Rotational elasticity and couplings to linear elasticity

En224: Linear Elasticity

The Elasticity of Elasticity

In this talk I assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrate my thesis by introducing implicit constitutive theories that can describe the nondissipative response of solids. I show that response which was hitherto untenable within the context of Cauchy or Green Elasticity are not only possible, they can explain phenomena that have thus...

Linear Elasticity and (Generalized) Stokes — Parallel Implementation

A Lagrangian meshfree method applied to linear and nonlinear elasticity

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully sim...

An Algebraic Multigrid Method for Linear Elasticity

We present an algebraic multigrid (AMG) method for the efficient solution of linear (block-)systems stemming from a discretization of a system of partial differential equations (PDEs). It generalizes the classical AMG approach for scalar problems to systems of PDEs in a natural blockwise fashion. We apply this approach to linear elasticity and show that the block-interpolation, described in thi...