Generalization of a Nonlinear Maxwell-Type Viscoelastoplastic Model and Simulation of Creep and Recovery Curves

A generalization of the physically nonlinear Maxwell-type constitutive equation with two material functions for non-aging rheonomic materials, whose general properties and area of application have been studied analytically in previous articles, was suggested. To extend the set of basic rheological phenomena simulated, a third strain component expressed as the Boltzmann–Volterra linear integral operator governed by an arbitrary creep function was added. For generality and convenience of managing the constitutive equation and its fitting to various materials and lists of effects simulated, a weight factor (degree of nonlinearity) was introduced into the constitutive relation, which enabled to combine the primary physically nonlinear Maxwell-type model with the linear viscoelasticity equation in arbitrary proportion to construct a hybrid model and to regulate the prominence of different phenomena described by the two constitutive equations. A general expression for creep and recovery curves produced by the constitutive equation proposed was derived and analyzed. The general properties of creep and recovery curves were studied assuming three material functions are arbitrary. New properties were established, which enabled the generalized model to adjust the form of creep and recovery curves and to simulate additional effects (in comparison with the primary Maxwell-type model) observed in creep and recovery tests of various materials at different stress levels.