The stress rate of hyperelasticity based on the updated Lagrangian formulation

Abstract

A rate-type constitutive equation of compressible isotropic hyperelasticity and a finite element formulation based on the Updated Lagrangian approach are proposed. The constitutive equations of compressible hyperelasticity are simplified by introducing modified tensors in an intermediate configuration, which separates the volumetric deformation from the distortional deformation. Selective integration and a mixed pressure/displacement formulation have been adopted to avoid volumetric locking and the hourglass modes. The deformation of a simple rectangle block was simulated to show the effect of the choice of the finite elements and the integration methods on the stability and the accuracy of proposed method. Moreover, loading tests were carried out on a prototype specimen of a vibration control device made from circumferential rubber parts and reinforcing steel layers in order to evaluate applicability of the proposed formulation to such devices.