It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities （cracks, pores, foreign particles）. From the theor...It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities （cracks, pores, foreign particles）. From the theory of elasticity, the formulation of the perturbance elastic fields, coming from a non-ellipsoidal inhomogeneity embedded in an infinitely extended material with remote constant loading, inevitably involve one or more integral equations. Up to now, due to the mathematical difficulty, there is almost no explicit analytical solution obtained except for the ellipsoidal inhomo- geneity. In this paper, we point out the impossibility to trans- form this inhomogeneity problem into a conventional Eshelby problem by the equivalent inclusion method even if the eigenstrain is chosen to be non-uniform. We also build up an equivalent model, called the second Eshelby problem, to investigate the perturbance stress. It is probably a better template to make use of the profound methods and results of conventional Eshelby problems of non-ellipsoidal inclusions.展开更多
The problem of an ellipsoidal inhomogeneity embedded in an infinitely extended elastic medium with sliding interfaces is investigated. An exact solution is presented for such an inhomogeneous system that is subject to...The problem of an ellipsoidal inhomogeneity embedded in an infinitely extended elastic medium with sliding interfaces is investigated. An exact solution is presented for such an inhomogeneous system that is subject to remote uniform shearing stress. Both the elastic inclusion and matrix are considered isotropic with a separate elastic modulus. Based on Lur’e’s approach to solving ellipsoidal cavity problems through Lamé functions, several harmonic functions are introduced for Papkovich-Neuber displacement potentials. The displacement fields inside and outside the ellipsoidal inclusion are obtained explicitly, and the stress field in the whole domain is consequently determined.展开更多
基金supported by the National Natural Science Foundation of China (10872086 and 11072105)
文摘It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities （cracks, pores, foreign particles）. From the theory of elasticity, the formulation of the perturbance elastic fields, coming from a non-ellipsoidal inhomogeneity embedded in an infinitely extended material with remote constant loading, inevitably involve one or more integral equations. Up to now, due to the mathematical difficulty, there is almost no explicit analytical solution obtained except for the ellipsoidal inhomo- geneity. In this paper, we point out the impossibility to trans- form this inhomogeneity problem into a conventional Eshelby problem by the equivalent inclusion method even if the eigenstrain is chosen to be non-uniform. We also build up an equivalent model, called the second Eshelby problem, to investigate the perturbance stress. It is probably a better template to make use of the profound methods and results of conventional Eshelby problems of non-ellipsoidal inclusions.
基金supported by the National Natural Science Foundation of China(Grant No.11102022)
文摘The problem of an ellipsoidal inhomogeneity embedded in an infinitely extended elastic medium with sliding interfaces is investigated. An exact solution is presented for such an inhomogeneous system that is subject to remote uniform shearing stress. Both the elastic inclusion and matrix are considered isotropic with a separate elastic modulus. Based on Lur’e’s approach to solving ellipsoidal cavity problems through Lamé functions, several harmonic functions are introduced for Papkovich-Neuber displacement potentials. The displacement fields inside and outside the ellipsoidal inclusion are obtained explicitly, and the stress field in the whole domain is consequently determined.
