Mechanics of Material Forces - Steinmann, Paul / Maugin, Gérard A. (eds.)
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This book covers new theoretical and numerical developments in the mechanics of material forces. Conceptually speaking, common continuum mechanics in the sense of Newton - which gives rise to the notion of spatial (mechanical) forces - considers the response to variations of spatial placements of "physical particles" with respect to the ambient space, whereas continuum mechanics in the sense of Eshelby - which gives rise to the notion of material (configurational) forces - is concerned with the response to variations of material placements of "physical particles" with respect to the ambient…mehr

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Produktbeschreibung
This book covers new theoretical and numerical developments in the mechanics of material forces. Conceptually speaking, common continuum mechanics in the sense of Newton - which gives rise to the notion of spatial (mechanical) forces - considers the response to variations of spatial placements of "physical particles" with respect to the ambient space, whereas continuum mechanics in the sense of Eshelby - which gives rise to the notion of material (configurational) forces - is concerned with the response to variations of material placements of "physical particles" with respect to the ambient material. Well-known examples of material forces are driving forces on defects like the Peach-Koehler force, the J-Integral in fracture mechanics, and energy release. The consideration of material forces goes back to the works of Eshelby, who investigated forces on defects; therefore this area of continuum mechanics is sometimes denoted Eshelbian mechanics.
The notion dealt with in this volume of proceedings is often traced back to the late 19th-century writings of a rather obscure scientist, C. V. Burton. A probable reason for this is that the painstaking de ciphering of this author's paper in the Philosophical Magazine (Vol. 33, pp. 191-204, 1891) seems to reveal a notion that was introduced in math ematical form much later, that of local structural rearrangement. This notion obviously takes place on the material manifold of modern con tinuum mechanics. It is more or less clear that seemingly different phe nomena - phase transition, local destruction of matter in the form of the loss of local ordering (such as in the appearance of structural defects or of the loss of cohesion by the appearance of damage or the exten sion of cracks), plasticity, material growth in the bulk or at the surface by accretion, wear, and the production of debris - should enter a com mon framework where, by pure logic, the material manifold has to play a prominent role. Finding the mathematical formulation for this was one of the great achievements of J. D. Eshelby. He was led to consider the apparent but true motion or displacement of embedded material inhomogeneities, and thus he began to investigate the "driving force" causing this motion or displacement, something any good mechanician would naturally introduce through the duahty inherent in mechanics since J. L. d'Alembert.
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Autorenporträt
Paul Steinmann, University of Kaiserslautern, Germany / Gérard A. Maugin, Université Pierre et Marie Curie, Paris, France