Variational models for microstructure and phase transitions

  title={Variational models for microstructure and phase transitions},
  author={Stefan M{\"u}ller},
A mesoscopic thermomechanically coupled model for thin-film shape-memory alloys by dimension reduction and scale transition
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
  • Dominik EnglCarolin Kreisbeck
  • Mathematics
    ZAMM - 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
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
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
  • S. AubryM. Ortiz
  • Materials Science
    Proceedings 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
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
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
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”
Material instabilities in nematic elastomers
Dislocation Microstructures and the Effective Behavior of Single Crystals
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


Microstructures with finite surface energy: the two-well problem
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
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
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
  • J. BallR. JamesF. Smith
  • Materials Science
    Philosophical 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
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
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
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.