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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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
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Lyapunov Functions for Thermomechanics with Spatially Varying Boundary Temperatures
TL;DR: In this paper, a continuous body subjected to conservative body and surface forces, with a part ∂Ω 2 of the boundary maintained at a temperature θ = θ 0(X) and with the remainder of boundary thermally insulated, is considered.
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Some Examples of Crinkles
TL;DR: In this paper, the authors discuss the problem of minimizing a given energy functional E[f] over a given class of admissible functions f under the assumption that the derivatives # are highly discontinuous and do not approach f in the limit.
Journal ArticleDOI
On failure of the complementing condition and nonuniqueness in linear elastostatics
Journal Article
Characteristics of stress-strain behaviour associated with thermoelastic martensitic transformation
TL;DR: The transformations martensitique thermoelastique as discussed by the authors are transformations du reseau without diffusion concernant des faibles deplacements d'atomes, and there exist a relation d'orientation entre la phase initiale and la martensite, sur le plan d'accolement.