Material Voids in Elastic Solids with Anisotropic Surface Energies

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
fonseca@andrew.cmu.edu

Nicola Fusco
Dipartimento di Matematica e Applicazioni ``R. Caccioppoli''
Università degli Studi di Napoli ``Federico II''
Napoli, Italy
n.fusco@unina.it

Giovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
giovanni@andrew.cmu.edu

Vincent Millot
Université Paris Diderot - Paris 7
CNRS UMR 7598 Laboratoire J.L. Lions
Paris, France
millot@math.jussieu.fr

Abstract: This work discusses the role of highly anisotropic interfacial energy for problems involving a material void in a linearly elastic solid. Using the calculus of variations it is shown that the qualitative features of the equilibrium shape of the void demonstrate a strong dependence on the smoothness and convexity of the interfacial energy. 1