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incompressible elasticity

What is incompressible solid?

Dear 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.

Arash_Yavari's picture

A Geometric Structure-Preserving Discretization Scheme for Incompressible Linearized Elasticity

In 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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