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Media type:
E-Book
Title:
Mathematical modeling of shock-wave processes in condensed matter
:
from statistical thermodynamics to control theory
Contains:
Models of continuum mechanics and their deficiencies -- Specific Features of Processes Far from Equilibrium -- Macroscopic Description in Terms of Non-equilibrium Statistical Mechanics.-Thermodynamic Concepts Out of Equilibrium -- New Approach to Modeling Non-equilibrium Processes -- Description of the Structure Evolution Using Methods of Control Theory of Adaptive Systems -- The Shock-Induced Planar Wave Propagation in Condensed Matter -- Evolution of Waveforms during Propagation in Solids -- Abnormal Loss or Growth of the Wave Amplitude -- The Stress-Strain Relationships for the Continuous Stationary Loading.
Description:
This book offers an interdisciplinary theoretical approach based on non-equilibrium statistical thermodynamics and control theory for mathematically modeling shock-induced out-of-equilibrium processes in condensed matter. The book comprises two parts. The first half of the book establishes the theoretical approach, reviewing fundamentals of non-equilibrium statistical thermodynamics and control theory of adaptive systems. The latter half applies the presented approach to a problem on shock-induced plane wave propagation in condensed matter. The result successfully reproduces the observed feature of waveform propagation in experiments, which conventional continuous mechanics cannot access. Further, the consequent stress–strain relationships derived with relaxation and inertia effect in elastic–plastic transition determines material properties in transient regimes.