04190nam a22005415i 4500 978-3-540-72373-8 DE-He213 20210617005121.0 cr nn 008mamaa 100301s2007 gw | s |||| 0|eng d 9783540723738 978-3-540-72373-8 10.1007/978-3-540-72373-8 doi TA349-359 TGMD bicssc SCI096000 bisacsh TGMD thema 531 23 Epstein, Marcelo. author. aut http://id.loc.gov/vocabulary/relators/aut Material Inhomogeneities and their Evolution [electronic resource] : A Geometric Approach / by Marcelo Epstein, Marek Elzanowski. 1st ed. 2007. Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2007. XIII, 261 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Interaction of Mechanics and Mathematics, 1860-6245 Inhomogeneity in Continuum Mechanics -- An overview of inhomogeneity theory -- Uniformity of second-grade materials -- Uniformity of Cosserat media -- Functionally graded bodies -- Material Evolution -- On energy, Cauchy stress and Eshelby stress -- An overview of the theory of material evolution -- Second-grade evolution -- Mathematical Foundations -- Basic geometric concepts -- Theory of connections -- Bundles of linear frames -- Connections of higher order. Inhomogeneity theory is of importance for the description of a variety of material phenomena, including continuous distributions of dislocations, fracture mechanics, plasticity, biological remodelling and growth and, more generally, all processes that entail changes in the material body driven by forces known in literature as material or configurational. This monograph presents a unified treatment of the theory using some of the tools of modern differential geometry. The first part of the book deals with the geometrical description of uniform bodies and their homogeneity (i.e., integrability) conditions. In the second part, a theory of material evolution is developed and its relevance in various applied contexts discussed. The necessary geometrical notions are introduced as needed in the first two parts but often without due attention to an uncompromising mathematical rigour. This task is left for the third part of the book, which is a highly technical compendium of those concepts of modern differential geometry that are invoked in the first two parts (differentiable manifolds, Lie groups, jets, principal fibre bundles, G-structures, connections, frame bundles, integrable prolongations, groupoids, etc.). To make the text as useful as possible to active researchers and graduate students, considerable attention has been devoted to non-standard topics, such as second-grade materials, Cosserat media and functionally graded bodies. Mechanics. Mechanics, Applied. Applied mathematics. Engineering mathematics. Solid Mechanics. https://scigraph.springernature.com/ontologies/product-market-codes/T15010 Mathematical and Computational Engineering. https://scigraph.springernature.com/ontologies/product-market-codes/T11006 Applications of Mathematics. https://scigraph.springernature.com/ontologies/product-market-codes/M13003 Classical Mechanics. https://scigraph.springernature.com/ontologies/product-market-codes/P21018 Elzanowski, Marek. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) Springer Nature eBook Printed edition: 9783540837992 Printed edition: 9783540723721 Interaction of Mechanics and Mathematics, 1860-6245 https://doi.org/10.1007/978-3-540-72373-8 ZDB-2-ENG ZDB-2-SXE Engineering (SpringerNature-11647) Engineering (R0) (SpringerNature-43712)