A two-scale modeling framework for strain localization in solids: XFEM procedures and computational aspects
Journal article, 2019

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.

Weakly periodic boundary conditions

Trust-region

Cohesive zone

XFEM

Computational homogenization

Localization

Author

Erik Svenning

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Martin Fagerström

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Computers and Structures

0045-7949 (ISSN)

Vol. 211 43-54

Subject Categories

Applied Mechanics

Computational Mathematics

Probability Theory and Statistics

DOI

10.1016/j.compstruc.2018.08.003

More information

Latest update

12/3/2018