Abstract

We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence of the operators. In particular the homogenization procedure, valid for elliptic systems in linear elasticity, depicts the macroscopic features of a composite material in the presence of plastic deformation.

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Keywords

  • Boundary value problems for elliptic systems
  • elastic problems
  • duality solutions
  • homogenization

Mathematics Subject Classification

35D30; 35J58

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Suggested citation

A. Garroni, A. Malusa. “Duality Arguments for Linear Elasticity Problems with Incompatible Deformation Fields.” Journal of Convex Analysis 28 (2021), No. 2, 569–580. https://doi.org/10.68381/jca28032

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.