Large deformation analysis of two-dimensional visco-hyperelastic beams and frames

Abstract

This contribution aims at developing a formulation for the large viscoelastic deformation of hyperelastic beams and frames under various loading and boundary conditions. To do so, the kinematics of deformation in two-dimensional space is formulated and basic kinematics and kinetic quantities are introduced. The quasi-linear viscoelasticity theory is employed to capture the time-dependent behavior of the underlying material. The corresponding time integration scheme and the consistent tangent moduli are then presented. Because of the highly nonlinear nature of governing equations at the large regime of deformations including time dependency, a nonlinear finite element formulation in the total Lagrangian framework is developed. Several numerical examples are provided to investigate the applicability of derived formulations. It is observed that the formulation can successfully capture the relaxation and creep phenomena in visco-hyperelastic beams and frames.