Computational Mechanics

, Volume 54, Issue 3, pp 803–820

A multiscale overlapped coupling formulation for large-deformation strain localization

Original Paper

DOI: 10.1007/s00466-014-1034-0

Cite this article as:
Sun, W. & Mota, A. Comput Mech (2014) 54: 803. doi:10.1007/s00466-014-1034-0

Abstract

We generalize the multiscale overlapped domain framework to couple multiple rate-independent standard dissipative material models in the finite deformation regime across different length scales. We show that a fully coupled multiscale incremental boundary-value problem can be recast as the stationary point that optimizes the partitioned incremental work of a three-field energy functional. We also establish inf-sup tests to examine the numerical stability issues that arise from enforcing weak compatibility in the three-field formulation. We also devise a new block solver for the domain coupling problem and demonstrate the performance of the formulation with one-dimensional numerical examples. These simulations indicate that it is sufficient to introduce a localization limiter in a confined region of interest to regularize the partial differential equation if loss of ellipticity occurs.

Keywords

Domain coupling Variational principle Energy based coupling method Multiscale modeling 

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Civil Engineering and Engineering MechanicsColumbia University in the City of New YorkNew YorkUSA
  2. 2.Mechanics of Materials DepartmentSandia National LaboratoriesLivermoreUSA

Personalised recommendations