Overview

This textbook is intended to introduce engineering graduate students to the essentials of modern continuum mechanics. The objective of an introductory course is to establish certain classical continuum models within a modern framework. Engineering students need a firm understanding of classical models such as linear viscous fluids (Navier-Stokes theory) and infinitesimal elasticity. This understanding should include an appreciation for the status of the classical models as special cases of general nonlinear continuum models. The relationship of the classical models to nonlinear models is essential in light of the increasing reliance, by engineering designers and researchers, on prepackaged computer codes. These codes are based upon models which have a specific and limited range of validity. Given the danger associated with the use of these computer codes in circumstances where the model is not valid, engineers have a need for an in-depth understanding of continuum mechanics and the continuum models which can be formu- lated by use of continuum mechanics techniques. Classical continuum models and others involve a utilization of the balance equations of continuum mechanics, the second law of thermo- dynamics, and the principles of material frame indifference and material symmetry. In addition, they involve linearizations of various types. In this text, an effort is made to explain carefully how the governing principles, linearizations, and other approximations combine to yield classical con- tinuum models. A fundamental understanding of how these models evolve is most helpful when one attempts to study models which account for a wider array of physical phenomena.

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