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Configuration forces as basic concepts of continuum physics. (English) Zbl 0951.74003
Applied Mathematical Sciences. 137. New York, NY: Springer. xiii, 249 p. (2000).
The author is one of the pioneers in this rather new branch of continuum mechanics. He has already published a long series of papers on this subject, and there is hardly anybody else more appropriate to write the first comprehensive textbook on it. Gurtin starts from the very beginning, reviewing the classical concepts of forces in continuum mechanics, and then introducing the new fields which constitute a new force concept. As many of the applications are closely linked to moving surfaces, a thorough introduction of migrating control volumes with jumps across the surface is outlined. The general theory of configurational forces is then developed in parallel to the classical ones, leading to analogous balances and constitutive structures. The material under consideration is rather general, including large deformations and dissipation from the outset. The entire theory is imbedded into a thermodynamic setting, assuring the compatibility with the second law. Applications of these new concepts are given in phase transition problems and in fracture mechanics. Gurtin uses a direct notation and a rigorous and clear mathematical language. Theoretically, the entire theory becomes a clear and sound structure, but on a rather general level. There remains a gap to be filled by further works to bring more physics into this theory. Because otherwise it would remain a sophisticated theory for a rather limited group of “fundamentalists”, rather than a strong and versatile new concept, capable of describing effects beyond classical mechanics and thermodynamics.

74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
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