Simulation of Inelastic Deformation of Polyethylene in Multiaxial State of Stress by Viscoelastic Constitutive Equtaion

Abstract

Polymers show significant strain recovery after reversal of the loading direction, and conventional constitutive equations can not describe inelastic deformations including the strain recovery properly. Then the present authors have proposed a viscoelastic constitutive equation for polyethylene in order to describe the inelastic deformations. In the formulation, a total strain was assumed to be the sum of an elastic strain and a viscous strain. The elastic strain was subjected to the Hooke’s law, and the viscous strain was derived from the kinematic hardening creep theory of Malinin and Khadjinsky, which was combined with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, a loading surface was defined in a viscoelastic strain space, and a new parameter was defined by using the loading surface. Then the nonlinear kinematic hardening rule was modified by using the parameter. Inelastic deformations in a uniaxial state of stress were simulated by using the constitutive equation and the validity of the formulation and the modification was verified by comparing the simulations with experimental results of polyethylene. Then inelastic deformations under typical cyclic loadings in the uniaxial state of stress were predicted, and features of the deformations were discussed.