20 research outputs found
Dynamic fracture of a discrete media under moving load
Most of the research concerting crack propagation in discrete media is
concerned with specific types of external loading: displacements on the
boundaries, or constant energy fluxes or feeding waves originating from
infinity. In this paper the action of a moving load is analysed on the simplest
lattice model: a thin strip, where the fault propagating in its middle portion
as the result of the moving force acting on the destroyed part of the
structure. We study both analytically and numerically how the load amplitude
and its velocity influence the possible solution, and specifically the way the
fracture process reaches its steady-state regime. We present the relation
between the possible steady-state crack speed and the loading parameters, as
well as the energy release rate. In particular, we show that there exists a
class of loading regime corresponding to each point on the energy-speed diagram
(and thus determine the same limiting steady-state regime). The phenomenon of
the forbidden regimes is discussed in detail, from both the points of view of
force and energy. For a sufficiently anisotropic structure, we find a stable
steady-state propagation corresponding to the slow crack. Numerical simulations
reveal various ways by which the process approaches - or fails to approach -
the steady-state regime. The results extend our understanding of fracture
processes in discrete structures, and reveal some new questions that should be
addressed
Universality classes of transition fronts in the FPU model
Steady transition fronts in nonlinear lattices are among the most important
dynamic coherent structures. We use the Fermi-Pasta-Ulam model with piecewise
linear nonlinearity to show that there are exactly three distinct classes of
such fronts which differ fundamentally in how (and whether) they produce and
transport oscillations. To make this Hamiltonian problem analytically
transparent, we construct a quasicontinuum approximation generating all three
types of fronts and then show that the interconnection between different
classes of fronts in the original discrete model is the same as in the
quasicontinuum model. The proposed framework unifies previous attempts to
classify the transition fronts as radiative, dispersive, topological or
compressive and categorizes them instead as different types of dynamic defects
Influence of fracture criteria on dynamic fracture propagation in a discrete chain
The extent to which time-dependent fracture criteria affect the dynamic
behavior of fracture in a discrete structure is discussed in this work. The
simplest case of a semi-infinite isotropic chain of oscillators has been
studied. Two history-dependent criteria are compared to the classical one of
threshold elongation for linear bonds. The results show that steady-state
regimes can be reached in the low subsonic crack speed range where it is
impossible according to the classical criterion. Repercussions in terms of load
and crack opening versus velocity are explained in detail. A strong qualitative
influence of history-dependent criteria is observed at low subsonic crack
velocities, especially in relation to achievable steady-state propagation
regimes
Analysis of dynamic failure of the discrete chain structure with non-local interactions
In the present work the steady-state crack propagation in a chain of
oscillators with non-local interactions is considered. The interactions are
modeled as linear springs while the crack is presented by the absence of extra
springs. The problem is reduced to the Wiener-Hopf type and solution is
presented in terms of inverse Fourier transform. It is shown that the non-local
interactions may change the structure of the problem solution well-known from
the classical local interactions formulation. In particular, it may change the
range of the region of stable crack motion. The conclusions of the analysis are
supported by numerical results. Namely, the observed phenomenon is partially
clarified by evaluation of the structure profiles on the crack line ahead