Chadwick, P. The application of the Stroh formalism to prestressed elastic media. (English) Zbl 1001.74515 Math. Mech. Solids 2, No. 4, 379-403 (1997). Summary: The Stroh formalism is a six-dimensional representation of the equations governing plane motions of an elastic body, stemming from a juxtaposition of the displacement and a traction vector. Crucially, the formalism leads to a sextic eigenvalue problem which is the mainspring of far-reaching theoretical developments. It is known that the formalism extends to prestressed unconstrained elastic media subject to a restriction on the prestress. In this paper, the limitation is removed, and it is shown that the sextic eigenvalue problem can also be constructed for a prestressed elastic medium which is incompressible. The latter problem is exhibited as the limit of the former in a process in which the condition of incompressibility is reached through a one-parameter family of nearly incompressible elastic materials. As an application of the theory, the analysis of surface waves in a homogeneously prestressed semi-infinite body of incompressible elastic material is carried as 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. Cited in 21 Documents MSC: 74B10 Linear elasticity with initial stresses PDFBibTeX XMLCite \textit{P. Chadwick}, Math. Mech. Solids 2, No. 4, 379--403 (1997; Zbl 1001.74515) Full Text: DOI References: [1] Stroh, A. N., J Math. Phys. 41 pp 77– (1962) · Zbl 0112.16804 [2] Chadwick, P., Advances in Applied Mechanics pp 303– (1977) [3] Chadwick, P., Elastic Wave Propagation pp 3– (1989) · Zbl 0686.73020 [4] Wu, J. J., Modem Theory of Anisotropic Elasticity and Applications (1991) [5] Ting, T.C.T., Anisotropic Elasticity. Theory and Applications (1996) [6] Chadwick, P., Proc. R. Soc. Lond. 366 pp 517– (1979) · Zbl 0411.73018 [7] Chadwick, P., Proc. R. Irish Acad. 94 pp 85– (1994) [8] Scott, N. H., J. Elasticity 16 pp 239– (1986) · Zbl 0594.73035 [9] Chadwick, P., Proc. R. Irish Acad. 94 pp 255– (1994) [10] Ogden, R. W., Non-Linear Elastic Deformations (1984) · Zbl 0541.73044 [11] Chadwick, P., Continuum Mechanics. Concise Theory and Problems (1976) [12] Chadwick, P., Arch. Rational Mech. Analysis 44 pp 41– (1971) [13] Musgrave, M.J.P., Crystal Acoustics (1970) [14] Pease, M. C. III, Methods of Matrix Algebra (1965) · Zbl 0145.03701 [15] Rogerson, G. A., Quart. J. Mech. Appl. Math. 45 pp 77– (1992) · Zbl 0760.73013 [16] Wang, L., Wave Motion 18 pp 77– (1993) [17] Ingebrigtsen, K. A., Phys. Rev. 184 pp 942– (1969) [18] Barnett, D. M., Proc. R. Soc. Lond. 402 pp 135– (1985) · Zbl 0587.73030 [19] Green, A. E., J. Rational Mech. Analysis 3 pp 713– (1954) [20] Dowaikh, M. A., I.M.A. J. Appl. Math. 44 pp 261– (1990) [21] Chadwick, P., Theoretical, Experimental and Numerical Contributions to the Mechanics of Fluids and Solids pp S51– (1995) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.