Journal of Theoretical
and Applied Mechanics

44, 1, pp. 19-30, Warsaw 2006

Algorithm for determination of $\widetilde{\sigma}_{ij}(n,\theta)$, $\widetilde{\varepsilon}_{ij}(n,\theta)$, $\widetilde{u}_i(n,\theta)$, $d_n(n)$, $I_n(n)$ functions in Hutchinson-Rice-Rosengren solution and its 3D generalization

Jarosław Gałkiewicz, Marcin Graba
In the paper the algorithm to determine $\widetilde{\sigma}_{ij}(n,\theta)$, $\widetilde{\varepsilon}_{ij}(n,\theta)$, $\widetilde{u}_i(n,\theta)$, $d_n(n)$, $I_n(n)$ functions that are necessary to obtain values of stresses, strains and displacements in the crack tip neighborhood according to the Hutchinson, Rice and Rosengren solutions is presented. The algorithm can also be used to determine $\widetilde{\sigma}_{ij}(n,\theta)$, $\widetilde{\varepsilon}_{ij}(n,\theta)$, $\widetilde{u}_i(n,\theta)$, $d_n(n)$, $I_n(n)$ functions for a 3D approximate solution of the stress field in front of the crack introduced by Guo Wanlin, where constraint due to the thickness effect is introduced through the $ T_z$ function.
Keywords: fracture mechanics; HRR fields; 3DHRR field approximation