## 606 Citations

A mesoscopic thermomechanically coupled model for thin-film shape-memory alloys by dimension reduction and scale transition

- Materials Science
- 2014

We design a new mesoscopic thin-film model for shape-memory materials which takes into account thermomechanical effects. Starting from a microscopic thermodynamical bulk model, we guide the reader…

On the interplay of anisotropy and geometry for polycrystals in single‐slip crystal plasticity

- MathematicsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- 2022

In this paper, we investigate a variational polycrystalline model in finite crystal plasticity with one active slip system and rigid elasticity. The task is to determine inner and outer bounds on the…

Variational modelling of nematic elastomer foundations

- MathematicsMathematical Models and Methods in Applied Sciences
- 2018

We compute the [Formula: see text]-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic…

Relaxation in crystal plasticity with three active slip systems

- Materials Science
- 2016

We study a variational model for finite crystal plasticity in the limit of rigid elasticity. We focus on the case of three distinct slip systems whose slip directions lie in one plane and are rotated…

The mechanics of deformation–induced subgrain–dislocation structures in metallic crystals at large strains

- Materials ScienceProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2003

We present a streamlined limiting case of the theory of Oritz & Repetto for crystals with microstructure in which the crystals are assumed to exhibit infinitely strong latent hardening. We take this…

Modeling of shape-memory alloys on the mesoscopic level

- Physics
- 2009

This contribution presents some recent results on modeling of phase transformation in the pseudo-elastic regime within the framework of continuum mechanics, and focuses on simulation results obtained by the presented model, performed on a single-crystal prismatic NiTi-specimen.

A sharp interface evolutionary model for shape memory alloys

- Materials Science
- 2015

We show the existence of an energetic solution to a quasistatic evolutionary model of shape memory alloys. Elastic behavior of each material phase/variant is described by polyconvex energy density.…

Dissipative Evolution of Microstructure in Shape Memory Alloys

- Materials Science
- 2000

This contribution surveys models for evolution of twinning and inelastic response of crystallic materials due to martensitic phase transformations. Then a focus is devoted to a “mesoscopical”…

Dislocation Microstructures and the Effective Behavior of Single Crystals

- Materials Science
- 2005

Abstract.We consider single-crystal plasticity in the limiting case of infinite latent hardening, which signifies that the crystal must deform in single slip at all material points. This requirement…

## References

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- Mathematics
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We study solutions of the two-well problem, i.e., maps which satisfy uεSO(n)A∪SO(n)B a.c. in Ω ⊂ℝn, where A and B are n×n matrices with positive determinants. This problem arises in the study of…

Dynamics of Labyrinthine Pattern Formation in Magnetic Fluids: A Mean‐Field Theory

- Physics
- 1998

Abstract.A viscous ferroliquid is trapped between two narrowly spaced parallel sheets of glass, the Hele‐Shaw cell. The ferroliquid fills a cylindrical domain with cross section Ω and the rest of the…

A model for twinning

- Mathematics
- 1986

The modelling of twins in crystals with strain gradient theories provides interesting problems both in thermodynamics and in the calculus of variations. Here, Dunn and Serrin's thermomechanical…

Proposed experimental tests of a theory of fine microstructure and the two-well problem

- Materials SciencePhilosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences
- 1992

Predictions are made based on an analysis of a new nonlinear theory of martensitic transformations introduced by the authors. The crystal is modelled as a nonlinear elastic material, with a…

Branching of twins near an austenite—twinned-martensite interface

- Materials Science
- 1992

Abstract We study the role of surface energy in determining twin width near an austenite—twinned-martensite interface. We find that there are two distinct regimes, depending on the relative values of…

Microstructures, phase transitions and geometry

- Materials Science
- 1998

Microstructures are structures on a scale between the atomic scale and the macroscopic scale on which we usually make observations. They are abundant in natural and man-made materials, and often the…

Microtwin sequences in thermoelastic NixAl100-x martensite studied by conventional and high-resolution transmission electron microscopy

- Materials Science
- 1993

Abstract Microtwin sequences in thermoelastic NixAl100-x martensite plates of different size and composition (62·5↬x↬66·0) were investigated by conventional and highresolution electron microscopy.…