Two-scale mechanism-based theory of nonlinear viscoelasticity

Abstract

The paper presents a mechanism-based two-scale theory for a generalized nonlinear viscoelastic continuum. The continuum is labeled as generalized since it contains extra degrees of freedom typical of past high-order continuum theories, though a new formulation is presented here tailored to meet the needs of the physical description of the viscoelastic solid. The microstress that appears in the equations, often criticized for a lack of physical meaning, is assigned in this work to viscous free chains superimposed on a nonlinear elastic backbone composed of crosslinks and reinforcement. Mathematically, hyperelasticity is used to describe the equilibrium backbone (macroscale), and an improvement of tube models for reptation dynamics describes the free chain motion at the microscale. Inhomogeneous deformation is described by inclusion of a microstrain gradient into the formulation. Thus, the theory is nicely suited for materials with microstructure where localization of strains and inhomogeneous deformation occur in addition to viscoelastic damping mechanisms due to free chains. Besides the microstress, physical meaning of the additional boundary conditions arising in the general theory is also presented. Since the proposed material model is mechanism-based, macroscopic performances are functions of microstructural variables describing the polymer chemistry so that parametric material design concepts may be gleaned from the model. Several physical phenomena are captured through numerical simulation of the class of materials of interest: size effects, strain localization, and the fracture process. Results agree qualitatively with both experimental data and direct numerical simulation for filled elastomeric solids.