Asymptotic analysis in Linear Elasticity: From the pioneering studies by Wieghardt and Irwin until today

The asymptotic analysis of the stress distribution around an elastic wedge-shaped domain is one of the most fundamental problems in Linear Elasticity. In occasion of the century anniversary of the pioneering paper by Wieghardt on splitting and cracking of elastic bodies, and of the half-a-century anniversary of the Irwin’s paper on the analysis of stresses and strains near the end of a crack, we propose a review of the most important contributions leading to fundamental advances in this research field. Special focus will be given to the epistemological steps towards a full appreciation of the mathematical and engineering relevance of the stress-singularities. We also provide the reader with a review of the geometrical configurations and mechanical conditions that can relieve or remove the singularities, including: re-entrant corners; power-law hardening constitutive laws; fractal cracks; multi-material junctions and wedges; nonhomogeneous materials.