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We consider integral functionals ▫${\mathcal F}^{(j)}_{\varepsilon }$▫, doubly indexed by ▫$\varepsilon > 0$▫ and ▫$j \in {\mathbb N}\cup \{ \infty \}$▫, satisfying a standard linear growth condition. We investigate the question of ▫$\Gamma$▫-closure, i.e., when the ▫$\Gamma$▫-convergence of all fam ...

We derive geometrically linearized theories for incompressible materials from nonlinear elasticity theory in the small displacement regime. Our nonlinear stored energy densities may vary on the same (small) length scale as the typical displacements. This allows for applications to multiwell energies ...

We consider two related models for the propagation of a curvature sensitive interface in a time independent random medium. In both cases we suppose that the medium contains obstacles that act on the propagation of the interface with an inhibitory or an acceleratory force. We show that the interface ...

In this work, we address the occurrence of infinite pinning in a random medium. We suppose that an initially flat interface starts to move through the medium due to some constant driving force. The medium is assumed to contain random obstacles. We model their positions by a Poisson point process and ...