In such a way, the entropy inequality becomes a restriction on the constitutive equations rather than a restriction on the processes. Finally, the last one, the dissipation principle, requires that materials, in reacting to the external agents, satisfy the second principle of thermodynamics in any process. The fourth is the equipresence principle postulating that, a priori, the fundamental variables of the thermokinetic process influence all the fields describing the answer of the body. The third one is the objectivity principle stating that the response of materials does not depend on the rigid frame of reference adopted to observe their behavior. The first two of them state that the answer of a material at a point depends, in a certain way, on past history of a neighborhood of that point. These axioms constitute general rules that any material must satisfy in answering to external agents. This chapter contains a wide discussion about the constitutive axioms. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics. This second edition expands the key topics and features to include: * Two new applications of fluid dynamics: meteorology and navigation * New exercises at the end of the existing chapters * The packages are rewritten for Mathematica 9 Continuum Mechanics using Mathematica®: Fundamentals, Applications and Scientific Computing is aimed at advanced undergraduates, graduate students and researchers in applied mathematics, mathematical physics and engineering. Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and one appendix * Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhäuser), 2010, ISBN 978-0-8176-4869-5). Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica® provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics and state changes (see A. This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics.
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