Introduction to Continuum Mechanics

  • W. Michael Lai, Professor of Mechanical Engineering and Orthopaedic Bioengineering, Columbia University, New York, USA
    • David Rubin, Principal, Weidlinger Associates, New York, USA
      • Erhard Krempl, Professor of Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

      Continuum mechanics studies the response of materials to different loading conditions. The concept of tensors is introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples and problems, many with solutions.

      Through the addition of more advanced material (solution of classical elasticity problems, constitutive equations for viscoelastic fluids, and finite deformation theory), this popular introduction to modern continuum mechanics has been fully revised to serve a dual purpose: for introductory courses in undergraduate engineering curricula, and for beginning graduate courses.

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      For graduates and undergraduates in engineering.


Book information

  • Published: January 1994
  • Imprint: PERGAMON
  • ISBN: 978-0-08-041700-4

Table of Contents

Chapter headings and selected subchapters: Prefaces. Introduction. Continuum theory. Contents of continuum mechanics. Tensors. Summation convention, dummy indices. Kronecker delta. Manipulations with the indicial notation. Tensor: a linear transformation. Dyadic product of two vectors. The dual vector of an antisymmetric tensor. Principal scalar invariants of a tensor. Tensor-valued functions of a scalar. Curl of a vector field. Polar coordinates. Kinematics of a Continuum. Description of motions of a continuum. Dilatation. Local rigid body displacements. Components of deformation tensors in other coordinates. Stress. Stress vector. Equations of motion written with respect to the reference configuration. Entropy inequality. The Elastic Solid. Mechanical properties. Linear elastic solid. Reflection of plane elastic waves. Stress concentration due to a small circular hole in a plate under tension. Constitutive equations for anisotropic elastic solid. Constitutive equation for an isotropic elastic solid. Change of frame. Bending of an incompressible rectangular bar. Newtonian Viscous Fluids. Fluids. Streamline, pathline, streakline, steady, unsteady, laminar and turbulent flow. Irrotational flows as solutions of Navier-Stokes equation. One-dimensional flow of a compressible fluid. Integral Formulation of General Principles. Green's theorem. Principle of moment of momentum. Non-Newtonian Fluids. Linear Maxwell fluid. Current configuration as reference configuration. Special single integral type nonlinear constitutive equations. Viscometric flow. Answers to problems. Index.