Continuum Mechanics with Eulerian Formulations of Constitutive Equations

M.B. Rubin (Autor)

Buch | Softcover

XIII, 277 Seiten

2021 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-57778-0 (ISBN)

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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.

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.

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.

"Continuum mechanics is an extremely interesting discipline ... . The book is structured ... . chapters are complemented by seven appendices focused on topics that extend concepts already analyzed or some new ones, and that make for a lighter reading of the entire work. It contains a very interesting point of view to clarify basic and key concepts of continuum mechanics. A book is recommended to all those who work in continuous mechanics." (Manuel de León, zbMATH 1516.74001, 2023)

“Continuum mechanics is an extremely interesting discipline ... . The book is structured ... . chapters are complemented by seven appendices focused on topics that extend concepts already analyzed or some new ones, and that make for a lighter reading of the entire work. It contains a very interesting point of view to clarify basic and key concepts of continuum mechanics. A book is recommended to all those who work in continuous mechanics.” (Manuel de León, zbMATH 1516.74001, 2023)

Erscheinungsdatum	12.10.2021
Reihe/Serie	Solid Mechanics and Its Applications
Zusatzinfo	XIII, 277 p. 25 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	450 g
Themenwelt	Sachbuch/Ratgeber ► Sport
	Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Technik ► Maschinenbau
Schlagworte	Continuum Mechanics • Eulerian formulation • growth of biological tissue • inelasticity • Plasticity • Porous Materials • Shock waves • thermodynamics of continua • viscoplasticity
ISBN-10	3-030-57778-3 / 3030577783
ISBN-13	978-3-030-57778-0 / 9783030577780
Zustand	Neuware