THE DYNAMIC INDENTATION OF A FINITE ELASTIC PLATE

The Shore hardness test has been widely used and has become the standa rd for characterizing materials in the rubber and plastics industries. The obtained hardness scale values, ASTM or IRHD, are often related t o the static elastic properties of rubber like-materials. Recently, pr ogress on the problem of obtaining dynamic viscoelastic properties has been made through the use of an oscillating spherical indentor and mo deling the measured input impedance by the radiation impedance of a ra diating sphere. When the sphere radius is small, such that ka<<1 for l ongitudinal waves, then the measured shear modulus and loss factor is in good agreement with that found using other dynamic methods such as the DMTA. This model is appropriate only for relatively soft materials or very thick hard materials where the thickness of the material can be ignored. The object of the current work is to extend the methodolog y to layers of finite thickness. The problem is studied under the assu mptions of linear lasticity and the condition that there is perfect ad hesion between the indentor and the elastic layer. The method of solut ion that is adopted will be described and as such it constitutes the f irst serious attempt to solve an elastodynamic boundary value problem of this type.