Geometry and thermomechanics of structural rearrangements: Ekkehart Kröner's legacy Plenary lecture presented at the 80th Annual GAMM Conference, Augsburg, 25‐28 March 2002

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik - Tập 83 Số 2 - Trang 75-84 - 2003
Gérard A. Maugin1
1Laboratoire de Modélisation en Mécanique, UMR CNRS 7607, Université Pierre et Marie Curie, case 162, 4 Place Jussieu, 75252 Paris Cedex 05, France

Tóm tắt

AbstractStarting with the influential ideas of E. Kröner on the Non‐Riemannian geometrical theory of defects and a brief review of his works, we show how this legacy has developed into a true mechanics of materials on the material manifold. This synthesis, that essentially combines Kröner's ideas and those of his contemporary, J. D. Eshelby, yields a powerful unification of some of the most fruitful developments of continuum thermomechanics at the end of the XXth century and the beginning of the XXIst. In particular, a general theory of material inhomogeneities emerges which includes the study of the progress, under the action of well defined driving forces, of many microscopic and macroscopic defects or field singularities. In particular, we emphasize the relationship between the notion of material Eshelby stress and the notion of local structural rearrangements that are responsible for many of the macroscopically observed irreversible behaviors of solid‐like matter (e.g., anelasticity, damage, phase transitions, growth). All these phenomena take place directly on the material manifold. That is, their arena and that of the associated driving forces, also called configurational forces, or material forces, require a general setting that emphasizes this material peculiarity. This is the object of the paper in which all types of applications are also mentioned.

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ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Tập 83 Số 2

75-84

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