Voronoi Cell Finite Element Method For Particle Reinforced Composites With Interfacial Phase

Particle reinforced composites are generally composed of matrix and inclusions,which are particles or fibers and randomly distributed in the matrix.As the bond between matrix and inclusion,interface has very important mechanical properties.In the manufacturing process of materials,the chemical reaction between the matrix and the inclusion,the bond state between the two phases,the fracture due to excessive load,or the artificial coating on the surface of the inclusion to protect the inclusion from external corrosion and other factors will lead to the imperfect interface.In order to study the influence of interface on the microstructure and macro mechanical properties of composite materials,the concept of boundary phase is introduced into Voronoi finite element model,and a new Voronoi element format is constructed.The main research contents are as follows:Firstly,based on the linear elastic theory,the finite element model of Voronoi element with interface phase is established,and the complementary energy functional formula of the element is derived.The reasonable stress field is constructed in the element domain,and the displacement field is constructed on the boundary.The stress field and displacement field are independent of each other in the element,and the stress field in the matrix,interface phase and inclusion domain is also independent of each other.According to the variational principle,H matrix and G matrix are obtained by first-order variational method for stress and node displacement,respectively.The element stiffness matrix is composed of these two matrices.The effectiveness of Voronoi finite element method is verified by analytical method and traditional finite element method.Then,the region refinement method and the given boundary method are given to calculate the average stress and strain in the representative volume element,so as to obtain the macroscopic elastic constant of the material.The influence of the ratio of inclusions,the thickness of interface phase and Young's modulus on the macro elastic properties of the material is analyzed.The results show that when the elastic modulus of interface phase is less than that of matrix and inclusion,the macroscopic Young's modulus of the material decreases with the increase of the thickness of interface phase and the ratio of inclusion.When the interface is too thin,the macroscopic Young's modulus of the material increases with the increase of the ratio of inclusion.When the young's modulus of interfacial phase is greater than that of matrix or inclusion,the macroscopic Young's modulus of the material increases with the increase of the ratio of inclusion and the thickness of interfacial phase.The thickness of interfacial phase and Young's modulus have little influence on the macro Poisson's ratio,and the macro Poisson's ratio is mainly affected by the fraction of inclusions,which is inversely proportional to it.In this paper,the Voronoi element finite element method is used to study the meso and macro mechanical behaviors of composite materials considering the influence of interface,and the influencing factors of macro elastic properties are analyzed.It plays an active role in the research of composite interface.