## Non-laminate microstructures in monoclinic-I martensite

Please always quote using this URN: urn:nbn:de:bvb:20-opus-72134

- We study the symmetrised rank-one convex hull of monoclinic-I martensite (a twelve-variant material) in the context of geometrically-linear elasticity. We construct sets of T3s, which are (non-trivial) symmetrised rank-one convex hulls of 3-tuples of pairwise incompatible strains. Moreover we construct a five-dimensional continuum of T3s and show that its intersection with the boundary of the symmetrised rank-one convex hull is four-dimensional. We also show that there is another kind of monoclinic-I martensite with qualitatively differentWe study the symmetrised rank-one convex hull of monoclinic-I martensite (a twelve-variant material) in the context of geometrically-linear elasticity. We construct sets of T3s, which are (non-trivial) symmetrised rank-one convex hulls of 3-tuples of pairwise incompatible strains. Moreover we construct a five-dimensional continuum of T3s and show that its intersection with the boundary of the symmetrised rank-one convex hull is four-dimensional. We also show that there is another kind of monoclinic-I martensite with qualitatively different semi-convex hulls which, so far as we know, has not been experimentally observed. Our strategy is to combine understanding of the algebraic structure of symmetrised rank-one convex cones with knowledge of the faceting structure of the convex polytope formed by the strains.…

Author: | Isaac Chenchiah, Anja Schlömerkemper |
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URN: | urn:nbn:de:bvb:20-opus-72134 |

Document Type: | Journal article |

Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |

Language: | English |

Year of Completion: | 2012 |

Source: | Archive for Rational Mechanics and Analysis, 2012, doi:10.1007/s00205-012-0552-1, http://www.springerlink.com/content/a294348v770061h2/, sowie Postprint-Version unter http://arxiv.org/abs/1201.6679 |

Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |

GND Keyword: | Martensit; Mehrskalenmodell; Phasenumwandlung; Variationsrechnung |

Tag: | T3s; geometrisch lineare Elastizitätstheorie; kubisch-monokliner Phasenübergang; semi-konvexe HüllenT3s; cubic-monoclinic martensites; geometrically linear elasticity; semi-convex hulls |

MSC-Classification: | 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Nxx Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26] / 74N15 Analysis of microstructure |

Release Date: | 2012/10/02 |

Contributing Corporation: | School of Mathematics, University of Bristol, UK |

Licence (German): | Deutsches Urheberrecht |