Constitutive Equations and Finite Element Implementation of Isochronous Nonlinear Viscoelastic Behavior

Abstract

We present a phenomenological three-dimensional (3D) nonlinear viscoelastic constitutive model for time-dependent analysis. Based on Schapery's single integral constitutive law, a solution procedure has been provided to solve nonlinear viscoelastic behavior. This procedure is applicable to 3D problems and uses time- and stress-dependent material properties to characterize the nonlinear behavior of material. The equations describing material behavior are chosen based on the measured material properties in a short test time frame. This estimation process uses the Prony series material parameters, and the constitutive relations are based on the nonseparable form of equations. Material properties are then modified to include the long-term response of material. The presented model is suitable for the development of a unified computer code that can handle both linear and nonlinear viscoelastic material behavior. The proposed viscoelastic model is implemented in a user-defined material algorithm in abaqus (UMAT), and the model validity is assessed by comparison with experimental observations on polyethylene for three uniaxial loading cases, namely short-term loading, long-term loading, and step loading. A part of the experimental results have been conducted by (Liu, 2007, “Material Modelling for Structural Analysis of Polyethylene,” M.Sc. thesis, University of Waterloo, Waterloo, ON Canada), while the rest are provided by an industrial partner. The research shows that the proposed finite element model can reproduce the experimental strain–time curves accurately and concludes that with proper material properties to reflect the deformation involved in the mechanical tests, the deformation behavior observed experimentally can be accurately predicted using the finite element simulation.