Simulation of Dissipation in Solids

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PI's Name, Institution : Adnan Akay, Carnegie Mellon UniversityProposal NumberProposal Title: Simulation of Dissipation in SolidsProject Abstract This project concerns modeling and simulating dissipation in solids. Although common forms of dissipation such as internal damping and contact damping have a very important role in dynamics, dissipation is still treated as an empiricalphenomenon without a description based on first principles. Dissipation in solids often describes conversion of kinetic energy to heat as in, for example, a sound wave passing through a solid exciting its atoms, and raising their energy level. The increased kinetic energy of the oscillations of atoms define the heat capacity of a solid with the assumption that they are inthermal equilibrium. Simulation of dissipation in a solid involves a 3-D lattice of oscillators that represent atoms connected to each other with springs. Springs represent displacement-dependent forces thatresult from the nonlinear potential between the atoms. The specific research tasks to accomplish this goal begin with a one-dimensional array of nonlinearly connected oscillators to investigate numerically the conditions of irreversibility and equipartitioning. The simulations will then be extended to nonideal lattices that include impurities to describe real solids to investigate their role in wavenumber (and frequency)conversion. An important aspect of this effort will be to determine the lower limit of the size of simulations to correctlydescribe dissipation in a solid and determine means to quantify dissipation characteristics of solids. The proposed investigation will also help clarify the theoretical requirements inherent in fuzzy damping by putting them on a more fundamental footing regarding energy equipartition and irreversible absorption of energy.