Abstract
A volume integral equation method (VIEM) is applied for the effective analysis of elastic wave scattering problems in unbounded solids containing general anisotropic inclusions. It should be noted that this numerical method does not require use of Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is necessary for the analysis. This new method can also be applied to general two-dimensional elastodynamic problems involving arbitrary shapes and numbers of anisotropic inclusions. A detailed analysis of SH wave scattering problems is developed for an unbounded isotropic matrix containing multiple orthotropic elliptical inclusions. Numerical results are presented for the displacement fields at the interfaces of the inclusions in a broad frequency range of practical interest. Through the analysis of plane elastodynamic problems in an unbounded isotropic matrix with multiple orthotropic elliptical inclusions, it is established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions of arbitrary shapes.
Highlights
A micrograph of the cross-section of a phosphate glass fiber/polymer composite is shown in Figure 1 [1]
Analysis of elastic wave scattering problems in heterogeneous solids often requires the use of numerical techniques based on the finite element method (FEM) or boundary element method (BIEM)
This approach is similar to the boundary integral equation method except for the presence of the volume integral over the inclusions instead of the surface integrals over the two sides of the interface
Summary
A micrograph of the cross-section of a phosphate glass fiber/polymer composite is shown in Figure 1 [1]. A number of analytical techniques are available for solving stress analysis of isotropic inclusion problems when the geometry of the inclusions is simple (i.e., cylindrical, spherical, or ellipsoidal) and when they are well separated [3,4,5,6] These approaches cannot be applied to more general problems where the inclusions are both anisotropic and arbitrary in shape when their concentration is high. Analysis of elastic wave scattering problems in heterogeneous solids often requires the use of numerical techniques based on the finite element method (FEM) or boundary element method (BIEM) Both methods encounter limitations in dealing with elastic wave scattering problems involving multiple anisotropic inclusions of arbitrary shapes. In order to investigate the influence of orthotropic elliptical inclusions on the interfacial field, a detailed
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