Calculation of strain amplification matrix for strain invariant failure theory based on representative volume element models with periodical boundary condition

Abstract

Strain invariant failure theory (SIFT) is a micro-mechanics-based failure theory for multi-scale failure analysis of composite materials originally proposed by Gosse and Christensen. In this paper, the approach for obtaining strain amplification matrix which is a key step for the execution of SIFT is improved by adopting representative volume element (RVE) finite element models considering periodical boundary condition, based on which more actual deformation mode is reflected. The deformation modes and strain data at the characteristic points of the centroid cell of multi-cell RVE model are analyzed and taken as a reference. It can be concluded that more reasonable deformation mode and relationship between the micro-mechanical and macro-mechanical strain states are obtained by employing the new model. Finally, numerical examples are provided to illustrate the determination of strain amplification factors within the RVEs considering periodical boundary condition at the characteristic points.