A GENERALIZATION OF THE LAME AND SOMIGLIANA STRESS FUNCTIONS FOR THE DYNAMIC THEORY OF LINEAR VOSCOELASTIC SOLIDS,
Abstract
A study is made of solutions of the displacement equations of motion appropriate to the dynamic linear theory of homogeneous isotropic, viscoelastic solids. These equations are derived from the fundamental system of field equations. In the absence of body forces, the divergence and curl of the displacement field (or the field itself, provided it is either irrotational or solenoidal) satisfy hereditary wave equations. Such an equation is simply the classical wave equation with the square of the wave velocity replaced by an integral operator of the Volterra type. It also follows that the displacement, strain, and stress fields satisfy iterated hereditary wave equations. Generalizations are introduced to viscoelasticity of the Lame and Somigliana stress function solutions of elastodynamics. By an adaptation of arguments the completeness of the generalized Lame functions is established, and, using this result, the completeness of the viscoelastic Somigliana solution is proved. Next, it is found that every displacement field can be decomposed into the sum of a solenoidal and an irrotational vector, each of which satisfies an hereditary wave equation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1964
- Accession Number
- AD0436826
Entities
People
- M. E. Gurtin
- W. S. Edelstein
Organizations
- Brown University