Mechanics of nanoparticle adhesion — A continuum approach

30J. TomasFigure 7. Constitutive models of contact deformation of smooth spherical particles in normal directionwithout (only compression +) and with adhesion (tension –). The basic models for elastic behaviorwere derived by Hertz [41], for constant adhesion by Yang [61], for constant adhesion byJohnson et al. [51], for plastic behavior by Thornton and Ning [60] and Walton and Braun [59], andfor plasticity with variation in adhesion by Molerus [13] and Schubert et al. [57]. This has been expandedstepwise to include nonlinear plastic contact hardening and softening equivalent to shearthickeningand shear-thinning in suspension rheology [91]. Energy dissipation was considered bySadd et al. [55] and time-dependent viscoplasticity by Rumpf et al. [62]. Considering all these theories,one obtains a general contact model for time- and rate-dependent viscoelastic, plastic, viscoplastic,adhesion and dissipative behaviors [91, 146–148, 151].