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_a9783540361251 _9978-3-540-36125-1 |
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_a10.1007/b10191 _2doi |
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_aDolzmann, Georg. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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_aVariational Methods for Crystalline Microstructure - Analysis and Computation _h[electronic resource] / _cby Georg Dolzmann. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2003. |
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300 |
_aXI, 217 p. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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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 |
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_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 |
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_iPrinted edition: _z9783662189177 |
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_iPrinted edition: _z9783540001140 |
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_aLecture Notes in Mathematics, _x0075-8434 ; _v1803 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/b10191 |
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