Multi-scale modeling of the elastic response of a structural component made from a composite material using the materials knowledge system

In this paper, we present the first implementation of the novel localization relationships, formulated in the recently developed mathematical framework called materials knowledge systems (MKS), into a finite element tool to enable hierarchical multiscale materials modeling. More specifically, the MKS framework was successfully integrated with the commercial finite element (FE) package ABAQUS through a user material subroutine. In this new MKS-FE approach, information is consistently exchanged between the microscale and macroscale levels in a fully coupled manner. The viability and computational advantages of the MKS-FE approach are demonstrated through a simple case study involving the elastic deformation of a component made from a composite material. It will be shown that the MKS-FE approach can be used to accurately capture the microscale spatial distributions of the stress or strain fields at each material point in the macroscale FE model with substantial savings in the computational cost.