Effective behavior of an interface propagating through a periodic elastic medium

@article{Dondl2012EffectiveBO,
  title={Effective behavior of an interface propagating through a periodic elastic medium},
  author={P. Dondl and K. Bhattacharya},
  journal={arXiv: Analysis of PDEs},
  year={2012}
}
We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the graph of the function $g$ which evolves according to the equation $g_t (x) = -(-\Delta)^{1/2}g (x) + \varphi(x, g(x)) + F$. This equation also arises in the study of dislocations and fracture. We show in the periodic setting that such interfaces exhibit a stick… Expand

Figures from this paper

Pinning of Interfaces by Localized Dry Friction.
Effective Toughness of Heterogeneous Materials
Bounds on precipitate hardening of line and surface defects in solids
Adhesion of heterogeneous thin films II: Adhesive heterogeneity
Fracture of Materials Undergoing Solid-Solid Phase Transformation
...
1
2
...

References

SHOWING 1-10 OF 22 REFERENCES
Pinning of interfaces in random media
Phase Boundary Propagation in Heterogeneous Media
Depinning transition in the failure of inhomogeneous brittle materials.
  • L. Ponson
  • Materials Science, Physics
  • Physical review letters
  • 2009
Γ-Limit of a Phase-Field Model of Dislocations
Pinning and de-pinning phenomena in front propagation in heterogeneous media
Existence of Solutions for a Model Describing the Dynamics of Junctions Between Dislocations
a Phase-Field Theory of Dislocation Dynamics, Strain Hardening
...
1
2
3
...