Computational Modeling of Softening in a Structural Phase Transformation

@article{Belk2005ComputationalMO,
  title={Computational Modeling of Softening in a Structural Phase Transformation},
  author={Pavel Bel{\'i}k and Mitchell Luskin},
  journal={Multiscale Model. Simul.},
  year={2005},
  volume={3},
  pages={764-781}
}
We develop a free energy density to model a structural first-order phase transformation from a high-temperature cubic phase to a low-temperature tetragonal phase. The free energy density models the softening of the elastic modulus controlling the low-energy path from the cubic to the tetragonal lattice, the loss of stability of the tetragonal phase at high temperatures, the loss of stability of the cubic phase at low temperatures, and the effect of compositional fluctuation on the… 

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References

SHOWING 1-10 OF 37 REFERENCES

Elastic anomalies in minerals due to structural phase transitions

Landau theory provides a formal basis for predicting the variations of elastic constants associated with phase transitions in minerals. These elastic constants can show substantial anomalies as a

Dynamics of Phase Transitions and Hysteresis in a Viscoelastic Ericksen's Bar on an Elastic Foundation

This work is a follow-up on the study [32] of interface dynamics and hysteresis in materials undergoing solid-solid phase transitions. We consider the dynamics of a viscoelastic bar with a

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

Elastic Energy Minimization and the Recoverable Strains of Polycrystalline Shape‐Memory Materials

Abstract.Shape‐memory behavior is the ability of certain materials to recover, on heating, apparently plastic deformation sustained below a critical temperature. Some materials have good shape‐memory

A phenomenological model for hysteresis in polycrystalline shape memory alloys

We propose a phenomenological model describing stress and temperature induced transformations in polycrystalline shape memory alloys. Polycrystallinity is mimicked on the level of a finite element

Local bifurcation theory for thermoelastic Bravais lattices

Some weak first order phase transitions encountered in shape-memory alloys seem to occur near bifurcations which are not actually observed. Being curious about the nature of these in particular, I