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A multiscale overlapped coupling formulation for large-deformation strain localization

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An Erratum to this article was published on 17 June 2014

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.

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Acknowledgments

We thank James W. Foulk III for providing us with the analytical solution of the singular bar problem. Thanks are also due to Micheal L. Parks for suggesting the one-dimensional patch test. Support for this work was received through the U.S. Department of Energy’s Advanced Simulation and Computing (ASC) Program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Authors and Affiliations

  1. Department of Civil Engineering and Engineering Mechanics, Columbia University in the City of New York, New York, NY , 10027, USA

    WaiChing Sun

  2. Mechanics of Materials Department, Sandia National Laboratories, Livermore, CA , 94550, USA

    Alejandro Mota

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  1. WaiChing Sun
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  2. Alejandro Mota
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Correspondence to WaiChing Sun.

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Sun, W., Mota, A. A multiscale overlapped coupling formulation for large-deformation strain localization. Comput Mech 54, 803–820 (2014). https://doi.org/10.1007/s00466-014-1034-0

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  • DOI: https://doi.org/10.1007/s00466-014-1034-0

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