Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials

Douglas N. Arnold, Richard S. Falk

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

We consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained, and formulate a simple necessary and sufficient condition for the fundamental boundary value problems to be well-posed. For materials fulfilling the condition, we establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system. As an application we determine the orthotropic materials for which the fundamental problems are well-posed in terms of their Young's moduli, shear moduli, and Poisson ratios. Finally, we derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unknown in addition to the displacements. For a two-dimensional constrained material a further reduction to a single scalar equation is outlined.

Original languageEnglish (US)
Pages (from-to)143-165
Number of pages23
JournalArchive For Rational Mechanics And Analysis
Volume98
Issue number2
DOIs
StatePublished - Jun 1987

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