Contact between viscoelastic media

Here we will focus upon a different type of general result, given, for elastic materials, by Dundurs and Stippes (1970) and Dundurs (1975) and for viscoelastic materials by Comninou (1976). This topic, in the three-dimensional case, will be discussed in this section. Stronger results for the plane case, also due to these authors, are presented in Sect. 2.10. 

If C(t) does not vary in time, apart from an initial, instantaneous change, the contact is said to be stationary. 

The basic assumption underlying the results proved in this and the following section is that the contact be receding. This excludes most contact problems in the ordinary usage of the term. Examples of contact problems which have this property are given by Dundurs (1975). The only configuration relevant to later chapters for which the contact is receding is a crack, initially closed, which opens under a tensile stress. In this example, Q is the entire crack face and C(t) is the closed portion of it, if any. 

The region C t) and its complement on the boundary C (t) correspond respectively to used earlier. 

Consider the frictionless, isothermal contact between two viscoelastic bodies, where the contact is receding. The constitutive relations for the two bodies have the form (1.8.8)  

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The attenuation and velocity of acoustic energy in polymers are very different from those in other materials due to their unique viscoelastic properties. The use of ultrasonic techniques, such as acoustic spectroscopy, for the characterization of polymers has been demonstrated [47,48]. For AW devices, the propagation of an acoustic wave in a substrate causes an oscillating displacement of particles on the substrate surface. For a medium in intimate contact with the substrate, the horizontal component of this motion produces a shearing force. In such cases, there can be sufficient interaction between the acoustic wave and the adjacent medium to perturb the properties of the wave. For polymeric materials, attenuation and velocity of the acoustic wave will be affected by changes in the viscoelastic behavior of the polymer. 

Fig. 5 Changes in / (solid line) and D (dashed line) at = 1 for a 5 MHz crystal in contact with a viscoelastic film characterized by a homogeneous thickness, viscosity, and elasticity of 1 gcm , 30mPas, and 1 MPa, respectively, and a thickness varying between 0 and 1 p.m. In a, the medium is air. In b, the medium is water. Also shown is the frequency shift according to the Sauerbrey equation (Eq. 1) for the same film (open diamonds)...

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