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Global view of microstructural evolution: Energetics,kinetics and dynamical systems
Authors:Yang Wei  Suo Zhigang
Institution:(1) Dept. Eng. Mech., Tsinghua Univ., 100084 Beijing, China;(2) Mech. Environ. Eng. Dept., Univ. California, 93106 Santa Barbara, CA, USA
Abstract:An evolving material structure is in a non-equilibrium state, with free energy expressed by the generalized coordinates. A global approach leads to robust computations for the generalized thermodynamic forces. Those forces drive various kinetic processes, causing dissipation at spots, along curves, surfaces and interfaces, and within volumetric regions. The actual evolution path, and therefore the final equilibrium state, is determined by the energetics and kinetics. A virtual work principle links the free energy landscape and the kinetic processes, and assigns a viscous environment to every point on the landscape. The approach leads to a dynamical system that governs the evolution of generalized coordinates. The microstructural evolution is globally characterized by a basin map in the coordinate space; and by a diversity map and a variety map in the parameter space. The control of basin boundaries raises the issue of energetic and kinetic bifurcations. The variation of basin boundaries under different sets of controlling parameters provides an analytical way to plot the diversity maps of structural evolution. The project supported by the National Science Foundation (USA) through grant MSS-9258115, and by the National Natural Science Foundation of China
Keywords:microstructural evolution  energetics  kinetics  dynamic system
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