Concentration versus oscillation effects in brittle damage
Prof. Jean-François Babadjian, Université Paris Sud
Aula Beltrami, Dipartimento di Matematica – Martedì 2 Luglio 2019 h.15:00
Abstract. This talk is concerned with an asymptotic analysis of a variational model of brittle damage, when the damaged zone concentrates into a set of zero Lebesgue measure, and, at the same, the stiffness of the damaged material becomes arbitrarily small. In the most interesting regime, the quadratic growth elastic energy degenerates into a linear growth energy as typically encountered in plasticity theory. The analysis requires a carefull study of the interplay between oscillations (due to homogenization effects) and concentration (due to the degeneracy of the energy growth) of minimizing sequences. This is a joint work with F. Iurlano and F. Rindler.