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Archive for Rational Mechanics and Analysis

, Volume 207, Issue 1, pp 39–74 | Cite as

Non-Laminate Microstructures in Monoclinic-I Martensite

  • Isaac Vikram Chenchiah
  • Anja Schlömerkemper
Article

Abstract

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 T 3s, which are (non-trivial) symmetrised rank-one convex hulls of three-tuples of pairwise incompatible strains. In addition, we construct a fivedimensional continuum of T 3s 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, as 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.

Keywords

Martensite Hull Convex Hull Convex Cone Transformation Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.School of MathematicsUniversity of Bristol, University WalkBristolUK
  2. 2.Chair of Mathematics in the Sciences, Institute for MathematicsUniversity of WürzburgWürzburgGermany

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