Quantitative rigidity results, besides their inherent geometric interest, have played a prominent role in the mathematical study of variational models related to elasticity\plasticity. For instance, the celebrated rigidity estimate of Friesecke, James, and Müller has been widely used in problems related to linearization, discrete-to-continuum or dimension-reduction within the framework of nonlinear elasticity.
In this talk I will discuss an appropriate generalization to the setting of variable domains, where the geometry of the domain comes into play, in terms of a suitable surface energy of its boundary. As an application, we rigorously derive a Blake-Zisserman-Kirchoff theory for thin elastic rods with material voids, in a situation allowing for fracture.
This is joint work with Manuel Friedrich and Leonard Kreutz.'
Romain Duboscq, David Lafontaine