Chapter 3 - Nonlinear Constitutive Models with Small Strains

Abstract

This chapter discusses nonlinear constitutive models in viscoelasticity at small strains, differential constitutive, and integral relations. Based on the concept of adaptive links, a new constitutive model for crosslinked polymeric materials and non-crosslinked polymers is discussed. Creep curves for two types of polypropylene and their approximation by the model are described. The model is based on the adaptive links existing at the initial instant and are divided into two types. Links of type I break under loading, whereas links of type II replace each other. Breakage and reformation of adaptive links are treated as kinetic processes, and kinetic equations are introduced for the numbers of links of type I and type II. Nonlinearity arises because the rates of kinetic processes depend on the stress intensity. As a possible mechanism of this phenomenon, stress-induced crystallization of polypropylene under large stresses, which leads to structural changes in material, is explained. However, available experimental data are not sufficient to confirm this hypothesis.