Effect of boundary conditions on values of homogenized fabrics’s elastic parameters and inelastic response

Abstract

The effect of displacement, periodic and surface traction boundary conditions (BCs) on predicted elastic parameters and inelastic response of a homogenized material equivalent to either a unidirectional or a randomly distributed short fibers reinforced composite has not been extensively studied. A few such studies have focused on their elastic analyses. Here, we analyze the effect of the three types of BCs on both elastic and inelastic deformations of weaves and braids with continuum damage mechanics used in the inelastic analyses. We employ simple unit cells, Hill’s theorem, and the displacement, periodic and uniform traction BCs to deduce from the finite element stiffness matrix K the matrix C of homogenized moduli. For both elastic and inelastic problems, it is seen that predictions using the displacement and the periodic BCs are close to those reported in the literature while those from the traction BCs are not. For unidirectional loading, it is found that the nonlinearity in the axial stress - axial strain curve, the localized deformations and the resin damage occurring in regions unsupported by fibers are significantly more for the traction BCs than that for the other two BCs. Also, there is more damage for the periodic BCs than that for the affine displacement BCs.