Green strain based FE modeling of rheological objects for handling large deformation and rotation

Abstract

Rheological object, such as clay, various food products, biological organs and tissues, has both elastic and plastic properties. Modeling of such objects has not been studied intensively comparing with elastic objects. Previous rheological models were mostly based on linear constitutive law of stress and strain, which is limited to small deformation. In this paper, finite element (FE) model of rheological objects based on linear Cauchy strain tensor was summarized at first. Nonlinear FE model formulated with Green strain tensor was then presented for simulating large deformation and deformation with rotation motion. Instead of constant and symmetrical connection matrices in the linear model, nonlinear model yields non-constant and unsymmetrical connection matrices, which vary with displacements of nodal points. Simulation results with both linear and nonlinear FE models were presented to show the differences. We found that the nonlinear model formulated with Green strain tensor demonstrates more natural simulation behaviors.