High-order triangular finite elements applied to visco-hyperelastic materials under plane stress

A finite element formulation for analysis of highly deformable viscoelastic materials under plane stresses is presented. The element is the isoparametric plane triangle of any-order. The constitutive modeling is based on a Lagrangian visco-hyperelastic framework, in which the multiplicative split of the deformation gradient is used. The internal variable employed is the viscous right Cauchy–Green stretch tensor. The work is restricted to the compressible neo-Hookean hyperelastic law, the Zener rheological model and an isochoric nonlinear evolution equation, although other models can be further implemented. The plane stress condensation and the compact 2D constitutive relation are described. Three large deformation problems are numerically analyzed to validate the methodology: a membrane with high compressive strain levels and mesh distortion; a perforated plate with stress concentration; and a circular ring under nonlinear bending. Meshes with different element orders (from linear to sixth) are employed. Results confirm that, except for the linear degree, mesh refinement completely remove locking problems, providing an accurate and, thus, a reliable prediction of the mechanical behavior. It is also demonstrated that the creep phenomenon can be reproduced in finite strain regime. The novelty of the paper is the convergence analysis regarding displacements, strains and stresses in the context of plane stress visco-hyperelasticity.