A Finite Element Solution to Normal Contact Forces of Viscoelastic Particles

In this paper, an approach to solve the normal contact forces of viscoelastic particles with the finite element method is presented. A viscoelastic constitutive model is deduced and established for the finite element solution, where the stress tensors of the Zener-type model expressed as partial differential equations are obtained by applying the generalized Hooke's law, and the incremental equations are further deduced with the backward difference method. An iterative matrix of the viscoelastic constitutive model that depends on the current strain, current stress and strain increment is derived; a user material subroutine is programed based on the iterative matrix to implement the viscoelastic constitutive model in the displacement-based finite element modeling. The validity of the finite element solution to the normal contact forces of elastic particles is validated with the Hertz contact force model, and that of the solution to the normal contact forces of viscoelastic particles is verified by the experimental data. The results obtained by the proposed solution agree well with those predicted by the Prony series, and the computational efficiency of this solution is higher for different values of the shear viscosity.