Journal ArticleDOI
Fine phase mixtures as minimizers of energy
TLDR
In this article, the authors explore a theoretical approach to these fine phase mixtures based on the minimization of free energy and show that the α-phase breaks up into triangular domains called Dauphine twins which become finer and finer in the direction of increasing temperature.Abstract:
Solid-solid phase transformations often lead to certain characteristic microstructural features involving fine mixtures of the phases. In martensitic transformations one such feature is a plane interface which separates one homogeneous phase, austenite, from a very fine mixture of twins of the other phase, martensite. In quartz crystals held in a temperature gradient near the α-β transformation temperature, the α-phase breaks up into triangular domains called Dauphine twins which become finer and finer in the direction of increasing temperature. In this paper we explore a theoretical approach to these fine phase mixtures based on the minimization of free energy.read more
Citations
More filters
Journal ArticleDOI
Discontinuous Order Parameters in Liquid Crystal Theories
John M. Ball,S. J. Bedford +1 more
TL;DR: In this paper, the authors focus on various issues surrounding the mathematical description of defects in models of liquid crystals, drawing on experience from solid mechanics, and highlight the roles played by a suitable choice of function space and by the growth properties of the free-energy density.
Journal ArticleDOI
Optimal use of the translation method and relaxations of variational problems
TL;DR: The optimal translation bound proves to be a better general lower bound on relaxations of variational problems than is the polyconvexification in three dimensions.
Journal ArticleDOI
Adaptive finite element methods for microstructures? Numerical experiments for a 2-well benchmark
Carsten Carstensen,K. Jochimsen +1 more
TL;DR: Despite the theoretical reliability-efficiency gap for the relaxed problem, numerical evidence supports that adaptive mesh-refining algorithms generate efficient triangulations and improve the experimental convergence rates optimally.
Journal ArticleDOI
Numerical approximation of parametrized measures
TL;DR: In this paper, an alternative approach to the numerical analysis of oscillations of nonconvex variational problems, based on the approximation of the underlying parametrized measure itself, is retaken.
Journal ArticleDOI
On Deformation of A-M Interface in Single Crystal Shape Memory Alloys and Some Related Issues
TL;DR: In this paper, two kinds of austenite-martensite (A-M) interfaces with different deformation features are identified and some fundamental issues on the property of A-M interface and the related micro- and macro-deformation features were discussed.
References
More filters
Journal ArticleDOI
Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen
TL;DR: In this article, the Berechnung der dielektrizitatatkonstanten and der Leitfahigkeiten fur Elektriatitat and Warme der Mischkorper aus isotropen Bestandteilen behandelt.
Book
The theory of transformations in metals and alloys : an advanced textbook in physical metallurgy
Journal ArticleDOI
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
Book
The theory of transformations in metals and alloys
J.W. Christian,H. M. Otte +1 more
TL;DR: In this paper, the authors present a general introduction to the theory of transformation kinetics of real metals, including the formation and evolution of martensitic transformations, as well as a theory of dislocations.