Three-Dimensional constitutive equations for hyper viscoelastic particulate reinforced composite materials based on damage parameter

The aim of the article is mathematical modeling of behavior of hyper viscoelastic particulate reinforced composite materials. Three dimensional hyper viscoelastic constitutive equations, which include an inherent damage parameter and its functions, have been developed. The model was used to demonstrate physical phenomenon such as the so called dewetting effect. New strain rate, damage rate and stress state sensitive dewetting criterion is proposed. At the same time dewetting criterion is the first order ordinary differential equation with respect to damage parameter and serves as its evolution law. The softening of the material due to dewetting during the loading is considered by means of the strain energy density function augmented by the damage parameter and its functions. The proposed material model simulates volumetric strains caused by the hydrostatic pressure, as well as the dilatation caused by the deviatoric part of the stress, namely deviatoric-bulk coupling is considered. The material model proposed in the framework of this article takes into account the behavior of particulate reinforced hyper viscoelastic composite materials such as strong nonlinearity, dewetting, complex coupling of the deviatoric bulk behavior. Mullins effect and temperature dependence have not been covered by this research. The proposed material model has been implemented into Finite Element package MSC. Marc by means of FORTRAN user subroutines “elevar” and “uelastomer” and it has been shown good correlation with test results.