Calculus of Variations and Geometric Measure Theory

P. Cermelli - G. Leoni

Interfacial energies for incoherent inclusions

created on 18 Jun 2001
modified on 22 Dec 2001


Published Paper

Inserted: 18 jun 2001
Last Updated: 22 dec 2001

Journal: Archive Rational Mech. and Anal.
Volume: 159
Pages: 335-361
Year: 2001



We study a variational problem describing an incoherent interface between a rigid inclusion and a linearly elastic matrix. The elastic material is allowed to slip relative to the inclusion along the interface, and the resulting mismatch is penalized by aninterfacial energy term that depends on the surface gradient of the relative displacement. The competition between the elastic and interfacial energies induces a threshold effect when the interfacial energy density is non-smooth: small inclusions are coherent (no mismatch); sufficiently large inclusions are incoherent. We also show that the relaxation of the energy functional can be written as the sum of the bulk elastic energy functional and the tangential quasiconvex envelope of the interfacial energy functional.

Keywords: existence of minimizers, interfacial energy, incoherent interfaces