Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials
(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.
equations of linear homogeneous anisotropic elasticity
scientific article; zbMATH DE number 4003597
scientific article