BIE fracture mechanics analysis: 25 years of developments

SummaryThe past twenty five years have shown in many ways that the BIE formulation and its BEM implementation provide important contributions in two and three dimensional fracture mechanics analysis. The Somigliana stress identity plays a key role in these many investigations and applications. The experiences show that the BIE has unique capabilities to provide analytical insights and special results for fracture mechanics problems that are not found in the finite element methods.The success of the BIE formalism for these problems is directly derived from the fact that the BIE is a complete representation of the equilibrium equations, even in its numerical form (BEM). This experience suggests that further attempts to couple the analytical and numerical behavior of BIE's could be equally beneficial to other problem areas in mechanics.Most recent work on fracture analysis has focused on the nature of the hypersingular form of the Somigliana stress identity. It is expected that the non-singular forms of this identity will be the basis of new work on Green's functions, focusing on the three dimensional problem.

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