Executive Summary : | Shock waves in solids are commonly encountered in applications such as planetary impacts, blast events, bullet/missile impacts, shock synthesis and even in medical applications such as shock-wave lithotripsy. A shock wave is defined as a surface of discontinuity across which density, pressure, velocity and various other physical quantities undergo a jump in their states. Mathematically, it is a surface of second order, i.e., only material continuity is ensured across this curve (or surface in 3 – D). Although the formulation of the mathematical theory of shock waves in solids started around 100 years ago and a significant amount of progress has taken place, with the discovery of every new material system, it is necessary to relook at the existence of shock waves, the evolution of the shocked states in such new material systems and finally, the mathematical theory that captures shock response of the material systems. Among the material systems studied so far, hydrogels have drawn significant attention from researchers across the world, due to their superior shock mitigation capabilities. Of particular interest is methylcellulose hydrogel. The present proposal is aimed at establishing a profound mathematical theory of shock waves in hydrogels and derive the existence of mathematical conditions based on continuum thermodynamics and shock theory and propose a suitable constitutive model for methylcellulose hydrogels to capture the shock propagation and attenuation. |