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# incompressible elasticity

## What is incompressible solid?

Sat, 2013-08-31 09:07 - BreslavskyDear Colleagues,

In the literature two definitions of incompressible solid can be found. The first one is: Poisson's ratio =0.5, and the second is: the third invariant of the Cauchy-Green deformation tensor J=1. I wish to understand the connections between these two definitions. To me, here is something strange. Poisson's ratio relates strains to stresses,and J as the combination of strain tensor components, doesn't depend on Poisson's ratio. I'll be grateful to you, if you explain me how these two definitions are connected.

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## A Geometric Structure-Preserving Discretization Scheme for Incompressible Linearized Elasticity

Wed, 2013-03-06 01:38 - Arash_YavariIn this paper, we present a geometric discretization scheme for incompressible linearized elasticity. We use ideas from discrete exterior calculus (DEC) to write the action for a discretized elastic body modeled by a simplicial complex. After characterizing the configuration manifold of volume-preserving discrete deformations, we use Hamilton's principle on this configuration manifold. The discrete Euler-Lagrange equations are obtained without using Lagrange multipliers.

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