Configurational variations for the primal and dual problem in elasticity

This contribution is concerned with variational methods and configurational variations for the primal and the dual problem in elasticity. The derivations of variational balance laws are based on energy minimization principles for the primal and the dual problem. Variations of the energy of the primal problem with respect to configurational changes lead to the primal material residual. We introduce an energy functional of the dual problem and we investigate configurational variations for this energy, which yield a novel material residual of the dual problem. Furthermore, we propose variational sensitivity relations for the primal and the dual solution due to configurational variations. The explicit formulations of the residuals and the sensitivity relations are derived for a hyperelastic material. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim