Parametrized multifield variational principles in elasticity: II. Hybrid functionals and the Free Formulation

Abstract

A one-parameter family of d-generalized hybrid/mixed variational principles for linear elasticity is constructed following a domain subdivision. The family includes the d-generalized Hellinger-Reissner and potential energy principles as special cases. The parametrized principle is discretized by independently varied internal displacements, stresses and boundary displacements. The resulting finite element equations are studied following a physically motivated decomposition of the stress and internal displacement fields. The free formulation of Bergan and Nygård is shown to be a special case of this element type, and is obtained by assuming a constant internal stress field. The parameter appears as a scale factor of the higher-order stiffness.