element method to simultaneously simulate the mechanical properties of the coupling of the two materials. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a composite material modeling method based on the meshless method, which can improve the modeling accuracy while ensuring the integrity of CAD data, and truly simulate the mechanical properties of the coupling of the two materials in the composite material.

[0007] The object of the present invention can be achieved by the following technical solutions: A composite material modeling method based on the meshless method, comprising the following steps:

[0008] S1. Obtain the CAD data of the composite material;

[0009] S2. Sort out the CAD data of the composite material to form standardized data;

[0010] S3. Based on the standardized data, perform meshless modeling for the matrix and 1D element modeling for the fibers respectively;

[0011] S4. Perform co-node processing on the matrix model and the fiber model to generate a co-node model, that is, obtain the composite material model.

[0012] Further, the step S2 is specifically to delete the data with penetration and interference problems in the CAD data of the composite material to obtain standardized data without penetration and interference.

[0013] Further, the step S3 includes the following steps:

[0014] S31. Based on the standardized data, perform meshless modeling for the matrix and discretize the matrix into particles;

[0015] S32. Based on the standardized data, set the fiber hierarchy, and then perform modeling for different fibers using corresponding 1D elements to obtain different fiber 1D element models.

[0016] Further, the step S31 is specifically to perform meshless modeling for the matrix using the SPG (Smoothed Particle Galerkin) method.

[0017] Further, when performing meshless modeling in the step S31, set the matrix to use isotropic materials.

[0018] Further, in the step S32, setting the fiber hierarchy is specifically to analyze the ply directions and corresponding volumes of the fibers in each direction according to the standardized data.

[0019] Further, the ply directions of the fibers in each direction include the radial direction, the circumferential direction, and the vertical direction.

[0020] Further, the 1D elements in the step S32 include rod elements, beam elements, cable elements, and fabric elements.

[0021] Further, when performing modeling using 1D elements in the step S32, set the fibers to use elastic materials or elastoplastic materials.

[0022] Further, step S4 specifically performs co - node coupling processing on the nodes of the fiber 1D unit model and the meshless particles, so as to couple the forces of the fiber model and the matrix model together to obtain a co - node model.

[0023] Compared with the prior art, the present invention has the following advantages:

[0024] The present invention takes into account the differences and force coupling characteristics between the matrix and fibers in the composite material, and designs to separately model the matrix and fibers. Among them, the matrix (resin) part is modeled by the meshless method, which can ensure the integrity of CAD data, get rid of the dependence on the mesh, and also eliminate the process of constructing the mesh, simplifying the pre - processing process of problem analysis and improving the calculation accuracy; the fiber part is modeled by the 1D unit, and finally the matrix model and the fiber 1D unit model are processed with co - nodes to obtain the composite material model, which can truly simulate the force coupling performance between the matrix and the fibers.

[0025] The present invention sorts out the CAD data of the composite material to form standard data, that is, obtains standard data without penetration and interference, and then separately performs matrix modeling and fiber modeling based on the standard data, which can improve the efficiency and accuracy of modeling.

[0026] The present invention uses the SPG method for matrix modeling, discretizes the matrix into particles. Compared with other meshless methods, it can directly perform spatial integration on the nodes, avoiding the limitations brought by the background grid spatial integration method; it can accurately simulate the cracking process of the material, and the nodes are not restricted by the mesh structure, and the positions of the nodes can be changed according to needs during the calculation, avoiding the calculation difficulties caused by mesh distortion in large - deformation analysis and mesh reconstruction when calculating moving discontinuities.

[0027] When the present invention models the fibers, first, the fiber layer is set, that is, the laying direction and corresponding volume of the fibers in each direction are analyzed according to the CAD design, and then the corresponding modeling process is carried out using the rod element, beam element, cable element, or fabric element of the 1D unit, which can ensure the accuracy of fiber modeling. Description of the Drawings

[0028] Figure 1 is the schematic flow chart of the method of the present invention;

[0029] Figure 2 is the schematic diagram of the application process of the embodiment;

[0030] Figure 3a is the CAD standard data corresponding to the composite material in the embodiment;

[0031] Figure 3b is the effect diagram of the matrix discretized into particles in the embodiment;

[0032] Figure 3c Effect diagram of generating fiber 1D units radially in the embodiment;

[0033] Figure 3d Effect diagram of generating fiber 1D units in the weft direction in the embodiment;

[0034] Figure 3e Effect diagram of generating fiber 1D units vertically in the embodiment;

[0035] Figure 3f Effect diagram of generating a composite material calculation model in the embodiment. Detailed implementation manners

[0036] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] Embodiment

[0038] To facilitate understanding of this solution, the following explanations of professional terms are given first:

[0039] 1. Finite element method

[0040] The finite element method, also known as the finite element method (FEM), is a numerical solution method for elastic mechanics problems that has developed rapidly with the development of electronic computers. In the early 1950s, it was first applied in the field of continuum mechanics - the static and dynamic characteristic analysis of aircraft structures to obtain the deformation, stress, natural frequency, and vibration mode of the structure. Due to the effectiveness of this method, the application of the finite element method has been extended from linear problems to nonlinear problems, and the analysis objects have been extended from elastic materials to plastic, viscoelastic, viscoplastic, and composite materials, and from continua to non-continua.

[0041] 2. Meshless method

[0042] The meshless method, as another branch in computational mechanics, is different from the finite element method. Due to the mesh characteristics of the finite element, mesh distortion will occur when solving some extreme problems, resulting in inability to calculate. However, the meshless method does not have this problem because it does not require mesh division. The meshless method usually constructs the weak form or collocation form of the problem to be solved by the weighted residual method, and constructs the shape function and establishes the discrete system equation through the nodes in the local support domain. It is a node-based numerical method. This method avoids mesh division and has the characteristics of being convenient for constructing high-order shape functions and easy for adaptive analysis. There are many types of meshless methods, and nearly forty meshless methods have been proposed so far. Commonly used meshless methods include the smoothed particle hydrodynamics method (SPH), smoothed particle Galerkin method (SPG), element-free Galerkin method (EFG), reproducing kernel particle method (RKPM), radial basis function collocation method (RBCM), stabilized collocation method (SCM), etc.

[0043] 3. Smoothed Particle Galerkin method (SPG)

[0044] The SPG (Smoothed Particle Galerkin method) is a typical meshless method. It directly performs spatial integration at nodes, avoiding the limitations brought by the background mesh spatial integration method adopted by other meshless methods. SPG satisfies that the shape functions add up to 1 and all satisfy first-order convergence. In order to accurately simulate the cracking process of materials, the SPG method has developed a bond fracture failure model. During the bond fracture failure process, no material points are deleted, which can ensure the conservation of mass and momentum. In SPG, the nodes are not restricted by the mesh structure, and the positions of the nodes can be changed according to needs during the calculation, avoiding the computational difficulties caused by mesh distortion in large deformation analysis and mesh reconstruction when calculating moving discontinuities. Therefore, it has obvious advantages in nonlinear structural analysis.

[0045] In the SPG method, a direct node integration (DNI) scheme is adopted, and a displacement smoothing technique is used to define the stable low-energy mode as follows:

[0046] Smoothed displacement field:

[0047]

[0048] Shape function of SPG:

[0049]

[0050] Stable strain field:

[0051]

[0052] Stable enhanced strain (second derivative of displacement);

[0053] represents the stability parameter related to the length scale;

[0054] NP: is the number of particles used in the domain discretization;

[0055] is the displacement smoothing function of s;

[0056] is the displacement shape function of α.

[0057] In the SPG method, when a = s, it represents stability. Using the smoothed displacement field, the semi-discrete Galerkin weak form can be obtained:

[0058]

[0059] The DIN of the stability term can be expressed as:

[0060]

[0061] J 0 : is the determinant of the Jacobian matrix

[0062] is the volume of particle N

[0063] is the stable stress

[0064] is the stable gradient matrix, which consists of and its derivatives.

[0065] Such as Figure 1 shown, a composite material modeling method based on the meshless method includes the following steps:

[0066] S1. Obtain the composite material CAD data;

[0067] S2. Sort out the composite material CAD data to form standard data. Specifically, delete the data with penetration and interference problems in the composite material CAD data to obtain standard data without penetration and interference;

[0068] S3. Based on the standard data, perform meshless modeling for the matrix and 1D element modeling for the fibers respectively. Specifically:

[0069] S31. Based on the standard data, perform meshless modeling for the matrix, discretize the matrix into particles, and in this embodiment, use the SPG (Smoothed Particle Galerkin) method to perform meshless modeling for the matrix, and set the matrix to use isotropic materials;

[0070] S32. Based on the standard data, set the fiber hierarchy, and then use corresponding 1D elements (including rod elements, beam elements, cable elements, fabric elements) to model different fibers, set the fibers to use elastic materials or elastoplastic materials to obtain different fiber 1D element models. Among them, setting the fiber hierarchy is to analyze the ply directions and corresponding volumes of the fibers in each direction according to the standard data, and the ply directions of the fibers in each direction include the radial direction, the weft direction, and the vertical direction;

[0071] S4. Perform co - node processing on the matrix model and the fiber model, that is, perform co - node coupling processing on the nodes of the fiber 1D element model and the meshless particles, so as to couple the forces of the fiber model and the matrix model together to generate a co - node model, that is, obtain the composite material model.

[0072] This embodiment applies the above solution to design a corresponding simulation software program to execute the data processing process as shown in Figure 2 :

[0073] 1. Input of composite material CAD data: The user first obtains the CAD data of the composite material.

[0074] 2. Data arrangement: Since the CAD data just obtained often has problems such as penetration and interference at the corners, it is necessary to arrange the CAD data to form standard data (as shown in Figure 3a ).

[0075] 3. Fiber layer setting: Analyze the laying direction and corresponding volume of the fibers in each direction according to the CAD design.

[0076] 4. Discretization of the matrix into particles: The matrix (resin) uses meshless modeling, which is equivalent to discretizing the matrix into particles (as shown in Figure 3b ). In this embodiment, the particles are simulated by the SPG method and isotropic materials are used.

[0077] 5. Generation of 1D elements for fibers: The fibers are modeled using 1D beam elements, rod elements, cable elements or fabric (seat belt) elements, and elastic materials or elastoplastic materials are used. Among them, the 1D unit models corresponding to the radial fibers, weft fibers and vertical fibers are shown in Figure 3c , 3d and 3e respectively.

[0078] 6. Co - node of discrete particles and 1D elements: The matrix particles and the fiber 1D elements share the same nodes.

[0079] 7. Generation of the composite material calculation model: Output the generated co - node model as the composite material calculation model (as shown in Figure 3f ).

[0080] In summary, this solution designs a modeling method for the composite material matrix using the meshless method, the fibers using 1D elements, and a modeling method of coupling the matrix and fibers with shared nodes to obtain the composite material calculation model. Among them, for the matrix (resin) part of the composite material, meshless modeling is adopted:

[0081] As the matrix component of the composite material, the resin needs to have a certain stiffness and stability and be bonded to the fiber reinforcement. Its main functions are as follows: 1. Transmitting the load, and at the same time providing rigidity and shape support for the composite material to keep the reinforcing fibers in the designed direction and position; 2. Isolation function, separating the fibers from each other so that they can play their respective roles without interfering with each other, which can effectively slow down the crack initiation and propagation process; 3. Protection function, protecting the reinforcing fibers from chemical erosion and mechanical damage in a certain environment, playing a role in protecting the reinforcing phase. The matrix is modeled using the meshless method, which can ensure the integrity of the CAD data.

[0082] Compared with the finite element method, the meshless method gets rid of the dependence on the mesh and also abandons the process of constructing the mesh, simplifying the preprocessing process of problem analysis. Using the least squares method, only the weight function that meets the conditions needs to be selected to easily construct a high-order interpolation function. Compared with the mature and widely used finite element method, the advantages of the element-free method can be summarized as follows: (1) Simple preprocessing. When analyzing using the element-free method, only the relevant information of the nodes is required in the calculation process, and the node layout is flexible, without the need to meet a series of requirements such as continuity in the finite element mesh. The adjustment of individual nodes will not affect the overall properties, and the adjustment of the node positions is also easy to operate. Moreover, the data itself has a low dimension and is easy to be substituted and stored. (2) Getting rid of the dependence on the inherent mesh, with strong self-regulation and adaptability of the method. The component modules such as the node layout method, the type of weight function, and the integration scheme can all be adjusted according to the actual application situation. (3) High calculation accuracy. The stress solution accuracy of the finite element method is relatively low, and it is even discontinuous in the case of first-order elements. This phenomenon is an incorrect simulation of the real physical problem. In the meshless method, due to the nature of its shape function being related to the weight function, it is relatively convenient and simple to meet the high-order continuity requirements without the need for stress equalization and other processing procedures.

[0083] In addition, in the way of separately modeling the matrix and fibers of the composite material, in the process of composite material modeling, the matrix (resin) is modeled using the meshless method, and the fibers are modeled using 1D elements. Moreover, the nodes of the 1D elements are co-nodal with the meshless particles, so that the force of the fiber model and the matrix model can be coupled together, and then the mechanical properties of the coupling of the two materials can be simulated simultaneously.

Claims

1. A composite material modeling method based on the meshless method, characterized in that It includes the following steps: S1. Obtain the composite material CAD data; S2. Organize the composite material CAD data to form standardized data; S3. Based on the standardized data, perform meshless modeling for the matrix and 1D element modeling for the fibers respectively; S4. Perform co - node processing on the matrix model and the fiber model to generate a co - node model, that is, obtain the composite material model; Among them, step S3 includes the following steps: S31. Based on the standardized data, perform meshless modeling for the matrix and discretize the matrix into particles; S32. Based on the standardized data, set the fiber hierarchy, and then use corresponding 1D elements for different fibers to perform modeling to obtain different fiber 1D element models; In step S32, setting the fiber hierarchy is specifically to analyze the ply directions and corresponding volumes of the fibers in each direction according to the standardized data. The ply directions of the fibers in each direction include the radial direction, the circumferential direction, and the vertical direction; Step S4 is specifically to perform co - node coupling processing on the nodes of the fiber 1D element model and the meshless particles to couple the forces of the fiber model and the matrix model together to obtain a co - node model.

2. The composite material modeling method based on the meshless method according to claim 1, wherein Step S2 is specifically to delete the data with penetration and interference problems in the composite material CAD data to obtain standardized data without penetration and interference.

3. A composite material modeling method based on the meshless method according to claim 1, characterized in that, Step S31 is specifically to perform meshless modeling for the matrix using the SPG method.

4. A composite material modeling method based on the meshless method according to claim 1, characterized in that When performing meshless modeling in step S31, set the matrix to use an isotropic material.

5. A method for modeling composite materials based on the meshless method according to claim 1, characterized in that, The 1D elements in step S32 include bar elements, beam elements, cable elements, and fabric elements.

6. A method for modeling composite materials based on the meshless method according to claim 1, characterized in that, When performing modeling using 1D elements in step S32, set the fibers to use elastic materials or elastoplastic materials.

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