Title: Well-posedness of the fundamental boundary value problems
for constrained anisotropic elastic materials
Authors: Douglas N. Arnold and Richard S. Falk
Source: Archive for Rational Mechanics and Analysis 98 (1987),
pp. 143-165
Status: Published
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.
Keywords: elasticity, anisotropic, constraint, well-posed
URL: http://www.math.rutgers.edu/~falk/papers/constrained-info.txt