A systematic development of EAS three-dimensional finite elements for the alleviation of locking phenomena

The treatment of locking phenomena in finite element analysis has been extensively studied over the last decades. Among other techniques, the use of Enhanced Assumed Strain (EAS) methods can lead to formulations that yield good results, although sometimes computationally expensive. This is mainly due to the use of enhancing parameters, element-wise defined and related to the element topology (2D, plate, shell or solid), integration scheme and even the problem itself to be solved (incompressible materials, thin-walled structures, etc.). The subspace analysis framework is based on a mathematical technique, where the constraints to be respected by the formulations are applied at each Gauss point of the finite element mesh. Although this methodology can be found in the literature for some locking pathology, it was never applied before to the analysis of transverse shear locking in 3D finite elements. Therefore, in the current work the authors expand the existing subspace methodology to take into account the occurrence of this type locking in solid elements. This analysis is developed for different integration schemes in order to assess their performances. Previous EAS formulations are analyzed and an alternative formulation for the EAS parameters is proposed and applied to a set of benchmark linear and nonlinear problems for solid and solid–shell elements, in order to evaluate the occurrence of locking phenomena and infer about their potential applications.