Micromechanical modeling of composite materials using the finite element method for balancing discretization and material modeling error

Abstract

The goal of this research is to advance computer modeling capabilities to combine with or replace experimental testing of composite materials. To be able to achieve this goal, modeling techniques are implemented, with the aim of combining computational efficiency and accuracy. To do this the sources of error need to be mitigated when performing meso-scale numerical tests on micromechanical composite materials. The sources of error are discretization when meshing in finite elements, and material modeling error. As the refinement of a finite element mesh increases, the error decreases and the computational cost increases. In some cases it has been shown that increasing the size of a material being homogenized increases the accuracy of the prediction of the material properties, as the size of the material approaches a representative volume. Various homogenization methods have different degrees of accuracy and computational efficiency. Homogenization often requires definition of a representative volume element (RVE). This definition creates a model of a finite magnitude that represents an equivalent homogenous material. The technique is used in the investigation of several simple structures in this work. A statistical volume element (SVE) at the meso-scale defines an element on a smaller scale than the RVE but is still larger than the micro-scale. The SVE is used to statistically analyze the stiffness properties of a model on the meso-scale, where the meso-scale is defined as any scale between the micro and macro-scales. Moving window (MW) homogenization is an improved alternative to homogenizing the entire structure. Moving window homogenization is shown to increase accuracy, when to compared to benchmark results.