Equivalence between enhanced assumed strain method and assumed stress hybrid method based on the Hellinger-Reissner principle

Abstract

An equivalence between the enhanced assumed strain (EAS) method based on the Hu-Washizu principle, recently proposed by Simo and Rifai, and assumed stress hybrid (hybrid) method based on the Hellinger-Reissner principle is investigated. It is proved that not only the displacements but also the stresses of the EAS-elements calculated from the strains are identical to those of the corresponding hybrid-elements at least at the Gauss integration points provided the spaces of the trial functions for enhanced assumed strains and for assumed stresses satisfy the orthogonality and the inclusion or the invertibility condition. By virtue of this equivalence, a stress recovery procedure of the EAS-elements is devised. This procedure is variationally consistent and more efficient than those proposed by Simo and Rifai and Andelfinger and Ramm. Since the classical method of incompatible displacement modes is a special case of the EAS-method, this procedure also can be used to evaluate variationally consistent stresses for the non-conforming elements.