The paper "Revisiting Brittle Fracture as an Energy Minimization Problem" by G. A. Francfort and J.-J. Marigo revisits the classical theory of brittle fracture, particularly Griffith's theory, and proposes a new variational model for quasistatic crack evolution. The authors aim to address the limitations of Griffith's theory, such as the inability to predict crack initiation, crack path, and crack jumps. The proposed model does not require a preexisting crack or a well-defined crack path but instead relies on the assumption of global energy minimization, which is a common postulate in material science. The model is formulated in a quasistatic setting and is applicable to any dimension and elastic material. It considers the entire lifespan of the cracking process, from initiation to complete failure, and can handle various loading scenarios, including delamination, fiber debonding, and surface cracks. The model is presented in Section 2, with explicit solutions discussed in Section 3, and general properties of the model explored in Section 4. Key findings include: 1. **Crack Initiation**: The model predicts crack initiation in a crack-free environment, which is a significant improvement over Griffith's theory. 2. **Crack Path**: The model allows for the quantification of crack initiation and path, addressing the limitations of Griffith's theory. 3. **Crack Jumps**: The model can handle non-smooth crack evolutions, including jumps along the crack path, which is not possible with Griffith's theory. The authors also compare their model with Griffith's theory, showing that while both theories agree in the strictly convex case, they differ in the concave case, where Griffith's theory predicts an unstable state and fails to provide a clear criterion for crack propagation. The proposed model, however, can handle both progressive and brutal crack growth, depending on the convexity properties of the energy functions involved. Overall, the paper provides a comprehensive and mathematically rigorous framework for understanding and predicting crack evolution in brittle materials, offering a valuable contribution to the field of fracture mechanics.The paper "Revisiting Brittle Fracture as an Energy Minimization Problem" by G. A. Francfort and J.-J. Marigo revisits the classical theory of brittle fracture, particularly Griffith's theory, and proposes a new variational model for quasistatic crack evolution. The authors aim to address the limitations of Griffith's theory, such as the inability to predict crack initiation, crack path, and crack jumps. The proposed model does not require a preexisting crack or a well-defined crack path but instead relies on the assumption of global energy minimization, which is a common postulate in material science. The model is formulated in a quasistatic setting and is applicable to any dimension and elastic material. It considers the entire lifespan of the cracking process, from initiation to complete failure, and can handle various loading scenarios, including delamination, fiber debonding, and surface cracks. The model is presented in Section 2, with explicit solutions discussed in Section 3, and general properties of the model explored in Section 4. Key findings include: 1. **Crack Initiation**: The model predicts crack initiation in a crack-free environment, which is a significant improvement over Griffith's theory. 2. **Crack Path**: The model allows for the quantification of crack initiation and path, addressing the limitations of Griffith's theory. 3. **Crack Jumps**: The model can handle non-smooth crack evolutions, including jumps along the crack path, which is not possible with Griffith's theory. The authors also compare their model with Griffith's theory, showing that while both theories agree in the strictly convex case, they differ in the concave case, where Griffith's theory predicts an unstable state and fails to provide a clear criterion for crack propagation. The proposed model, however, can handle both progressive and brutal crack growth, depending on the convexity properties of the energy functions involved. Overall, the paper provides a comprehensive and mathematically rigorous framework for understanding and predicting crack evolution in brittle materials, offering a valuable contribution to the field of fracture mechanics.