Crack opening displacements under remote stress gradient: Derivation with a canonical basis of sixth order tensors

Abstract : In this paper, we derive the crack opening displacement of a penny-shaped crack embedded in an infinite isotropic elastic medium and subjected to a remote constant stress gradient. The solution is derived by taking advantage of the solution of the equivalent ellipsoidal inclusion problem subjected to a linear polarization. The case of the penny-shaped crack is thereafter investigated by considering the case of a spheroidal cavity which has one principal axis infinitesimally small compared to both others. The derivation of the explicit solution for the inhomogeneity subjected to a remote stress gradient raises the problem of the inversion of a sixth order tensor. For the problem having a symmetry axis (including the case of penny shaped crack), this problem can be tackled by using a decomposition oin the canonical basis for transversely isotropic sixth order tensors.
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Vincent Monchiet, Guy Bonnet. Crack opening displacements under remote stress gradient: Derivation with a canonical basis of sixth order tensors. International Journal of Engineering Science, Elsevier, 2015, 91, pp.1-11. ⟨10.1016/j.ijengsci.2015.01.002⟩. ⟨hal-01165843⟩

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