FEM-VCFEM Two-Scale Simulation Of Damage Evolution And Failure In Particle Reinforced Composites Structure

As a cornerstone of modern technological development,composite materials have a significant impact on the speed of technological development in various fields.Among them,particle-reinforced composite materials are widely used due to their many advantages,becoming a supporting material for many high-tech fields,especially in aerospace,automotive,weapons,and other areas.However,particlereinforced composite materials can undergo micro-damage during the manufacturing or application process,such as micro-cracks and micropores,which can lead to material fracture and failure,seriously affecting the service life of the material.Therefore,the study of structural damage evolution and failure of particlereinforced composite materials has become one of the focuses of material science research.Studying the mechanical properties and structural damage behavior of particle-reinforced composite materials has significant guiding significance for their material design and application.However,the micro-scale damage of composite materials and the overall performance of the material are at different scales.How to comprehensively,quickly,conveniently,and correctly consider these cross-scale factors to analyze the structural damage evolution and failure of particle-reinforced composite materials is a challenging and important interdisciplinary issue.However,the current analysis methods for the problem of crack damage in heterogeneous multiphase materials have left many regrets.Existing methods cannot fully consider the impact of these cross-scale factors on material properties.To address the above issues,this paper establishes a FEM-VCFEM cross-scale model calculation method based on the stress hybrid element theory and micro-scale analysis using Voronoi Cell Finite Element Method(VCFEM).This method is used to solve the large-scale numerical calculation and simulation problems of structural damage and failure of particle-reinforced composite materials,providing important theoretical analysis and technical means for the research and development of composite materials.The main focus of this paper includes the following aspects:1.Propose a new unit model that can reflect the interface debonding and matrix cracking of particle-reinforced composite materials,and construct a functional that contains cracked particle-reinforced composite materials.These allow for the simulation of crack initiation and propagation,and further extends to the new hybrid unit of the matrix.The Williams polynomial is used to construct the interface crack,introducing stress functions to calculate the stress intensity factor at the interface crack tip.The stress function of the matrix is described by the Airy stress function polynomial,which includes the interaction stress function polynomial that describes the elliptical shape and the Williams polynomial that describes the interface crack.The corresponding Fortran program is written to solve the new unit,and the results of the stress field and the crack tip stress intensity factor are compared and analyzed with the commercial finite element software ABAQUS.The results are relatively consistent,which verifies the effectiveness of the proposed method in simulating the fracture failure behavior caused by particle debonding in particle-reinforced composite materials.2.Establishing a new unit model that can reflect the particle fracture of particlereinforced composite materials,and constructing a functional for the inclusion containing cracked particles.The new inclusion unit is derived to simulate the crack initiation,crack propagation within the unit,and the damage evolution process of the crack penetrating the unit.A mesh refinement algorithm is developed for the crack propagation within the unit,which replaces the original crack tip node with a new node based on the crack propagation angle determined by the fracture criterion.This enables the automatic propagation of cracks within the unit from the interface to the matrix,from the inclusion to the matrix,and to adjacent units,achieving the simulation of crack propagation in multiscale particle-reinforced composite materials,and analyzing the crack propagation mechanism.The effectiveness of the proposed method is verified by comparing the results of the stress field and the crack tip stress intensity factor with the ABAQUS calculation results.3.A cross-scale model with a micro-macro scale grid coexistence is established based on the superiority of the proposed new VCFEM method,which avoids the limitations of homogenization theory.This method enables tracking of crack initiation and propagation through adaptive grid refinement,allowing for real-time adjustments to the material phase parameters and the expression of their characteristic information.The cross-scale model uses Voronoi cells for micro-scale analysis and is suitable for parallel computing,resulting in extremely high computational efficiency.The extended Voronoi cells proposed for micro-scale analysis are coupled to macro-scale elements using the master-slave node method,which is based on the multiple grid adaptation strategy.This method ensures that the edge lengths of the finite element and VCFEM are essentially the same,and the two types of elements are connected by shared nodes according to the edge displacement interpolation order,ensuring that the displacement field on both sides of the connecting elements is coordinated and the corresponding stiffness matrix is consistent.This method is practical and straightforward,and has relatively high accuracy.The effectiveness of the proposed method is verified by performing cross-scale comparative calculations on large-scale crack damage in particle-reinforced composites with different inclusion volume fractions and numbers.