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
Revisiting brittle fracture as an energy minimization problem
TL;DR: In this paper, a variational model of quasistatic crack evolution is proposed, which frees itself of the usual constraints of that theory : a preexisting crack and a well-defined crack path.
Journal ArticleDOI
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications
TL;DR: In this paper, a review of continuum-based variational formulations for describing the elastic-plastic deformation of anisotropic heterogeneous crystalline matter is presented and compared with experiments.
Journal ArticleDOI
A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy
TL;DR: In this paper, the shape memory effect due to martensitic transformation and reorientation of polycrystalline shape memory alloy (SMA) materials is modeled using a free energy function and a dissipation potential.
Journal ArticleDOI
High temperature shape memory alloys
TL;DR: Shape memory alloys (SMAs) with high transformation temperatures can enable simplifications and improvements in operating efficiency of many mechanical components designed to operate at tem... as mentioned in this paper, which can enable simplified and improved operating efficiency.
Journal ArticleDOI
Proposed experimental tests of a theory of fine microstructure and the two-well problem
John M. Ball,Richard D. James +1 more
TL;DR: In this paper, the authors make predictions based on an analysis of a new nonlinear theory of martensitic transformations introduced by the authors, where the crystal is modelled as a nonlinear elastic material, with a free-energy function that is invariant with respect to both rigid-body rotations and the appropriate crystallographic symmetries.
References
More filters
Journal ArticleDOI
Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity
TL;DR: In this article, the existence of singular solutions to the nonlinear elastostatics problem with respect to radial motion has been studied for a class of strongly elliptic materials by means of the direct method of the calculus of variations, and it has been shown that the only radial equilibrium solutions without cavities are homogeneous.
Journal ArticleDOI
Lectures on the Calculus of Variations and Optimal Control Theory.
Hans Sagan,L. C. Young +1 more
Journal ArticleDOI
W1,p-quasiconvexity and variational problems for multiple integrals
John M. Ball,François Murat +1 more
TL;DR: In this article, a new condition on g, called W 1,p-quasiconvexity is introduced which generalizes in a natural way the quasiconvxity condition of C. B. Morrey, it being shown in particular necessary for sequential weak lower semicontinuity of I Ω and for the existence of minimizers for certain related integrals.