The goal of this text is to introduce students to the topic of continuum mechanics, with analysis of the kinematic and mechanical behavior of materials modeled under the continuum assumption. This includes the derivation of fundamental balance equations, based on the classical laws of physics, and the development of constitutive equations characterizing the behavior of idealized materials. Such background provides the starting point for the studies of thermoelasticity, fluid mechanics, and viscoelasticity that are provided in the text. Furthermore, the material covered also imparts students with sufficient background for studying more advanced topics in continuum mechanics, such as wave propagation, polar materials, mixture theory, shell theory, piezoelectricity, and electromagnetic and magnetohydrodynamic fluid mechanics.

A few years ago, I was involved in a project that required fundamental understanding of immiscible multiphase mixtures. I was not (and am still not) satisfied with the current formulations of continuum mechanics in this area, but this is a subject that will be taken up in future publications. Nevertheless, my extensive studies necessitated a deeper understanding of many aspects of single-phase continuum mechanics. Such studies provided me valuable insights and have enabled me to write the present book as an outgrowth of my efforts. At the same time, they have enabled me to become a better teacher of the subject. I hope that the results might be useful to other teachers and students as well. The book is intended for use by students in engineering, science, and applied mathematics. As pre-requisites, a student should have knowledge of multivariable calculus, linear algebra, and differential equations, which are standard in undergraduate programs of engineering and science.

I started writing this book in 2004 to fill a number of gaps that I felt limited my understanding and application of the beautiful theory of continuum mechanics – especially on the relation between continuum mechanics and thermodynamics. I became quite dissatisfied with existing textbooks. Some were delightful but superficial, others wonderful but ancient. Of course many excellent monographs existed, such as The Classical Field Theories by Truesdell and Toupin, The Non-Linear Field Theories of Mechanics by Truesdell and Noll, and Mechanics of Continua by Eringen. Unfortunately, such books were and have been out of print for quite a while and, in the case of the first two, they are challenging works that are not intended for use in a classroom.