Energy and volume changes due to the formation of a circular inhomogeneity in a residual deviatoric stress field
- 25 Downloads
An inclusion of purely dilatational eigenstrain in an infinitely extended isotropic elastic matrix, independently of its shape, causes a deviatoric stress field around it. The present paper analyses the energy and volume changes due to the formation of a circular inhomogeneity in a deviatoric stress field coming from a circular inclusion of dilatational eigenstrain. It is found that the elastic stress inside the inhomogeneity remains deviatoric and the inhomogeneity formation does not change the volume of the inclusion-matrix system; it is argued that the same occurs for any inclusion shape and non-uniform eigenstrain. The elastic energy changes occurring in the domains occupied by matrix, inhomogeneity, and inclusion are calculated, and its dependence on the elastic properties and geometrical parameters of inhomogeneity and matrix is numerically investigated. Strengthening effects of the matrix-inhomogeneity system are examined by means of the energy force and expanding moment acting on the inhomogeneity.
- 5.Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. (trans. JRM Radok) Noordhoff (1953)Google Scholar
- 11.Hutchinson, J.W.: On Steady Quasi-Static Crack Growth. Harvard University Rep. Division of Applied Sciences (1974). DEAP S-8Google Scholar
- 13.Eshelby, J.D.: Energy relations and energy momentum tensor in continuum mechanics. In: Kanninen, M.F., Alder, M.F., Rosenfield, A.R., Jaffe, R.I. (eds.) Inelastic Behavior of Solids. McGraw-Hill, New York (1970)Google Scholar
- 14.Guell, D.L., Dundurs, J.: Further results on center of dilatation and residual stresses in joined elastic half-spaces. Developments in Theoretical and Applied Mechanics, Proceeding of the Third Southeastern Conference on Theoretical and Applied Mechanics, pp. 105–115 (1967)Google Scholar
- 27.Dundurs, J.: Some properties of elastic stresses in a composite. In: Proceedings of the 6th Annual Meeting of the Society of Engineering Science, vol. 5, pp. 203–216 (1970)Google Scholar