000 03744nam a22005415i 4500
001 978-3-540-72373-8
003 DE-He213
005 20161121231203.0
007 cr nn 008mamaa
008 100301s2007 gw | s |||| 0|eng d
020 _a9783540723738
_9978-3-540-72373-8
024 7 _a10.1007/978-3-540-72373-8
_2doi
050 4 _aTA405-409.3
050 4 _aQA808.2
072 7 _aTG
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aTEC021000
_2bisacsh
082 0 4 _a620.1
_223
100 1 _aEpstein, Marcelo.
_eauthor.
245 1 0 _aMaterial Inhomogeneities and their Evolution
_h[electronic resource] :
_bA Geometric Approach /
_cby Marcelo Epstein, Marek Elżanowski.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2007.
300 _aXIII, 261 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInteraction Mechanics, Mathematics,
_x1860-6245
505 0 _aInhomogeneity 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.
520 _aInhomogeneity 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.
650 0 _aEngineering.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 0 _aMechanics.
650 0 _aContinuum mechanics.
650 1 4 _aEngineering.
650 2 4 _aContinuum Mechanics and Mechanics of Materials.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aApplications of Mathematics.
650 2 4 _aMechanics.
700 1 _aElżanowski, Marek.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540723721
830 0 _aInteraction Mechanics, Mathematics,
_x1860-6245
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-540-72373-8
912 _aZDB-2-ENG
950 _aEngineering (Springer-11647)
999 _c509844
_d509844