Material models in principal stretches for elastodynamics

Abstract

AbstractIn the present work we deal with the conserving integration of elastic bodies undergoing finite deformations. In particular, we make use of constitutive laws formulated in terms of principal stretches.Most material models for hyperelastic isotropic materials are described in terms of principal stretches (Simo and Taylor [1]), like the Neo–Hooke material which is a special case of the Ogden material, or in invariants. The main advantage of principal stretches is the fact that they can be measured directly, which means that the numerical results can be compared easily with experimental ones, see for example, Ogden [2]. Moreover, it is advantageous to describe viscoelastic material behaviour (e.g. rubberlike materials) in terms of principal stretches.Concerning the discretization in space we apply the enhanced assumed strain (EAS) method, see Simo and Armero [3]. For the discretization in time we aim at numerical integrators which inherit fundamental conservation laws from the underlying continuous system. In particular, we propose an energy and momentum conserving time–stepping scheme which relies on the notion of a discrete gradient (or derivative) in the sense of Gonzalez [4]. The proposed approach starts from our previous developments in [5]. Numerical examples demonstrate the advantageous properties of the present formulation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)