Multiscale analysis of composite material reinforced by randomly-dispersed particles

A multiscale analysis method is presented in which detailed information on the microscopic level is incorporated into macroscopic models capable of simulating damage evolution and ultimate failure. The composite considered is reinforced by randomly-dispersed particles, which reflects the statistical characteristics of real materials, such as cement-based materials. Specifically, a three-dimensional material body is decomposed into many unit cells. Each unit cell is reinforced by a cylindrical particle, the orientation of which is characterized by three Euler angles generated by the random number generator. Based on a detailed finite element analysis, the material properties of the representative volume element are obtained. As verification, the properties of the cylindrical particles are set equal to those of the matrix and the computed ‘composite’ properties reduce exactly to those of the ‘isotropic’ material, as expected. Through coordinate transformation, the effective material properties of each unit cell are calculated. The assembly of stiffness matrices of all unit cells leads to the stiffness matrix of the whole specimen. Under the simple tension loading condition, the initial damaged unit cell can be identified according to the von Mises yield criterion. The stiffness of the damaged unit cell will then be reduced to zero and it will cause stress redistribution and trigger further damage. It was found that the reinforcement is effective to mitigate and arrest the damage propagation, and therefore prolongs the material's lifetime. These results suggest that the hierarchical coupling approaches used here may be useful for material design and failure protection in composites.