| Abstract: |
| Rigidity results in elasticity are powerful statements that allow to derive global properties of a deformation from local ones. The classical Liouville theorem states that every local isometry of a domain corresponds to a rigid body motion. If connectedness of the set fails, clearly, global rigidity can no longer be true.
In this talk, I will present a new type of asymptotic rigidity lemma, which shows that if an elastic body contains sufficiently stiff connected components arranged into fine parallel layers, then macroscopic rigidity up to horizontal shearing prevails in the limit of vanishing layer thickness. The optimal scaling between layer thickness and stiffness can be identified using suitable bending constructions. This result constitutes a useful tool for proving homogenization results of variational problems modeling high-contrast bilayered composites. We will finally utilize it to characterize the homogenized Gamma-limits of two models inspired by nonlinear elasticity and finite crystal plasticity. |
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