Abstract: In this paper we solve a simple dead load problem for an isotropic constrained material according to the linearized finite theory of elasticity. We show that the solution of such a problem can be obtained by linearizing with respect to the displacement gradient the solution of the corresponding problem in finite elasticity for an isotropic material subject to the same constraint, exac...

Quasicrystals can carry, in addition to the classical phonon displacement field, a phason displacement field, which requires a generalized theory of elasticity. In this paper, the third-order strain invariants (including phason strain) of icosahedral quasicrystals are determined. They are connected with 20 independent third-order elastic constants. By means of non-linear elasticity, phason stra...

The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numeri...