Green's function molecular dynamics including viscoelasticity

The contact mechanical response of various polymers is controlled by the viscoelastic behavior of their bulk and the adhesive properties of their interface. Due to the interplay between viscoelasticity and adhesion it is difficult to predict the contact response, even more when surfaces are rough. Numerical modeling could be of assistance in this task, but has so far mostly dealt with either adhesion or viscoelasticity and focused on simple geometries. Ideally, one would need a model that can concurrently describe viscoelasticity, surface roughness, and interfacial interactions. The numerical technique named Green's function molecular dynamics (GFMD) has the potential to serve this purpose. To date, it has been used to model contact between adhesive elastic bodies with self-affine surfaces. Here, as a first step, we extend the GFMD technique to include the transient contact response of frictionless viscoelastic bodies. To this end, we derive the constitutive equation for a viscoelastic semi-infinite body in reciprocal space, then integrate it using the semi-analytical method, and find the quasi-static solution through damped dynamics of the individual modes. The new model is then applied to study indentation as well as rolling of a rigid cylinder on a frictionless isotropic half-plane that follows the Zener model when loaded in shear. Extension of the method to a generalized viscoelastic model is straightforward, but the computational effort increases with the number of time-scales required to describe the material. The steady-state response of the rolling cylinder was provided analytically by Hunter in the sixties. Here, we use his analytical solution to validate the steady-state response of our model and provide additionally the transient response for bodies with various shear moduli.