Accession Number : AD0429806

Title :   UNIQUENESS THEOREMS IN THE LINEAR THEORY OF ANISOTROPIC VISCOELASTIC SOLIDS,

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Edelstein,W. S. ; Gurtin,M. E.

Report Date : FEB 1964

Pagination or Media Count : 26

Abstract : Some uniquenes theorems appropriate to dynamic linear viscoelasticity theory (small deformations) are proved. The first theorem asserts that the mixed problem of dynamic viscoelasticity theory has at most one solution provided the relaxation tensor is initially symmetric and initially positive definite. The proof of this theorem uses techniques which were employed by Volterra to establish a similar theorem in quasistatic viscoelasticity. The second result, the proof of which utilizes the Laplace transform techniques of Breuer and Onat, removes the initial symmetry requirement on the relaxation tensor G. This is done, however, only at the expense of requiring that G be independent of x, and the both G and the solution in question possess a Laplace transform with respect to the time. The third theorem which is the most difficult to prove, says if G is independent of x, initially symmetric, and initially strongly elliptic, then the displacement problem of dynamic viscoelasticity has at most one solution. Notice that if G has the usual symmetries and is initially positive definite, the G is also initially strongly elliptic. In this sense, the third theorem is more general than the first. (Author)

Descriptors :   (*ELASTIC PROPERTIES, MATHEMATICAL ANALYSIS), DYNAMICS, VISCOSITY, DIFFERENTIAL EQUATIONS, CALCULUS OF VARIATIONS, MATRICES(MATHEMATICS), POTENTIAL THEORY, INTEGRAL TRANSFORMS, DEFORMATION

Distribution Statement : APPROVED FOR PUBLIC RELEASE