On the effective surface energy in viscoelastic Hertzian contacts
Abstract
Viscoelasticity and ratedependent adhesion of soft matter lead to difficulties in modelling the 'relatively simple' problem of a rigid sphere in contact with a viscoelastic halfspace. For this reason, approximations in describing surface interactions and viscous dissipation processes are usually adopted in the literature.
Here, we develop a fully deterministic model in which adhesive interactions are described by LennardJones potential and the material behaviour with the standard linear solid model.
Normal loadingunloading cycles are carried out under different driving conditions. When loading is performed in quasistatic conditions and, hence, unloading starts from a completely relaxed state of the material, the effective surface energy is found to monotonically increase with the contact line velocity up to an asymptotic value reached at high unloading rates. Such result agrees with existing theories on viscoelastic crack propagation.
If loading and unloading are performed at the same nonzero driving velocity and, hence, unloading starts from an unrelaxed state of the material, the trend of the effective surface energy Δγ_{eff} with the contact line velocity is described by a bellshaped function in a doublelogarithmic plot. The peak of Δγ_{eff} is found at a contact line velocity smaller than that makes maximum the tangent loss of the viscoelastic modulus. Furthermore, we show Gent&Schultz assumption partly works in this case as viscous dissipation is no longer localized along the contact perimeter but it also occurs in the bulk material.
 Publication:

Journal of Mechanics Physics of Solids
 Pub Date:
 January 2022
 DOI:
 10.1016/j.jmps.2021.104669
 arXiv:
 arXiv:2107.03796
 Bibcode:
 2022JMPSo.15804669A
 Keywords:

 Viscoelasticity;
 Adhesion hysteresis;
 Effective surface energy;
 Crack propagation;
 Finite element modelling;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 doi:10.1016/j.jmps.2021.104669