The Contact Stresses Between a Rigid Indenter and a Viscoelastic Half-Space

Abstract

The Hertz problem for a rigid spherical indenter on a viscoelastic half-space was studied by Lee and Radok [1] in which the radius a(t) of the contact area is a monotonically increasing function of time t. Later, Hunter [2] studied the rebound of a rigid sphere on a viscoelastic half-space so that the contact radius a(t) increases monotonically to a maximum and then decreases to zero monotonically. The contact problem in which a(t) increases for the second time and decreases again does not seem to have been studied; nor has the contact problem in which a(t) is nonzero initially and decreases monotonically been studied. In this paper, a method is introduced so that the contact problem can be solved for arbitrary a(t). The rigid indenter is assumed to be smooth and axisymmetric but otherwise arbitrary. The viscoelastic solutions are expressed in terms of the associated elastic solutions. A means for measuring the viscoelastic Poisson’s ratio is suggested.

Effect of rogue particles on the sub-surface damage of fused silica during grinding/polishing

“…13b). Hunter [22] and Ting [23] have shown approaches to account for the surface displacement. Ting's approach provides an analytical expression for the total displacement in terms of the contact zone radius and can be applied to high strain which is given by: (16) where r is radial distance away from the center of the particle.…”

Determination of work of adhesion of biological cell under AFM bead indentation

“…For its viscoelastic counterpart, both Radok (Lee and Radok, 1960) and Ting (Ting, 1966) offered a general solution to linear viscoelastic Boussinesq problem provided the contact radius is non-decreasing as mutual approach increases. According to their theory, substituting the elastic modulus in the Hertz contact model with the modulus-displacement convolution in the time domain leads to the relationship between the indentation depth and the applied force as (Yu et al, 2013):…”

Indentation of power law creep solids by self-similar indenters

“…polymers, composites, biomaterials and food products, are "soft", or exhibit viscoelastic behavior such as creep. In fact theoretical studies of liner viscoelastic bodies in contact became active since the mid 1950s by work of Lee [1], Radok [2], Lee and Radok [3], Hunter [4], Graham [5,6], Yang [7], and Ting [8,9]. In recent years, a number of authors have extended the early work to the analysis of indentation measurements in viscoelastic solids using either conical or spherical indenters [10][11][12][13][14][15].…”