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
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Crystallography Study on the Internal Twinning of Ti–Nb‐Based Shape Memory Alloys
Journal ArticleDOI
A comparison of classical and new finite element methods for the computation of laminate microstructure
TL;DR: A geometrically nonlinear continuum theory has been developed for the equilibria of martensitic crystals based on elastic energy minimization as mentioned in this paper, and detailed numerical studies of the available finite element discretizations in this paper validate the theory.
Journal ArticleDOI
Adaptive algorithms for scalar non-convex variational problems
Carsten Carstensen,Petr Plecháč +1 more
TL;DR: This paper addresses the question of efficiency and considers the ZZ-indicator, named after Zienkiewicz and Zhu, and discusses its performance compared with the rigorous indicator introduced by the authors.
Journal ArticleDOI
Functionals defined on piecewise rigid functions: Integral representation and $\Gamma$-convergence
TL;DR: In this article, integral representation and convergence properties of functionals defined on piecewise rigid functions have been analyzed, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is constant and lies in a set without rank-one connections.
Journal ArticleDOI
Numerical energy relaxation to model microstructure evolution in functional magnetic materials
TL;DR: In this paper, an energy relaxation-based approach for the modeling of magnetostriction, with a particular focus on single crystalline magnetic shape memory alloy response, is proposed, and the key features that characterize the extended approach are (i) the incorporation of elastic deformations, whose distribution among the individual phases occurs in an energy minimizing fashion, (ii) a finite magnetocrystalline anisotropy energy, that allows magnetization rotations away from easy axes, and (iii) dissipative effects, that are accounted for in an incremental variational setting for standard dissipative materials
References
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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.