Mathematical Modeling of Shock-Wave Processes in Condensed Matter

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 stressstrain relationships derived with relaxation and inertia effect in elasticplastic transition determines material properties in transient regimes.

Offers a mathematical modeling for non-equilibrium processes in condensed matter mechanics Describes transient processes beyond the capability of continuum mechanics Opens pathways to technologies that provide materials with desired structure

Auteur

Tatiana Aleksandrovna Khantuleva is a professor at Saint Petersburg State University. Her research is primarily concerned with non-equilibrium phenomena and complex systems and their mathematical modeling. She received her Ph.D. degree in fluid and plasma mechanics from the State Institute of Mathematics and Mechanics, Saint Petersburg, Russia, in 1977. She joined Saint Petersburg State University as an associate professor in 1999 and was promoted to her current position in 2007. She received certificates of honor from Saint Petersburg State University and the Russian Academy of Science in 2007, 2010, and 2017.

She currently focuses on the problems related to modeling transient and shock-induced processes, out-of-equilibrium thermodynamic evolution, and synergetic effects at a mesoscopic scale and on developing several new original special courses of lectures for graduate students.

Contenu
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.