Three-Dimensional Volume Integral Equation Method for Solving Isotropic/Anisotropic Inhomogeneity Problems

In this paper, the volume integral equation method (VIEM) is introduced for the analysis of an unbounded isotropic solid composed of multiple isotropic/anisotropic inhomogeneities. A comprehensive examination of a three-dimensional elastostatic VIEM is introduced for the analysis of an unbounded isotropic solid composed of isotropic/anisotropic inhomogeneity of arbitrary shape. The authors hope that the volume integral equation method can be used to compute critical values of practical interest in realistic models of composites composed of strong anisotropic and/or heterogeneous inhomogeneities of arbitrary shapes.

The Dynamic Three-Dimensional Localization of Fields in Active Percolating Systems

We study a dynamic three-dimensional (3D) field localized states in a medium with percolation disorder, where the percolation cluster is filled by the active nanoemitters. In such a system, the incipient percolating cluster generates a fractal radiating structure in which the field is radiated and scattered by the anisotropic inhomogeneity. Our numerical 3D simulations show that such a nonlinear system with noninteger fractal dimension has well-defined localized solutions for fields (3D speckles). The statistics of speckles is studied too.

Anisotropic Inhomogeneous Poroelastic Inclusions: With Application to Underground Energy-Related Problems

Understanding the stress change in a reservoir generated by fluid production/injection is important for field development purposes. In this paper, we provide the Eshelby solution for stress and strain distribution inside and outside of an anisotropic poroelastic inhomogeneity due to pore pressure changes inside the inhomogeneity. The term anisotropic inhomogeneity refers to an inhomogeneity with anisotropic poroelastic constants. Some graphical results for strain and stress ratios for different material properties and geometries are presented as well. Anisotropy in elastic properties has been studied extensively in the last century; however, anisotropy in poroelastic properties, despite its potential significant impact in different engineering problems, has not been explored thoroughly. The results show how neglecting the effect of anisotropic poroelastic properties may result in large differences in calculated stresses. Due to the authors' primary interest in geomechanical problems, the discussions and examples are chosen for applications involving fluid withdrawal/injection into hydrocarbon reservoirs.