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Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. (English) Zbl 0618.73012

(From the authors’ abstract.) The authors consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained (compliance tensor is semi- definite), and formulate a simple necessary and sufficient condition for the fundamental boundary value problem to be well-posed. For materials fulfilling the condition, they establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system. As an application the authors 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, they derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unkown in addition to the displacements. For a two-dimensional constrained material a further reduction to a single scalar equation is outlined.
Reviewer: G.Jaiani

MSC:

74E10 Anisotropy in solid mechanics
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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