# 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

#### 11 Citations

Bounds on precipitate hardening of line and surface defects in solids

- Mathematics, Materials Science
- 2019

#### References

SHOWING 1-10 OF 22 REFERENCES

Depinning transition in the failure of inhomogeneous brittle materials.

- Materials Science, Physics
- Physical review letters
- 2009

Γ-Limit of a Phase-Field Model of Dislocations

- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 2005

Existence of Solutions for a Model Describing the Dynamics of Junctions Between Dislocations

- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 2009