NUMERICAL IMPLEMENTATION OF THE TSCHOEGL–CHANG–BLOCH NONLINEAR VISCOELASTIC CONSTITUTIVE LAW FOR UNVULCANIZED CARBON BLACK–FILLED RUBBERS

Abstract

Rubber engineering design analysis requires a fundamental understanding of the mechanical behavior of polymers, especially in their unvulcanized state. It necessitates the establishment of a three-dimensional constitutive material to account for the observed mechanical behavior. This law is required to produce realistic descriptions of the viscoelastic performance in a mathematically simple form that is easy to implement in engineering applications. This article describes the theory of the Tschoegl–Chang–Bloch time-dependent nonlinear viscoelastic constitutive law. The experimental verification of this law is provided under different deformation fields and multiple load steps. Laboratory test procedures to obtain the parameters required to describe the material under consideration are provided in detail. A recursive form of the constitutive law, suitable for finite element application, is derived and coded in the finite element commercial code Abaqus via the user subroutine UMAT. Comparisons between the experimental observations, the theoretical results, and the numerical data are drawn for simple test models examined under creep or shear relaxation conditions. The excellent agreements observed indicate the suitability of the governing law in analyzing viscoelastic problems of unvulcanized carbon black–filled rubbers.