Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study.

Key Features

  • Uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics
  • Covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures
  • Offers a unique approach to modeling incompressibility and thermal expansion, based on the authors’ own research


Engineers and scientists involved in mathematical and computational modeling in solid mechanics, fluid mechanics, thermodynamics, and materials science; graduate students in engineering, physics, applied mathematics, and materials science.

Table of Contents

  • Dedication
  • Preface
    • Continuum Mechanics: The New Pedagogy
    • Acknowledgments
    • Chapter 1: What Is a Continuum?
      • Abstract
    • Chapter 2: Our Mathematical Playground
      • Abstract
      • 2.1 Real numbers and euclidean space
      • 2.2 Tensor algebra
      • 2.3 Eigenvalues, eigenvectors, polar decomposition, invariants
      • 2.4 Tensors of order three and four
      • 2.5 Tensor calculus
      • 2.6 Curvilinear coordinates
    • Chapter 3: Kinematics: Motion and Deformation
      • Abstract
      • 3.1 Body, configuration, motion, displacement
      • 3.2 Material derivative, velocity, acceleration
      • Exercises
      • 3.3 Deformation and strain
      • Exercises
      • Exercises
      • Exercises
      • 3.4 Velocity gradient, rate of deformation tensor, vorticity tensor
      • Exercises
      • 3.5 Material point, material line, material surface, material volume
      • 3.6 Volume elements and surface elements in volume and surface integrations
    • Chapter 4: The Fundamental Laws of Thermomechanics
      • Abstract
      • 4.1 Mass
      • 4.2 Forces and moments, linear and angular momentum
      • 4.3 Equations of motion (mechanical conservation laws)
      • 4.4 The first law of thermodynamics (conservation of energy)
      • 4.5 The transport and localization theorems
      • Exercises
      • 4.6 Cauchy stress tensor, heat flux vector
      • 4.7 The energy theorem and stress power
      • 4.8 Local forms of the conservation laws
      • Exercises
      • 4.9 Lagrangian forms of the integral conservation laws
      • 4.10 Piola-kirchhoff stress tensors, referential heat flux vector
      • Exercises
      • 4.11 The lagrangian form of the energy theorem
      • 4.12 Local conservatio


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About the authors

Stephen Bechtel

Stephen Bechtel is a professor emeritus in the Department of Mechanical & Aerospace Engineering at The Ohio State University. He obtained his Ph.D. in Mechanical Engineering from the University of California, Berkeley. He is a Fellow of the American Society of Mechanical Engineers (ASME) and a two-time winner of the Ohio State University College of Engineering Lumley Research Award. His research interests include advanced materials, including polymer/nanoparticle composites, magnetorheological fluids, ferroic solids, and piezoelectric crystals; industrial polymer processing and fiber manufacturing; and shear and extensional characterization of polymer melts and solutions.

Affiliations and Expertise

Professor Emeritus in the Department of Mechanical & Aerospace Engineering at The Ohio State University

Robert Lowe

Robert Lowe is a Presidential Fellow and former American Society of Mechanical Engineers (ASME) Graduate Teaching Fellow in the Department of Mechanical & Aerospace Engineering at The Ohio State University. He conducts research in the Computer Applications of Mechanics Laboratory and the Computational Fluid Dynamics Laboratory. He obtained his B.S. in Mechanical Engineering from Ohio Northern University and his M.S. in Mechanical Engineering from Ohio State. His research interests include theoretical and computational mechanics, vibrations and elastic waves in structures, finite-deformation continuum electrodynamics, and polymer processing.

Affiliations and Expertise

Presidential Fellow in the Department of Mechanical & Aerospace Engineering at The Ohio State University