Hybridization of a Linear Viscoelastic Constitutive Equation and a Nonlinear Maxwell-Type Viscoelastoplastic Model, and Analysis of Poisson’s Ratio Evolution Scenarios under Creep

Abstract

A generalization of a physically nonlinear Maxwell-type viscoelastoplastic constitutive equation with four material functions is formulated, whose general properties and range of applicability were discussed in a series of our previous studies. In order to expand the range of rheological effects and materials that can be described by the equation, it is proposed to add a third strain component expressed by a linear integral Boltzmann–Volterra operator with arbitrary functions of shear and volumetric creep. For generality and for the convenience of using the model, as well as for fitting the model to various materials and simulated effects, a weight factor (degree of nonlinearity) is introduced into the constitutive equation, which allows combining the original nonlinear equation and the linear viscoelastic operator in arbitrary proportions to control the degree of different effects modeled. Equations are derived for families of creep curves (volumetric, shear, longitudinal, and transverse) generated by the proposed constitutive equation with six arbitrary material functions, and an expression is obtained for the Poisson ratio as a function of time. Their general properties and dependence on loading parameters and characteristics of all material functions are studied analytically and compared with the properties of similar relations produced by two combined constitutive equations separately. New qualitative effects are identified which can be described by the new constitutive equation in comparison with the original ones, and it is verified that the generalization eliminates some shortcomings of the Maxwell-type viscoelastoplastic constitutive equation, but retains its valuable features. It is confirmed that the proposed constitutive equation can model sign alternation, monotonic and nonmonotonic changes in transverse strain and Poisson’s ratio under constant stress, and their stabilization over time. Generally accurate estimates are obtained for the variation range, monotonicity and nonmonotonicity conditions of Poisson’s ratio, and its negativity criterion over a certain time interval. It is proven that neglecting volumetric creep (the postulate of bulk elasticity), which simplifies the constitutive equation, greatly limits the range of possible evolution scenarios of Poisson’s ratio in time: it increases and cannot have extremum and inflection points. The analysis shows that the proposed constitutive equation provides ample opportunities for describing various properties of creep and recovery curves of materials and various Poisson’s ratio evolution scenarios during creep. It can significantly expand the range of described rheological effects, the applicability of the Maxwell-type viscoelastoplastic equation, and deserves further research and application in modeling.