Showing papers by "J. L. Ericksen published in 1974"

Complex exponential solutions of linear elasticity equations

Abstract: We consider linear elasticity equations of the type encountered in the theory 'of small deformations superposed on large, when the large deformation leaves the material in a homogeneous configuration. Said differently, we consider cases where these are linear equations with constant coefficients. Such equations admit a variety of complex exponential solutions. As is discussed by Truesdell & Noll [1, §§ 71, 73], for example, one subset, the plane waves, has been studied in some detail. Another type is encountered in the various studies of surface waves, whose amplitude varies with position, but not time. Judging from conversations I have had with various workers, it seems not to be a matter of common knowledge that there also exist waves whose amplitude increases or decreases exponentially with time. Failure to appreciate this seems to have led to some confusion concerning elastic stability theory. I t thus seems worthwhile to at tempt a more general exploration of complex exponential solutions, hereafter abbreviated as CES. We here establish some of their properties. We restrict our attention to equations of strongly elliptic type. Various interpretations and implications of this condition are discussed by Truesdell & Noll [1, §§ 44, 45, 48, 52, 68, 71, 74, 90]. For reasons discussed by Ericksen [2, 3], elasticities violating this condition are not likely to be observed.