THE APPLICATION OF THE STROH FORMALISM TO PRESTRESSED ELASTIC MEDIA

The Stroh formalism is a six-dimensional representation of the equatio ns governing plane motions of an elastic body, stemming from a juxtapo sition of the displacement and a traction vector. Crucially, the forma lism leads to a sextic eigenvalue problem which is the mainspring of f ar-reaching theoretical developments. It is known that the formalism e xtends to prestressed unconstrained elastic media subject to a restric tion on the prestress. In this paper, the limitation is removed, and i t is shown that the sextic eigenvalue problem can also be constructed for a prestressed elastic medium which is incompressible. The latter p roblem is exhibited as the limit of the former in a process in which t he condition of incompressibility is reached through a one-parameter f amily of nearly incompressible elastic materials. As an application of the theory, the analysis of surface waves in a homogeneously prestres sed semi-infinite body of incompressible elastic material is carried a s far as the derivation of the secular equation, determining the speed of propagation. Complete results are obtained in the special case in which the material is orthotropic, with the symmetry axes aligned with the principal axes of prestress and the surface wave basis.