21 research outputs found
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
Steady-State Cracks in Viscoelastic Lattice Models II
We present the analytic solution of the Mode III steady-state crack in a
square lattice with piecewise linear springs and Kelvin viscosity. We show how
the results simplify in the limit of large width. We relate our results to a
model where the continuum limit is taken only along the crack direction. We
present results for small velocity, and for large viscosity, and discuss the
structure of the critical bifurcation for small velocity. We compute the size
of the process zone wherein standard continuum elasticity theory breaks down.Comment: 17 pages, 3 figure
Does the continuum theory of dynamic fracture work?
We investigate the validity of the Linear Elastic Fracture Mechanics approach
to dynamic fracture. We first test the predictions in a lattice simulation,
using a formula of Eshelby for the time-dependent Stress Intensity Factor.
Excellent agreement with the theory is found. We then use the same method to
analyze the experiment of Sharon and Fineberg. The data here is not consistent
with the theoretical expectation.Comment: 4 page
Oscillatory wave fronts in chains of coupled nonlinear oscillators
Wave front pinning and propagation in damped chains of coupled oscillators
are studied. There are two important thresholds for an applied constant stress
: for (dynamic Peierls stress), wave fronts fail to propagate,
for stable static and moving wave fronts coexist, and
for (static Peierls stress) there are only stable moving wave
fronts. For piecewise linear models, extending an exact method of Atkinson and
Cabrera's to chains with damped dynamics corroborates this description. For
smooth nonlinearities, an approximate analytical description is found by means
of the active point theory. Generically for small or zero damping, stable wave
front profiles are non-monotone and become wavy (oscillatory) in one of their
tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.
Energy radiation of moving cracks
The energy radiated by moving cracks in a discrete background is analyzed.
The energy flow through a given surface is expressed in terms of a generalized
Poynting vector. The velocity of the crack is determined by the radiation by
the crack tip. The radiation becomes more isotropic as the crack velocity
approaches the instability threshold.Comment: 7 pages, embedded figure
Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators
We present a stability theory for kink propagation in chains of coupled
oscillators and a new algorithm for the numerical study of kink dynamics. The
numerical solutions are computed using an equivalent integral equation instead
of a system of differential equations. This avoids uncertainty about the impact
of artificial boundary conditions and discretization in time. Stability results
also follow from the integral version. Stable kinks have a monotone leading
edge and move with a velocity larger than a critical value which depends on the
damping strength.Comment: 11 figure
Beyond Kinetic Relations
We introduce the concept of kinetic equations representing a natural
extension of the more conventional notion of a kinetic relation. Algebraic
kinetic relations, widely used to model dynamics of dislocations, cracks and
phase boundaries, link the instantaneous value of the velocity of a defect with
an instantaneous value of the driving force. The new approach generalizes
kinetic relations by implying a relation between the velocity and the driving
force which is nonlocal in time. To make this relations explicit one needs to
integrate the system of kinetic equations. We illustrate the difference between
kinetic relation and kinetic equations by working out in full detail a
prototypical model of an overdamped defect in a one-dimensional discrete
lattice. We show that the minimal nonlocal kinetic description containing now
an internal time scale is furnished by a system of two ordinary differential
equations coupling the spatial location of defect with another internal
parameter that describes configuration of the core region.Comment: Revised version, 33 pages, 9 figure