A morphing strategy to couple non-local to local continuum mechanics

Abstract
A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. © 2012 Elsevier Ltd.

Citation
Lubineau, G., Azdoud, Y., Han, F., Rey, C., & Askari, A. (2012). A morphing strategy to couple non-local to local continuum mechanics. Journal of the Mechanics and Physics of Solids, 60(6), 1088–1102. doi:10.1016/j.jmps.2012.02.009

Acknowledgements
Funding for this research was provided by KAUST baseline funding and by the BOEING company (agreement "Analysis methods for multifunctional composite materials in the presence of electromagnetic effect"). The authors are grateful to KAUST and the BOEING company for their financial support.

Publisher
Elsevier BV

Journal
Journal of the Mechanics and Physics of Solids

DOI
10.1016/j.jmps.2012.02.009

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