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


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.


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

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