Continuum Mechanics with Eulerian Formulations of Constitutive Equations

1. Auflage 2021
ISBN: 978-3-030-57775-9
Verlag: Springer International Publishing

Buch, Englisch, Band 265, 277 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 606 g

Reihe: Solid Mechanics and Its Applications

This book focuses on the need for an Eulerian formulation of constitutive equations. After introducing tensor analysis using both index and direct notation, nonlinear kinematics of continua is presented. The balance laws of the purely mechanical theory are discussed along with restrictions on constitutive equations due to superposed rigid body motion. The balance laws of the thermomechanical theory are discussed and specific constitutive equations are presented for: hyperelastic materials; elastic–inelastic materials; thermoelastic–inelastic materials with application to shock waves; thermoelastic–inelastic porous materials; and thermoelastic–inelastic growing biological tissues.

Zielgruppe

Research

Autoren/Hrsg.

Rubin, M. B.

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Elastizität, Plastizität, Rheologie
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Technische Thermodynamik

Inhaltsverzeichnis

Introduction.- Basic tensor analysis.- Kinematics.- Balance laws for the purely mechanical theory.- Purely mechanical constitutive equations.- Thermomechanical Theory.- Eigenvalues, Eigenvectors, and Principal Invariants of a Tensor.- Consequences of Continuity.- Lagrange Multipliers.- Stationary Values of Normal And Shear Stresses.- Isotropic Tensors.- An introduction to tensors with respect to curvilinear coordinates.- Summary of tensor operations in specific coordinate systems.

Über Autor(innen)

The author received his Ph.D in Applied Mechanics under the supervision of Professor PM Naghdi at the University of California, Berkeley. After working at SRI International (formerly the Stanford Research Institute) for three years he joined the Faculty of Mechanical Engineering at Technion, where he completed his entire academic career, retiring as a Professor Emeritus. He conducted research as a visiting Faculty at Lawrence Livermore National Laboratory for over thirty years. He has taught Continuum Mechanics at Technion for thirty-five years and has authored over 180 journal papers. In addition, in 2000 he published a book entitled: Cosserat Theories: Shells, Rods and Points.