Mechanics of nonlinear visco-hyperelastic-hysteresis membranes

Abstract

This contribution aims at developing a general formulation for the large deformation analysis of membranes considering both hysteresis and viscoelastic effects. Firstly, the kinematics of the deformation of thin membranes in three-dimensional space is formulated. Afterward, the visco-hyperelastic-hysteresis formulation of membranes is derived based upon the multiplicative decomposition of the deformation gradient tensor in the hysteretic and viscoelastic branches of the model. Evolution equations of the hysteresis and viscoelastic internal variables are obtained based on dissipation inequality. The formulation admits using both Newtonian and non-Newtonian fluid models to model the viscous dashpots. For the time integration of the evolution equations, the implicit Euler-backward method is employed. Variational formulation of the problem for development of a nonlinear finite element formulation, in the Total Lagrangian framework, is presented. To investigate the capability of the developed formulation, several numerical examples are provided. The results are in excellent agreement with the data available in the literature.