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024 7 _a10.1007/b10191
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100 1 _aDolzmann, Georg.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aVariational Methods for Crystalline Microstructure - Analysis and Computation
_h[electronic resource] /
_cby Georg Dolzmann.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2003.
300 _aXI, 217 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
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_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1803
505 0 _aIntroduction -- Semiconvex Hull of Compact Sets -- Macroscopic Energy for Nematic Elastomers -- Uniqueness and Stability of Microstructure -- Applications to Martensitic Transformations -- Algorithmic Aspects -- Bibliographic Remarks -- A. Convexity Conditions and Rank-one Connections -- B. Elements of Crystallography -- C. Notation -- References -- Index.
520 _aPhase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, often referred to as mathematical materials science, with deep connections to the calculus of variations and the theory of partial differential equations. This volume gives a brief introduction to the essential physical background, in particular for shape memory alloys and a special class of polymers (nematic elastomers). Then the underlying mathematical concepts are presented with a strong emphasis on the importance of quasiconvex hulls of sets for experiments, analytical approaches, and numerical simulations.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aNumerical analysis.
650 0 _aMathematical physics.
650 0 _aMechanics.
650 1 4 _aMathematics, general.
_0http://scigraph.springernature.com/things/product-market-codes/M00009
650 2 4 _aCondensed Matter Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P25005
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aClassical Mechanics.
_0http://scigraph.springernature.com/things/product-market-codes/P21018
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662189177
776 0 8 _iPrinted edition:
_z9783540001140
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1803
856 4 0 _uhttps://doi.org/10.1007/b10191
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