Continuum Mechanics with Eulerian Formulations of Constitutive Equations

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • M. B. Rubin

   Pages 1-10

3. Basic Tensor Analysis

   • M. B. Rubin

   Pages 11-31

4. Kinematics

   • M. B. Rubin

   Pages 33-79

5. Balance Laws for the Purely Mechanical Theory

   • M. B. Rubin

   Pages 81-111

6. Purely Mechanical Constitutive Equations

   • M. B. Rubin

   Pages 113-176

7. Thermomechanical Theory

   • M. B. Rubin

   Pages 177-232

8. Back Matter

   Pages 233-277

   PDF

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.

• Continuum mechanics
• thermodynamics of continua
• Eulerian formulation
• inelasticity
• plasticity
• viscoplasticity
• growth of biological tissue
• shock waves
• porous materials

“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)

• Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel

  M.B. Rubin

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.

Policies and ethics