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BIE fracture mechanics analysis: 25 years of developments. (English) Zbl 0946.74073
From the introduction: We review the capabilities of the boundary integral equation (BIE) method for problems in fracture mechanics. The problem class will be limited to static problems of elastic and elastoplastic fracture. The paper draws on the extensive literature that has been developed over the past twenty-five years. Fracture mechanics problems have provided one of the most important applications of BIE formulations in solid mechanics and is one of the principal areas of application of BIE methods. In particular, the paper focuses on the special role played by the Somigliana stress identity in providing algorithms and analytical results for fracture mechanics analysis that are not possible when using the finite element method. Finally, we also identify special problems associated with BIE modeling of cracks, and various strategies that have been developed to successfully treat these problems.
MSC:
74S15Boundary element methods in solid mechanics
74R10Brittle fracture
74-02Research monographs (mechanics of deformable solids)
74R20Anelastic fracture and damage
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