The legacy of José Domínguez: Contributions to boundary element formulations in fracture mechanics

This work reviews and critically assesses the scientific legacy of José Domínguez in the development of boundary element formulations for fracture mechanics. The review focuses on methodological advances that shaped the modern use of the boundary element method (BEM) for crack problems, with emphasis on: (i) crack-tip element technology – including singular quarter-point and discontinuous quarter-point elements – that enables direct extraction of fracture parameters from boundary integral equations; (ii) regularization procedures for singular and hypersingular kernels that preserve standard BEM infrastructure; and (iii) extensions from linear elastostatics to coupled-field solids and to dynamic fracture via frequency- and time-domain formulations. The scope is restricted to linear fracture formulations under the assumptions of pre-existing sharp cracks and small-scale yielding, both in classical elasticity and in linear coupled-field settings. The discussion covers quasi-static and dynamic fracture analyses, three-dimensional extensions, and the systematic generalization to anisotropic, piezoelectric, and magnetoelectroelastic solids, where multifield coupling introduces additional theoretical and numerical challenges. Rather than aiming at an exhaustive survey, the paper traces the coherent research line initiated by Domínguez and continued by his collaborators, highlighting how these contributions established a unified framework for fracture analysis that remains foundational in current boundary element research.