A two-scale modeling framework for strain localization in solids: XFEM procedures and computational aspects

Abstract

We present a novel two-scale finite element model for strain localization in solids, covering the complete evolution of microscale damage into macrocracks. We start off with a continuous-discontinuous homogenization strategy, whereby the bulk response is modeled using standard first order computational homogenization of Statistical Volume Elements (SVEs). At the onset of macroscale strain localization, we inject macroscale discontinuities by means of the eXtended Finite Element Method (XFEM) and employ smeared macro-to-micro discontinuity transitions. As a consequence, the macroscale constitutive response in the bulk as well as at macroscale localization interfaces is obtained from simulations on SVEs. A novelty compared to existing models is thereby that the proposed model is free from restrictive assumptions on the microscale constitutive response and from any subscale damage pattern identification. The use of XFEM on the macroscale, in combination with softening model behavior, gives rise to several previously unaddressed computational issues for which we propose remedies in the present work. In particular, we discuss numerical aspects related to predicting macroscale localization and we also propose to use a trust-region method to improve the robustness of the Newton iterations. Numerical examples in two spatial dimensions are presented, demonstrating the capabilities of the proposed scheme.