Nonlinear Dynamics and Elasticity

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This grant supports theoretical research on nonlinear dynamics and elasticity, in particular, the physics of deformed solids. The problems concern the way that building matter from atoms determines its mechanical behavior on large scales. These problems have largely been solved in cases where the solid object deforms only a small amount. However, when the deformations are large enough to rip atoms apart from their neighbors the problems become more difficult and the connection between small and large scales is more challenging to determine quantitatively. Some particular questions to be addressed include: Why do theory and experiment still differ by a factor of two for the fracture energy of silicon, and how can the problem be resolved? Can methods that successfully solve brittle fracture problems be generalized to more complicated materials with structure on multiple scales? How can one describe cracks traveling faster than the shear wave speed in rubber, and why do they spontaneously begin to oscillate? Can dry sliding friction be explained by the motion of thousands of earthquake-like self-healing fractures? What sorts of shock waves form in metals and semiconductors impacted by petawatt laser pulses? Are leaves, flowers, and ripped garbage bags all similarly described as sheets of non-uniform metrics, and how do their macroscopic geometrical properties depend on microscopic lengths? While these questions come from many different subdisciplines of physics and engineering, they are unified by underlying theoretical techniques, by a common set of numerical tools, and by the overarching question in condensed matter physics, of how the macroscopic world follows from its microscopic foundation.The research will generate theoretical and computational tools to solve multiscale physics problems, will provide new concepts for engineering mechanics including concepts of commercial value, will create material for teacher preparation, and will supply interesting new physics problems easily understood by a broad public.%%% This grant supports theoretical research on nonlinear dynamics and elasticity, in particular, the physics of deformed solids. The problems concern the way that building matter from atoms determines its mechanical behavior on large scales. These problems have largely been solved in cases where the solid object deforms only a small amount. However, when the deformations are large enough to rip atoms apart from their neighbors the problems become more difficult and the connection between small and large scales is more challenging to determine quantitatively. The research will generate theoretical and computational tools to solve multiscale physics problems, will provide new concepts for engineering mechanics including concepts of commercial value, will create material for teacher preparation, and will supply interesting new physics problems easily understood by a broad public.***