ON LARGE STRAIN VISCOELASTICITY: CONTINUUM FORMULATION AND FINITE ELEMENT APPLICATIONS TO ELASTOMERIC STRUCTURES

Abstract

This article deals with the continuum formulation of finite strain viscoelasticity and provides its numerical simulation with the finite element method. In particular, elastomeric solids which are of essential engineering interest are discussed. In order to simulate the significant different bulk/shear-response of polymeric media the deformation is decomposed into volumetric elastic and isochoric viscoelastic parts. The constitutive equations are presented within the context of internal variable models and a Lagrangian kinematical description is adopted throughout. For sufficiently slow processes the material responds in a rubbery elastic manner which is assumed to be modelled with an Ogden-type strain energy function well-known from rubber elasticity. The stresses and the symmetric consistent tangent moduli are briefly discussed along with a second-order approximation of the constitutive rate equation. The main thrust of this paper on the computational side is to show the meaningful time-dependent behaviour and the general applicability of the three-dimensional constitutive model. By applying assumed enhanced strain elements which are well-suited for (nearly) incompressible problems three representative numerical examples illustrate relaxation and creeping phenomena at large strains and the equilibrium finite elastic response, which is asymptotically obtained.