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Numerische Mathematik

, Volume 96, Issue 4, pp 641–660 | Cite as

Multiscale resolution in the computation of crystalline microstructure

  • Sören Bartels
  • Andreas ProhlEmail author
Article

Summary.

This paper addresses the numerical approximation of microstructures in crystalline phase transitions without surface energy. It is shown that branching of different variants near interfaces of twinned martensite and austenite phases leads to reduced energies in finite element approximations. Such behavior of minimizing deformations is understood for an extended model that involves surface energies. Moreover, the closely related question of the role of different growth conditions of the employed bulk energy is discussed. By explicit construction of discrete deformations in lowest order finite element spaces we prove upper bounds for the energy and thereby clarify the question of the dependence of the convergence rate upon growth conditions and lamination orders. For first order laminates the estimates are optimal.

Keywords

Phase Transition Austenite Martensite Surface Energy Lamination 
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 Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Mathematisches Seminar, Christian-Albrechts-Universität zu KielKielGermany
  2. 2.Department of MathematicsETHZZurichSwitzerland

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