Nonlinear viscosity law for rate-dependent response of high damping rubber: FE implementation and verification

A simple computational strategy for implementation of a finite strain viscohyperelasticity model in a standard FEM code is discussed. To this end, a recently published evolution law that takes the nonlinear dependence of viscosity into account is considered. Such a law considers the maximum overstress experienced in past history and deformation as the internal variables. In order to simulate the stress-response for a particular boundary value problem, an analytical solution scheme using the Bernoulli's principle has been applied to derive the stress expressions. The expressions have been incorporated in a finite element code. Limited numerical trials show the applicability of the procedure for simulating rate dependent responses obtained from one dimensional experiments e.g. uniaxial compression or simple shear tests on natural rubber and high damping rubber specimens. The limitations of this approach for solving an arbitrary boundary value problem are also discussed.