Nonlinear Visco-Elastic Materials

Abstract

Linear visco-elastic models in the simplest form require three parameters, two springs and one damper, as two-parameter models, i.e. Maxwell and Kelvin–Voight models, either relax stress or creep, but are not capable of doing both. Three-element linear models can be expanded by adding further linear elements (Wiechert model). Nonlinearity can be attributed to linear models, e.g., by power Hertzian springs and exponential functions applied to springs and dampers. Still, the basic structure of such models is linear, as long as they consist of springs and dampers. In visco-elastic materials such as polymers, the Young’s modulus is commonly used for the materials’ stiffness characterisation, often without referring to the strain rate applied. Dependency of the Young’s modulus on the strain rate is an inherent property of visco-elasticity. By definition, the Young’s modulus is determined at small strain as is the Poisson’s ratio.