Mathematics

Linear elasticity can be rigorously derived from finite elasticity in the case of small loadings in terms of $\Gamma$-convergence. This was first done in 2002 by Dal Maso-Negri-Percivale in the case of one-well energies with super-quadratic growth, employing the rigidity estimate by Friesecke-James-Müller. In this talk I will discuss recent developments in the case of multi-well energies where the distance between the wells is arbitrary. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions which turn out to be optimal.  This is joint work with Roberto Alicandro (Cassino), Gianni Dal Maso (SISSA) and Mariapia Palombaro (Sussex).