# Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model

@article{Plans2008HomogeneousNO, title={Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model}, author={I. Plans and Ana Carpio and Luis L. Bonilla}, journal={EPL}, year={2008}, volume={81}, pages={36001} }

A novel analysis of homogeneous nucleation of dislocations in sheared two-dimensionalcrystals described by periodized-discrete-elasticity models is presented. When the crystal issheared beyond a critical strain F = Fc, the strained dislocation-free state becomes unstable via a subcritical pitchfork bifurcation. Selecting a fixed final applied strain Ff >Fc, different simultaneously stable stationary configurations containing two or four edge dislocations may be reached by setting F = Ff t/tr… Expand

#### 16 Citations

Homogeneous nucleation of dislocations

- Materials Science
- 2011

When a two-dimensional crystal described by a dissipative discrete elasticity model is sheared beyond a critical stress F = Fc, the strained dislocationfree state becomes unstable via a subcritical… Expand

Discontinuous yielding of pristine micro-crystals

- Physics
- 2021

We study the mechanical response of a dislocation-free 2D crystal under homogenous shear using a new mesoscopic approach to crystal plasticity, a Landau-type theory, accounting for the global… Expand

Toy nanoindentation model and incipient plasticity

- Materials Science, Physics
- 2009

A toy model of two dimensional nanoindentation in finite crystals is proposed. The crystal is described by periodized discrete elasticity whereas the indenter is a rigid strain field of triangular… Expand

Dynamics and nucleation of dislocations in crystals

- Materials Science
- 2007

Periodized discrete elasticity models [1, 2, 3] are the simplest correction to linear elasticity equations allowing for nucleation and motion of dislocations in crystals. Two ingredients are needed… Expand

Landau-Type Theory of Planar Crystal Plasticity.

- Physics, Medicine
- Physical review letters
- 2019

We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as a Landau theory with an infinite number of equivalent energy wells whose… Expand

Dislocations in graphene

- Physics, Materials Science
- 2008

We study the stability and evolution of various elastic defects in a flat graphene sheet and the electronic properties of the most stable configurations. Two types of dislocations are found to be… Expand

Nucleation of Dislocations in 3.9 nm Nanocrystals at High Pressure.

- Physics, Materials Science
- Physical review letters
- 2020

The formation of dislocations within individual 3.9 nm Au nanocrystals under nonhydrostatic pressure in a diamond anvil cell is reported, indicating thatdislocations are still active at single nanometer length scales and can lead to permanent plasticity. Expand

A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory

- Physics
- 2014

Crack initiation under dynamic loading conditions is studied under the framework of dynamic bifurcation theory. An atomistic model for BCC iron is considered to explicitly take into account the… Expand

Defects, singularities and waves

- Materials Science
- 2007

Crystal defects such as dislocations are the basis of macroscopic properties such as the strength of materials and control their mechanical, optical and electronic properties. In recent times,… Expand

On the critical nature of plastic flow: one and two dimensional models

- Physics, Mathematics
- 2012

Steady state plastic flows have been compared to developed turbulence because the two phenomena share the inherent complexity of particle trajectories, the scale free spatial patterns and the power… Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

Pop-in effect as homogeneous nucleation of dislocations during nanoindentation

- Materials Science
- 2003

Using advanced depth-sensitive hardness measurements, the homogenous nucleation of dislocations has been observed in dislocation-free single crystals. This process is related to a sudden displacement… Expand

Discrete models of dislocations in crystal lattices: formulation, analysis and applications

- Physics
- 2007

Real crystal lattices are not perfect. They have defects such as dislocations, vacancies, and cracks that control the mechanical properties of materials, including crystal plasticity, creep, fatigue,… Expand

Dislocation emission around nanoindentations on a (001) fcc metal surface studied by scanning tunneling microscopy and atomistic simulations.

- Materials Science, Medicine
- Physical review letters
- 2002

Simulations reproduce the nucleation and glide of these dislocation loops that originate from loops of interstitial character emitted along the <110> directions and are usually located at hundreds of angstroms away from the indentation point. Expand

Nature

- Medicine
- Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery
- 2009

I am writing with a simple plea to balance the voluminous articles about treatment in your journal with a modicum of information about nature and caring effects to rekindle the perception of physicians as healers, not only treaters, who relish the gifts of nature, and foster the humanistic aspect of medicine that has thrived for millennia. Expand

Physica A

- Physica A
- 2007

Computer simulations of dislocations (Oxford

- 2006

Phys. Rev. B

- Phys. Rev. B
- 2006

Phys. Rev. B

- Phys. Rev. B
- 2006

Phys. Rev. B

- Phys. Rev. B
- 2005

J. Mech. Phys. Solids

- J. Mech. Phys. Solids
- 2004