586 research outputs found
Fluid-plasticity of thin cylindrical shells
Dynamic plastic response of a thin cylindrical shell, immersed in a potential fluid initially at rest and subjected to internal pressure pulse of arbitrary shape and duration, is examined. The shell is assumed to respond as a rigid-perfectly plastic material while the fluid is taken as inviscid and incompressible. The fluid back pressure is incorporated into the equation of motion of the shell as an added mass term. Since arbitrary pulses can be reduced to equivalent rectangular pulses, the equation of motion is solved only for a rectangular pulse. The influence of the fluid in reducing the final plastic deformation is demonstrated by a numerical example
Statistical mechanics of damage phenomena
This paper applies the formalism of classical, Gibbs-Boltzmann statistical
mechanics to the phenomenon of non-thermal damage. As an example, a non-thermal
fiber-bundle model with the global uniform (meanfield) load sharing is
considered. Stochastic topological behavior in the system is described in terms
of an effective temperature parameter thermalizing the system. An equation of
state and a topological analog of the energy-balance equation are obtained. The
formalism of the free energy potential is developed, and the nature of the
first order phase transition and spinodal is demonstrated.Comment: Critical point appeared to be a spinodal poin
Acoustic Emission Monitoring of the Syracuse Athena Temple: Scale Invariance in the Timing of Ruptures
We perform a comparative statistical analysis between the acoustic-emission time series from the ancient Greek Athena temple in Syracuse and the sequence of nearby earthquakes. We find an apparent association between acoustic-emission bursts and the earthquake occurrence. The waiting-time distributions for acoustic-emission and earthquake time series are described by a unique scaling law indicating self-similarity over a wide range of magnitude scales. This evidence suggests a correlation between the aging process of the temple and the local seismic activit
Ordering effect of kinetic energy on dynamic deformation of brittle solids
The present study focuses on the plane strain problem of medium-to-high strain-rate loading of an idealized brittle material with random microstructure. The material is represented by an ensemble of “continuum particles” forming a two-dimensional geometrically and structurally disordered lattice. Performing repeated lattice simulations for different physical realizations of the microstructural statistics offers possibility to investigate universal trends in which the disorder and loading rate influence mechanical behavior of the material. The dynamic simulations of the homogeneous uniaxial tension test are performed under practically identical inplane conditions although they span nine decades of strain rate. The results indicate that the increase of the dynamic strength with the loading-power increase is also accompanied with a significant reduction of the strength dispersion. At the same time, increase in the loading rate results in transition from random to deterministic damage evolution patterns. This ordering effect of kinetic energy is attributed to the diminishing flaw sensitivity of brittle materials with the loading-rate increase. The uniformity of damage evolution patterns indicates an absence of the cooperative phenomena in the upper strain-rate range, in opposition to the coalescence of microcracks into microcrack clouds, which may represent the dominant toughening mechanism in brittle materials not susceptible to dislocation activities
Applicability and non-applicability of equilibrium statistical mechanics to non-thermal damage phenomena: II. Spinodal behavior
This paper investigates the spinodal behavior of non-thermal damage
phenomena. As an example, a non-thermal fiber-bundle model with the global
uniform (meanfield) load sharing is considered. In the vicinity of the spinodal
point the power-law scaling behavior is found. For the meanfield fiber-bundle
model the spinodal exponents are found to have typical meanfield values.Comment: Version related: More careful explanation for the critical
slowing-down. General: The topological properties of non-thermal damage are
described by the formalism of statistical mechanics. This is the continuation
of arXiv:0805.0346. Comments, especially negative, are very welcom
Universality behind Basquin's law of fatigue
One of the most important scaling laws of time dependent fracture is
Basquin's law of fatigue, namely, that the lifetime of the system increases as
a power law with decreasing external load amplitude, , where the exponent has a strong material
dependence. We show that in spite of the broad scatter of the Basquin exponent
, the fatigue fracture of heterogeneous materials exhibits intriguing
universal features. Based on stochastic fracture models we propose a generic
scaling form for the macroscopic deformation and show that at the fatigue limit
the system undergoes a continuous phase transition when changing the external
load. On the microlevel, the fatigue fracture proceeds in bursts characterized
by universal power law distributions. We demonstrate that in a range of
systems, including deformation of asphalt, a realistic model of deformation,
and a fiber bundle model, the system dependent details are contained in
Basquin's exponent for time to failure, and once this is taken into account,
remaining features of failure are universal.Comment: 4 pages in Revtex, 4 figures, accepted by PR
A simplified multiscale damage model for the transversely isotropic shale rocks under tensile loading
Oscillatory Finite-Time Singularities in Finance, Population and Rupture
We present a simple two-dimensional dynamical system where two nonlinear
terms, exerting respectively positive feedback and reversal, compete to create
a singularity in finite time decorated by accelerating oscillations. The power
law singularity results from the increasing growth rate. The oscillations
result from the restoring mechanism. As a function of the order of the
nonlinearity of the growth rate and of the restoring term, a rich variety of
behavior is documented analytically and numerically. The dynamical behavior is
traced back fundamentally to the self-similar spiral structure of trajectories
in phase space unfolding around an unstable spiral point at the origin. The
interplay between the restoring mechanism and the nonlinear growth rate leads
to approximately log-periodic oscillations with remarkable scaling properties.
Three domains of applications are discussed: (1) the stock market with a
competition between nonlinear trend-followers and nonlinear value investors;
(2) the world human population with a competition between a
population-dependent growth rate and a nonlinear dependence on a finite
carrying capacity; (3) the failure of a material subjected to a time-varying
stress with a competition between positive geometrical feedback on the damage
variable and nonlinear healing.Comment: Latex document of 59 pages including 20 eps figure
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