Branching during axial compression histories of solid cylinders of time-dependent materials

Abstract

This work considers the uniaxial compression of a solid circular cylinder of time-dependent material. Initially, the cylinder undergoes a homogeneous compression history. The purpose is to determine a time when this deformation history can form a new inhomogenous branch. Material time dependence is described by a nonlinear single-integral constitutive equation that relates the stress in the material to its deformation history. A criterion is developed for determining branching times using a Pipkin–Rogers constitutive equation for nonlinear incompressible isotropic viscoelastic solids. For the purpose of numerical examples, material parameters are chosen so that the material acts as a neo-Hookean material in its short-time response and a softer one in its long-time equilibrium response. Examples show that characteristic relaxation times and deformation histories influence the time to branch and the corresponding compressive stretch and compressive force.

Keywords

Deformation history branching branching criterion nonlinear viscoelasticity integral constitutive equations

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