04246nam 22008535 450 991014463460332120220524164641.03-540-36125-110.1007/b10191(CKB)1000000000229428(SSID)ssj0000327536(PQKBManifestationID)12116680(PQKBTitleCode)TC0000327536(PQKBWorkID)10301753(PQKB)10074579(DE-He213)978-3-540-36125-1(MiAaPQ)EBC6281600(MiAaPQ)EBC5592095(Au-PeEL)EBL5592095(OCoLC)1066179083(PPN)155180339(EXLCZ)99100000000022942820121227d2003 u| 0engurnn#008mamaatxtccrVariational Methods for Crystalline Microstructure - Analysis and Computation /by Georg Dolzmann1st ed. 2003.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2003.1 online resource (XI, 217 p.)Lecture Notes in Mathematics,0075-8434 ;1803Bibliographic Level Mode of Issuance: Monograph3-540-00114-X Introduction -- 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.Phase 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.Lecture Notes in Mathematics,0075-8434 ;1803MathematicsCondensed matterPartial differential equationsNumerical analysisPhysicsMechanicsMathematics, generalhttps://scigraph.springernature.com/ontologies/product-market-codes/M00009Condensed Matter Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P25005Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Classical Mechanicshttps://scigraph.springernature.com/ontologies/product-market-codes/P21018Mathematics.Condensed matter.Partial differential equations.Numerical analysis.Physics.Mechanics.Mathematics, general.Condensed Matter Physics.Partial Differential Equations.Numerical Analysis.Mathematical Methods in Physics.Classical Mechanics.620.1129974N15msc65M20msc74B20mscDolzmann Georgauthttp://id.loc.gov/vocabulary/relators/aut67423MiAaPQMiAaPQMiAaPQBOOK9910144634603321Variational methods for crystalline microstructure - analysis and computation2983363UNINA