ASPECTS OF THE DYNAMICS OF A RUBBERLIKE MATERIAL

Abstract

The first part of this paper, consisting of sections 1 and 2, presents a general analysis of continuous isentropic motions of a particular class of isotropic elastic solids. The materials in question have been shown to simulate the essential thermo-mechanical properties of solid polymers exhibiting rubberlike behaviour and, in the present context, their most important characteristic is near-incompressibility. The actual motion considered is accordingly viewed as an isochoric motion, generally involving finite deformations, on which is superimposed a dilatational disturbance of small amplitude. The main objectives of the analysis are a rationally conceived definition of the isochoric motion and an approximation procedure enabling the dilatational motion to be calculated to leading order, and for these purposes the constitution of the moving body is fully specified by a single response function representing the influence of the polymer network on the thermoelastic behaviour of the material. The isochoric motion is characterized by a strain-energy function formed by appropriately specializing the network response function, and the perturbation displacement is shown to be governed by a non-homogeneous wave equation in which the source term is derived from the isochoric motion. In the second part of the paper (sections 3 and 4) the general theory is applied to spherically symmetric motions of an infinite body excited by the application of a uniform time-dependent pressure to the surface of a cavity. The isochoric approximant to the actual motion is studied in section 3 and detailed results are worked out for an empirical network response function which, in a variety of situations, has been found to yield theoretical predictions in good agreement with experimental findings. The perturbation wave field is determined in section 4. A discussion of its properties shows that the combined motion conforms to an expected pattern and that certain peculiarities associated with the isochoric motion are annulled by superposition of the dilatational disturbance.