The Mathematical Theory of Equilibrium Cracks in Brittle Fracture by G.I. Barenblatt discusses the mathematical formulation and analysis of equilibrium cracks in brittle materials. The paper addresses the problem of cracks in solids under load, emphasizing the non-linear nature of the problem due to the presence of cracks. It highlights the distinction between cracks and cavities, noting that cracks can expand significantly under small increases in load, unlike cavities. The paper discusses the classical theory of elasticity and its limitations in the context of cracks, where the assumption of small boundary changes is not valid. It introduces the concept of stress intensity factors and the role of molecular cohesion in determining crack behavior. The paper also explores the conditions for crack stability and the energy release rate, which is crucial for understanding crack propagation. It reviews the development of the theory of equilibrium cracks, including contributions from Griffith, Irwin, and others, and discusses the importance of considering the finite nature of stresses and smooth closure of crack faces. The paper concludes with the formulation of the fundamental problem in the theory of equilibrium cracks, emphasizing the need to determine the stress and displacement fields and the crack contours under given loads. The analysis of stress and strain near the crack edges is also discussed, showing that the stress intensity factor plays a critical role in determining the behavior of cracks. The paper concludes that the structure of cracks near their edges is characterized by finite stresses and smooth closure of the crack faces, which is a key aspect of the theory of brittle fracture.The Mathematical Theory of Equilibrium Cracks in Brittle Fracture by G.I. Barenblatt discusses the mathematical formulation and analysis of equilibrium cracks in brittle materials. The paper addresses the problem of cracks in solids under load, emphasizing the non-linear nature of the problem due to the presence of cracks. It highlights the distinction between cracks and cavities, noting that cracks can expand significantly under small increases in load, unlike cavities. The paper discusses the classical theory of elasticity and its limitations in the context of cracks, where the assumption of small boundary changes is not valid. It introduces the concept of stress intensity factors and the role of molecular cohesion in determining crack behavior. The paper also explores the conditions for crack stability and the energy release rate, which is crucial for understanding crack propagation. It reviews the development of the theory of equilibrium cracks, including contributions from Griffith, Irwin, and others, and discusses the importance of considering the finite nature of stresses and smooth closure of crack faces. The paper concludes with the formulation of the fundamental problem in the theory of equilibrium cracks, emphasizing the need to determine the stress and displacement fields and the crack contours under given loads. The analysis of stress and strain near the crack edges is also discussed, showing that the stress intensity factor plays a critical role in determining the behavior of cracks. The paper concludes that the structure of cracks near their edges is characterized by finite stresses and smooth closure of the crack faces, which is a key aspect of the theory of brittle fracture.