Nonequilibrium Thermodynamics of Amorphous Materials I: Internal Degrees of Freedom and Volume Deformation
arXiv:0903.1521 · doi:10.1103/PhysRevE.80.031131
Abstract
This is the first of three papers devoted to the nonequilibrium thermodynamics of amorphous materials. Our focus here is on the role of internal degrees of freedom in determining the dynamics of such systems. For illustrative purposes, we study a solid whose internal degrees of freedom are vacancies that govern irreversible volume changes. Using this model, we compare a thermodynamic theory based on the Clausius-Duhem inequality to a statistical analysis based directly on the law of increase of entropy. The statistical theory is used first to derive the the Clausius-Duhem inequality. We then use the theory to go beyond those results and obtain detailed equations of motion, including a rate factor that is enhanced by deformation-induced noisy fluctuations. The statistical analysis points to the need for understanding how both energy and entropy are shared by the vacancies and their environments.
7 pages. First of a three-part series
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- The Dynamics of Rapid Fracture: Instabilities, Nonlinearities and Length Scales
- Nonequilibrium Thermodynamics of Amorphous Materials III: Shear-Transformation-Zone Plasticity
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- Thermal Effects in Dislocation Theory
- Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold
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- Diffusion in mesoscopic lattice models of amorphous plasticity
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- A Small-gap Effective-Temperature Model of Transient Shear Band Formation During Flow
- Nonequilibrium Thermodynamics of the Soft Glassy Rheology Model
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