Speaker
Description
We discuss the derivation of a linear elastic model starting from a nonlinear energy functional with infinitely many wells. Since the ground states of the elastic energy are unbounded, even a sequence of deformations with very small energy may still display very large deformation gradients and converge to a deformation with jumps. This may be interpreted as formation of plastic slips. We avoid such phenomenon by including a sufficiently large perturbation in terms of the second gradient, which penalises transitions from one well to another. In our analysis we employ a suitable weak convergence for deformation gradients excluding small subsets of the reference configuration, hence we may prove compactness by applying a rigidity estimate for incompatible fields.