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.
In general, the viscoelastic constitutive equation will be employed for structural analyses such as a FEM. Thus the applicability and the capability of the constitutive equation to predict deformations in a multiaxial state of stress are important. In the present paper, inelastic deformations of polyethylene in a two-axial state of stress by the combination of a normal stress and a shear stress are simulated by using the viscoelastic constitutive equation. As a loading condition, proportional and non-proportional strain paths under the total strain control at constant strain rate are considered. Inelastic deformations under cyclic loadings are focused on in particular. Results of the simulations are compared with experimental results of polyethylene and the validity of the constitutive equation is verified in the multiaxial state. And features of the inelastic deformations of polyethylene are inspected by simulations under various loading conditions.