Analysis of Anisotropic Elastic Medium with Multiple Elliptical Holes Subjected to Uniform Load of in-Plane and Out-of-Plane Shear at Infinity

Abstract

In this paper, a stress concentration around two holes of a 3D-printed material and stress intensity factors (SIFs) at straight crack tips of a rock are shown graphically as several practical calculation examples. The stress components and SIFs are calculated using the two-dimensional elastic theory. The elastic constitutive equation of materials has been used as isotropy or orthotropy in most previous analyses. Consequently, the mutual influence of the in-plane and out-of-plane shear problem has rarely been discussed. Therefore, at the first in this paper, the solutions that take into consideration the general constitutive equation with such mutual influence, are derived by the modified Lekhnitskii formulation. Next, numerical calculations for a 3D-printed polycarbonate plate subjected to uniform tension are performed in order to evaluate the mutual influence of anisotropy on the stress concentration for two circular holes. By changing the distance between the holes and angle formed by the stack and tensile directions, not only the effect of these parameters on the magnitude of out-of-plane shear stress but also the stress concentration factor for tension are clarified. Further, SIF for fracture mode I is calculated for a straight crack group in granite, and the mutual influence of SIF for fracture mode III is evaluated. As the results, it is found about SIF for fracture mode III that it becomes zero for enough crack spacing, whereas it is increasing continuously with increase of crack density.