185 research outputs found
Cracks Cleave Crystals
The problem of finding what direction cracks should move is not completely
solved. A commonly accepted way to predict crack directions is by computing the
density of elastic potential energy stored well away from the crack tip, and
finding a direction of crack motion to maximize the consumption of this energy.
I provide here a specific case where this rule fails. The example is of a crack
in a crystal. It fractures along a crystal plane, rather than in the direction
normally predicted to release the most energy. Thus, a correct equation of
motion for brittle cracks must take into account both energy flows that are
described in conventional continuum theories and details of the environment
near the tip that are not.Comment: 6 page
Some exact results for the velocity of cracks propagating in non-linear elastic models
We analyze a piece-wise linear elastic model for the propagation of a crack
in a stripe geometry under mode III conditions, in the absence of dissipation.
The model is continuous in the propagation direction and discrete in the
perpendicular direction. The velocity of the crack is a function of the value
of the applied strain. We find analytically the value of the propagation
velocity close to the Griffith threshold, and close to the strain of uniform
breakdown. Contrary to the case of perfectly harmonic behavior up to the
fracture point, in the piece-wise linear elastic model the crack velocity is
lower than the sound velocity, reaching this limiting value at the strain of
uniform breakdown. We complement the analytical results with numerical
simulations and find excellent agreement.Comment: 9 pages, 13 figure
Supersonic crack propagation in a class of lattice models of Mode III brittle fracture
We study a lattice model for mode III crack propagation in brittle materials
in a stripe geometry at constant applied stretching. Stiffening of the material
at large deformation produces supersonic crack propagation. For large
stretching the propagation is guided by well developed soliton waves. For low
stretching, the crack-tip velocity has a universal dependence on stretching
that can be obtained using a simple geometrical argument.Comment: 4 pages, 3 figure
On selection criteria for problems with moving inhomogeneities
We study mechanical problems with multiple solutions and introduce a
thermodynamic framework to formulate two different selection criteria in terms
of macroscopic energy productions and fluxes. Studying simple examples for
lattice motion we then compare the implications for both resting and moving
inhomogeneities.Comment: revised version contains new introduction, numerical simulations of
Riemann problems, and a more detailed discussion of the causality principle;
18 pages, several figure
Vortex-type elastic structured media and dynamic shielding
The paper addresses a novel model of metamaterial structure. A system of
spinners has been embedded into a two-dimensional periodic lattice system. The
equations of motion of spinners are used to derive the expression for the
chiral term in the equations describing the dynamics of the lattice. Dispersion
of elastic waves is shown to possess innovative filtering and polarization
properties induced by the vortextype nature of the structured media. The
related homogenised effective behavior is obtained analytically and it has been
implemented to build a shielding cloak around an obstacle. Analytical work is
accompanied by numerical illustrations.Comment: 24 pages, 13 figure
Discrete models of dislocations and their motion in cubic crystals
A discrete model describing defects in crystal lattices and having the
standard linear anisotropic elasticity as its continuum limit is proposed. The
main ingredients entering the model are the elastic stiffness constants of the
material and a dimensionless periodic function that restores the translation
invariance of the crystal and influences the Peierls stress. Explicit
expressions are given for crystals with cubic symmetry: sc, fcc and bcc.
Numerical simulations of this model with conservative or damped dynamics
illustrate static and moving edge and screw dislocations and describe their
cores and profiles. Dislocation loops and dipoles are also numerically
observed. Cracks can be created and propagated by applying a sufficient load to
a dipole formed by two edge dislocations.Comment: 23 pages, 15 figures, to appear in Phys. Rev.
Thermal Radiation From Carbon Nanotube in Terahertz Range
The thermal radiation from an isolated finite-length carbon nanotube (CNT) is
theoretically investigated both in near- and far-field zones. The formation of
the discrete spectrum in metallic CNTs in the terahertz range is demonstrated
due to the reflection of strongly slowed-down surface-plasmon modes from CNT
ends. The effect does not appear in semiconductor CNTs. The concept of CNT as a
thermal nanoantenna is proposed.Comment: 5 pages, 3 figure
Feeding and dissipative waves in fracture and phase transition.
Abstract Wave conÿgurations for modes I and II of crack propagation in an elastic triangular-cell lattice are studied. [Mode III was considered in Part I of the paper: Slepyan, L.I. Feeding and dissipative waves in fracture and phase transition. I. Some 1D structures and a square-cell lattice. J. Mech. Phys. Solids 4
Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture
We generalize lattice models of brittle fracture to arbitrary nonlinear force
laws and study the existence of arrested semi-infinite cracks. Unlike what is
seen in the discontinuous case studied to date, the range in driving
displacement for which these arrested cracks exist is very small. Also, our
results indicate that small changes in the vicinity of the crack tip can have
an extremely large effect on arrested cracks. Finally, we briefly discuss the
possible relevance of our findings to recent experiments.Comment: submitted to PRE, Rapid Communication
- …