Nonlinear viscoelasticity of incompressible isotropic solids

Abstract

The development of isotropic nonlinear viscoelastic solid constitutive models constitutes an integral part of solid mechanics. In this work, a general constitutive behavior framework for nonlinear viscoelastic solid materials is developed via systematic stress relaxation and creep experiments on polypropylene (PP). Results indicates that the infinite hyperelastic-plastic constitutive behavior serves as the sole physical boundary for evaluating structural delayed stability. Thus, the threshold stress between low-stress creep stability and high-stress creep fracture of nonlinear viscoelastic solid is determined. It is revealed that the nonlinear viscoelastic constitutive behavior represents a convergence process from instantaneous hyperelasticity to infinite hyperelasticity. To fully characterize their relaxation and creep viscoelastic properties, we propose a novel architecture based on series-parallel combinations of hyperelastic springs and dampers. By integrating Maxwell and Kelvin linear viscoelastic theories with the incompressible Mooney-Rivlin hyperelastic model, we develop incompressible nonlinear viscoelastic stress relaxation and creep constitutive models. The developed models exhibit excellent predictive performance. Boltzmann's equations are derived based on the Boltzmann nonlinear superposition principle, revealing the constitutive relations for nonlinear solids. These equations establish a connection between special and generalized relaxation / creep constitutive behaviors. This research focuses on small deformations in incompressible solids, laying the groundwork for future investigations into large deformations in compressible solids.