SUMMARYA multi-domain method of solving three-dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The 4 displacement and l/dL traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the l / f i term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, I1 and I11 are obtained directly from crack-front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny-shaped crack.

SUMMARYGeneral two-dimensional linear elastic fracture problems are investigated using the boundary element method. The displacement and 1/& traction behaviour near a crack tip are incorporated in special crack elements. Stress intensity factors of both modes I and I1 are obtained directly from crack-tip nodal values for a variety of crack problems, including straight and curved cracks in finite and infinite bodies. A multidomain approach is adopted to treat cracks in an infinite body. The body is subdivided into two regions: an infinite part with a finite hole and a finite inclusion. Numerical results, compared with exact solution whenever possible, are accurate even with a coarse discretization.

A phase‐field method (PFM) is used to investigate cracking behaviours, including crack initiation and propagation, in interlayered rocks with preexisting flaws subjected to tension. An example with a bi‐material plate with a centre flaw is used to validate the PFM. Then, numerical simulations of cracking behaviours in interlayered rocks with a single flaw and a cross‐flaw are carried out using PFM. Moreover, the load‐displacement responses are numerically investigated. The PFM numerical results show that the crack propagation trajectories and peak loads of rock specimens depend on the preexisting flaw configuration and the mechanical properties of the interlayers.

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SUMMARYA multi region boundary-element method is employed to study the scattering of time-harmonic waves by cracks in a three-dimensional elastic solid. Special shape functions are employed to model the near-crack singularity. The multi region formulation enables removal of singularities from all boundary integral equations. The matter of fictitious eigenfrequencies is discussed and resolved. Values of dynamic stress intensity factors for three problems involving penny-shaped cracks are compared with results of other investigators.

A multidomain boundary element method (BEM) is employed to study the scattering of time-harmonic acoustic waves by knife-edge structures in an acoustic field. Analysis shows that singularities exist in such structures, and that the behavior of the acoustic pressure and its derivative near a knife edge resembles that of the displacement and stress near a crack tip in an elastic body. Singular elements are employed to model the behavior on the part of the boundary in the vicinity of the singularity. The advantage of the singular elements is seen through several numerical examples involving mufflerlike structures containing baffles and one with a knife-edge scattering in full space. For a given level of mesh refinement, both the near-field and far-field solutions are improved with the introduction of singular elements.

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