External influences on the growth and decay of one-dimensional shock waves in elastic non-conductors

Abstract

IN THIS paper, we study the influence of discontinuous external body force and external radiation on the behavior of shock waves in elastic materials which do not conduct heat. To this end, we derive a differential equation relating the strain Eand grain gradient E; behind a shock when the material region ahead is unstrained and at constant entropy. First, this equation implies the existence of an externally induced critical strain gradient A, proportional to the external body force and external radiation behind the wave. Next, for a compression shock Is-1 will, in general, increase, decrease, or remain constant accordingly as 8; is greater than, less than, or equal to A. These results should be compared with those given by Chen and Gurtin [l], who studied the behavior of shock waves in elastic nonconductors of heat, assuming that the external body force and external radiation are absent. In their paper, they showed that the conditions under which a shock will grow or decay are, in general, qualitatively the same as in the purely mechanical theory. Finally, we outline a particular experiment for which the external radiation is indeed discontinuous across the shock and give a procedure for determining A as a function of E-. In principle, this experiment can be readily conducted in the laboratory.