Size effects in adhesive contacts of viscoelastic media

Is the maximum force required to detach a rigid sphere from a viscoelastic substrate dependent on the initial value of the contact radius? Experimental and theoretical investigations reported in the literature have given opposite responses. Here, we try to answer the above question by exploiting a fully deterministic model in which adhesive interactions are described by Lennard-Jones potential and the viscoelastic behaviour with the standard linear solid model. When the approach and retraction phases are performed under quasi-static conditions, the substrate behaves as an elastic medium and, as expected, the pull-off force FPO (i.e., the maximum tensile force) is found to be independent of the maximum contact radius amax reached at the end of loading. Size-dependent effects are instead observed (i.e., the pull-off force FPO changes with amax) when transient effects occur as the larger the contact area, the greater the size of the bulk volume involved in the dissipation. Results are also discussed in the light of viscoelastic crack Persson's theory, which is modified to capture size effects related to amax.