On the FE·Meshless computational homogenization for the analysis of two-dimensional heterogeneous periodic materials

Abstract

Over the last few years, substantial progresses have been made in the two-scales com- putational homogenization. This method is essentially based on the assessment of the macroscopic constitutive behavior of heterogeneous materials through the boundary value problem (BVP) of a statistically representative volume element, named as unit cell (UC). In this framework, the first-order method has now matured to a standard tool and several extensions have been addressed in the literature [1, 2]. In the present study, a first-order homogenization scheme based on a discontinuous- continuous approach is presented. At the mesoscopic level the formation and propagation of fracture is modeled employing a UC consisting of an elastic unit surrounded by elasto- plastic zero-thickness interfaces, characterized by a discontinuous displacement field. At the macroscopic level, instead, the model maintains the continuity of the displacement field. The inelastic effects are enclosed in a smeared way, introducing a strain localization band established on the basis of a spectral analysis of the UC acoustic tensor. Another key-point is the numerical solution of the UC BVP, which is obtained by means of a more cost-effectiveness mesh-free model. Both linear and periodic boundary conditions have been applied to the UC.