Finite Element Analysis of Hyperelastoplastic Mixed-Hardening Materials Under Plane Stresses

A finite element formulation for the analysis of elastoplastic materials under finite strain levels, plane stress conditions, and mixed hardening is developed. The 3D hyperelastoplastic framework is condensed into a compact 2D form following the plane stress condition. The constitutive modeling accounts for the finite elastoplastic strains, associative plasticity, and mixed hardening. A kinematical approximation is based on the positional description and the isoparametric triangular membrane element of any order. Some examples are used to test the numerical formulation proposed. Several meshes are employed for each problem, varying the number of elements and approximation degree, which increases up to the fourth order. The results show that mesh refinement improves accuracy, avoiding locking problems and hourglass instabilities in plane stress problems involving large elastoplastic deformation, stress concentration, bending, mesh distortion, and post-buckling behavior. In addition to the convergence analysis regarding displacements and forces, some final values of the isotropic hardening parameter, the equivalent stress, and the backstress components are provided in order to assess the performance of all the element orders more completely. A comparison of the present results with finite element solutions from the scientific literature available is done, highlighting the similarities and differences for each problem.