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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Book ChapterDOI
Microstructures, phase transitions and geometry
TL;DR: In this article, the authors introduce the concept of microstructures, which are structures on a scale between the atomic scale and the macroscopic scale on which we usually make observations.
Journal ArticleDOI
Computations of needle-like microstructures
TL;DR: In this article, numerical results on the computation of needle-like microstructures at mesoscopic scale obtained by applying the mesh transformation method, which basically includes a mesh optimization into the finite element approximations, on a nonquasiconvex elastic crystal model.
Journal ArticleDOI
When Rank-One Convexity Meets Polyconvexity: An Algebraic Approach to Elastic Binodal
Yury Grabovsky,Lev Truskinovsky +1 more
TL;DR: A systematic methodology for identifying a part of the binodal corresponding to simple laminates by showing that in this case the supporting null-Lagrangians, establishing polyconvexity, can be constructed explicitly.
Journal ArticleDOI
Theory and finite element computations of a unified cyclic phase transformation model for monocrystalline materials at small strains
Erwin Stein,Ole Zwickert +1 more
TL;DR: In this article, a rate-independent macroscopic unified PT material model (including mass conservation with respect to phase fractions and covexified free energy) is presented for describing SME and SE effects within a linear kinematic setting.
Book ChapterDOI
On SO(n)-Invariant Rank 1 Convex Functions
TL;DR: A necessary and sufficient condition for the rank 1 convexity of a function defined on the set n×n of all real square matrices of order n is given in this paper.
References
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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
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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.