A modified version of the enhanced assumed strain method is proposed and as its application, four-node plane element and eight-node solid element are developed. The modified version of the enhanced assumed strain method consists of a new hybrid/mixed functional and a refined enhanced strain interpolation derived from a new stress interpolation via an equivalence between the enhanced assumed strain method and the assumed stress hybrid method.
As mathematical bases of a combined approach of the enhanced assumed strain method and the assumed stress hybrid method, an equivalence between the enhanced assumed strain method and the assumed stress hybrid method is investigated. It is proven that not only the displacements but also the stresses of enhanced assumed strain elements calculated from the strains are identical to those of the corresponding assumed stress hybrid elements at least at the Gauss integration points, provided that the spaces of the trial functions for enhanced strains and for stresses satisfy the orthogonality and the inclusion or the invertibility condition. By virtue of this equivalence, a efficient stress recovery procedure of enhanced assumed strain elements and a rational approach to select optimal stress terms for stress interpolation are devised.
To overcome the variationally consistent stress recovery problem of the previous version, a three-field hybrid/mixed functional, which assumes displacements, strains, and stresses, is proposed. This functional is a special case of Felippa‘s parameterized functional and also Lees combined mixed functional. By introducing enhanced strain concept to the proposed functional, a extended finite element formulation for the enhanced assumed strain method, which can evaluate stresses explicitly, is derived.
Also, a refined stress interpolation is developed by using stress interpolation techniques of the assumed stress hybrid method. Modified incompatible modes are introduced and incorporated into the constraint equations for assumed stresses. The physical meaning of the results is discussed. The present stress interpolation, which can consider the mesh distortion more rigorously, is based on the physical interpretation of the role of modified incompatible modes and substantiated with simple mesh distortion measures defined in this paper. Also, a new enhanced strain interpolation is derived from proposed stress interpolation via the equivalence.
Based on the modified formulation, the proposed interpolation is adapted to the previous four-node plane the enhanced assumed strain element, EAS7 and the eight-node solid element, EAS30, which results in a new refined four-node plane element, MEAS7 and an eight-node solid element, MEAS30, respectively. Numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion, no volumetric locking, and high-accuracy of stresses.