We obtain an integral representation for the relaxation, in the space of functions of bounded deformation, of the energy

$\begin{displaymath}\int_{\Omega}f({\mathcal E}u(x))dx \end{displaymath}$

with respect to L¹-convergence. Here ${\mathcal E}u$ represents the absolutely continuous part of the symmetrized distributional derivative Eu and the function f satisfies linear growth and coercivity conditions.

Keywords : functions of bounded deformation, relaxation, E-quasiconvexity

1991 Mathematics Subject Classification: 35J50, 49J45, 49Q20, 73E99. 2000 Mathematics Subject Classification: 35J50, 49J45, 49Q20, 74C15, 74G65.

Abstract: