| A volume integral equation method is introduced as a new numerical scheme for the solution of certain plane elastodynamic and elastostatic problems in unbounded solids containing multiple inclusions and voids or cracks. Multiple scattering problems in elastodynamics are considered first. The effectiveness of the method is compared with the boundary integral equation method for different problem geometries. For the single inclusion problem, both methods are found to work very well. For multiple inclusions, the volume integral equation method is shown to be much more convenient for numerical formulation and to give very accurate results. Next, elastostatic problems containing multiple inclusions, voids and cracks are considered as a special case of the corresponding elastodynamic problem in the limiting case of zero frequency. The influence of fiber-matrix interphases and fiber-cores on the interfacial stresses in metal matrix composites subject to arbitrary loading is investigated. The stress intensity factors for microcracks in the matrix in presence of interacting fibers are calculated for a variety of model geometries. Finally, a combination of volume and boundary integral equation methods is introduced for the solution of elastodynamic and elastostatic problems in solids containing multiple inclusions and voids or cracks. |
