Homogenization of 3D laminated micro-structures including bending effects

Abstract

In this paper, a homogenization method which captures intrinsic size effect associated with fiber diameter is revisited and adapted for three-dimensional laminated micro -structures. Based on a unit-cell composed of matrix and reinforcement layers, enhanced deformation gradients varying through the thickness, are introduced with the aid of an additional kinematic variable reflecting the difference between the homogenized and constituent level deformation gradients. In the current work, as opposed to the original formulation, higher order terms are preserved for both phases and therefore bending stiffness of the matrix phase can be taken into account as well. The formulation is implemented within the commercial finite element solver Abaqus through user element (UEL) subroutine considering a finite strain hyperelastic response for the reinforcement layers and a von Mises type hyper-elastoplastic one for the matrix phase. Explicitly discretized unit-cells with varying reinforcement phase fraction, layer inclination angle and layer thicknesses are used as references to assess the predictive capabilities of the homogenized model and the significance of bending stiffness of the phases. Similarly, explicitly discretized model of a beam type structure with a crossed lamellar micro -structure is used to evaluate the performance of the homogenized model under more general, non-periodic boundary conditions. The findings of both cases support the effectiveness of the homogenized model.