Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations

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Preface
This book on Continuum Mechanics and Thermodynamics (CMT) (together with the companion book, by Tadmor and Miller, on Modeling Materials (MM) [TM11]) is a comprehensive framework for understanding modern attempts at modeling materials phenomena
from first principles. This is a challenging problem because material behavior is dictated by
many different processes, occurring on vastly different length and time scales, that interact
in complex ways to give the overall material response. Further, these processes have traditionally been studied by different researchers, from different fields, using different theories
and tools. For example, the bonding between individual atoms making up a material is
studied by physicists using quantum mechanics, while the macroscopic deformation of
materials falls within the domain of engineers who use continuum mechanics. In the end
a multiscale modeling approach – capable of predicting the behavior of materials at the
macroscopic scale but built on the quantum foundations of atomic bonding – requires a
deep understanding of topics from a broad range of disciplines and the connections between
them. These include quantum mechanics, statistical mechanics and materials science, as
well as continuum mechanics and thermodynamics, which are the focus of this book.
Together, continuum mechanics and thermodynamics form the fundamental theory lying
at the heart of many disciplines in science and engineering. This is a nonlinear theory dealing
with the macroscopic response of material bodies to mechanical and thermal loading.
There are many books on continuum mechanics, but we believe that several factors set our
book apart. First, is our emphasis on fundamental concepts. Rather than just presenting
equations, we attempt to explain where the equations come from and what are the underlying
assumptions. This is important for those seeking to integrate continuum mechanics within
a multiscale paradigm, but is also of great value for those who seek to master continuum
mechanics on its own, and even for experts who wish to reflect further upon the basis
of their field and its limitations. To this end, we have adopted a careful expository style,
developing the subject in a step-by-step fashion, building up from fundamental ideas and
concepts to more complex principles. We have taken pains to carefully and clearly discuss
many of the subtle points of the subject which are often glossed over in other books.
A second difference setting our CMT apart from other books on the subject is the integration of thermodynamics into the discussion of continuum mechanics. Thermodynamics
is a difficult subject which is normally taught using the language of heat engines and
Carnot cycles. It is very difficult for most students to see how these concepts are related
to continuum mechanics. Yet thermodynamics plays a vital role at the foundation of continuum mechanics. In fact, we think of continuum mechanics and thermodynamics as a
single unified subject. It is simply impossible to discuss thermomechanical processes in

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