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