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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Necessary Conditions at the Boundary for Minimizers in Finite Elasticity
TL;DR: In this article, the authors derived pointwise algebraic conditions on the elasticity tensor C(x, ∇f(x)) that are necessary for a deformation f to be a local minimizer of the energy of an elastic body that is subjected to dead loads.
Journal ArticleDOI
Dynamic stability of non–minimizing phase mixtures
Gero Friesecke,J. B. McLeod +1 more
TL;DR: In this paper, the dynamics of pattern formation in the one-dimensional partial differential equation (PDE) was studied and proved to be locally dynamically stable (theorem 1.1), and other properties of these equilibria were investigated.
Journal ArticleDOI
Macroscopic constitutive relations for elastomers reinforced with short aligned fibers: Instabilities and post-bifurcation response
TL;DR: In this article, a lower energy, post-bifurcation solution is constructed where "striped domain" microstructures consisting of layers with alternating fiber orientations develop in the composite.
Journal ArticleDOI
The two-well problem in three dimensions
TL;DR: In this paper, the authors studied the properties of generalized convex hulls of the set K = {SO 3, SO 4, SO 5, SO 6, SO 7, SO 8, SO 9, SO 10, SO 11, SO 12, SO 13, SO 14, SO 15, SO 16, SO 17, SO 18, SO 19, SO 20, SO 21, SO 22, SO 23, SO 24, SO 25, SO 30, SO 32, SO 34, SO 35, SO 36, SO 39, SO 40, SO 41, SO
Journal ArticleDOI
A two well liouville theorem
TL;DR: In this paper, the authors analyse the structure of approximate solutions to the compatible two well problem with the constraint that the surface energy of the solution is less than some fixed constant and prove a quantitative estimate that can be seen as a two well analogue of the Liouville theorem of Friesecke James Muller.
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.