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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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.
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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
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Journal ArticleDOI
On the existence of solutions to some problems of optimal design for bars and plates
Abstract: The problem of the optimal control of the material characteristics of continuous media necessitates an extension of the initial class of materials to the set of composites assembled from elements belonging to the initial class Such an extension guarantees the existence of an optimal control and is equivalent to the construction of theG-closureGU of the initial setU In this paper, we consider some problems of constructingG-closures for the operators ▽·2D·▽ and ▽·▽·4D··▽▽, where2D and4D denote self-adjoint tensors of 2nd and 4th rank, respectively, their components belonging to bounded sets ofL∞ These operators arise in the theory of the torsion of bars and in the theory of bending of thin plates A procedure is suggested that provides estimates of some sets Σ containingGU These estimates are expressed through weak limits of certain functions of the elements of theU-set The estimates are based on the weak convergence of the elastic energy and, for operators of 4th order, also on the weak convergence of the second invariant of deformation,
$$I_2 (e) = w_{xx} w_{yy} - w_{xy}^2 - I_2 (e^0 ) = w_{xx}^0 w_{yy}^0 - (w_{xy}^0 )^2 $$
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Explicit relaxation of a variational problem in optimal design
TL;DR: For vector-valued functions u on Lipschitz domains Q c R, the left side of (1) is a problem of optimal design: it minimizes Area(H \ S) + fQ \Vus\ 2 dx, among all sets S c O , where us solves the variational problem.