Modeling stock market crash dynamics using analysis of anti-plane shear deformation of a cracked finite isotropic wedge

This paper introduces a novel approach to modeling stock market crash dynamics by drawing an analogy to the mechanics of anti-plane shear deformation in a cracked finite isotropic wedge. Financial markets under stress exhibit patterns of stress concentration, failure propagation, and systemic breakdown, much like cracked elastic media under mechanical deformation. The main objective of this study is to develop a mathematical model that describes the evolution of financial crises as mechanical fracture processes in elastic media. To this end, the specific objectives are: (1) to establish a formal correspondence between the physical variables of the elastic model and financial indicators of risk and instability; (2) to derive critical conditions for crisis propagation using methods from elasticity theory and fracture mechanics; and (3) to analyze the influence of parameters such as the shear modulus ( ), interpreted as market resilience, on the dynamics of recovery or collapse. This will be achieved by using methods from fracture mechanics and elasticity theory, we derive a framework that captures the spread of financial distress, the collapse of price stability, and the conditions for market recovery. The model provides insights into liquidity crises, systemic risk, and intervention strategies.