198 research outputs found
Anomalous strength of membranes with elastic ridges
We report on a simulational study of the compression and buckling of elastic
ridges formed by joining the boundary of a flat sheet to itself. Such ridges
store energy anomalously: their resting energy scales as the linear size of the
sheet to the 1/3 power. We find that the energy required to buckle such a ridge
is a fixed multiple of the resting energy. Thus thin sheets with elastic ridges
such as crumpled sheets are qualitatively stronger than smoothly bent sheets.Comment: 4 pages, REVTEX, 3 figure
Unsteady Crack Motion and Branching in a Phase-Field Model of Brittle Fracture
Crack propagation is studied numerically using a continuum phase-field
approach to mode III brittle fracture. The results shed light on the physics
that controls the speed of accelerating cracks and the characteristic branching
instability at a fraction of the wave speed.Comment: 11 pages, 4 figure
Properties of Ridges in Elastic Membranes
When a thin elastic sheet is confined to a region much smaller than its size
the morphology of the resulting crumpled membrane is a network of straight
ridges or folds that meet at sharp vertices. A virial theorem predicts the
ratio of the total bending and stretching energies of a ridge. Small strains
and curvatures persist far away from the ridge. We discuss several kinds of
perturbations that distinguish a ridge in a crumpled sheet from an isolated
ridge studied earlier (A. E. Lobkovsky, Phys. Rev. E. 53 3750 (1996)). Linear
response as well as buckling properties are investigated. We find that quite
generally, the energy of a ridge can change by no more than a finite fraction
before it buckles.Comment: 13 pages, RevTeX, acknowledgement adde
The Statistics of Crumpled Paper
A statistical study of crumpled paper is allowed by a minimal 1D model: a
self-avoiding line bent at sharp angles -- in which resides the elastic energy
-- put in a confining potential. Many independent equilibrium configurations
are generated numerically and their properties are investigated. At small
confinement, the distribution of segment lengths is log-normal in agreement
with previous predictions and experiments. At high confinement, the system
approaches a jammed state with a critical behavior, whereas the length
distribution follows a Gamma law which parameter is predicted as a function of
the number of layers in the system
Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids
We use the shear transformation zone (STZ) theory of dynamic plasticity to
study the necking instability in a two-dimensional strip of amorphous solid.
Our Eulerian description of large-scale deformation allows us to follow the
instability far into the nonlinear regime. We find a strong rate dependence;
the higher the applied strain rate, the further the strip extends before the
onset of instability. The material hardens outside the necking region, but the
description of plastic flow within the neck is distinctly different from that
of conventional time-independent theories of plasticity.Comment: 4 pages, 3 figures (eps), revtex4, added references, changed and
added content, resubmitted to PR
Mechanism of Deep-focus Earthquakes Anomalous Statistics
Analyzing the NEIC-data we have shown that the spatial deep-focus earthquake
distribution in the Earth interior over the 1993-2006 is characterized by the
clearly defined periodical fine discrete structure with period L=50 km, which
is solely generated by earthquakes with magnitude M 3.9 to 5.3 and only on the
convergent boundary of plates. To describe the formation of this structure we
used the model of complex systems by A. Volynskii and S. Bazhenov. The key
property of this model consists in the presence of a rigid coating on a soft
substratum. It is shown that in subduction processes the role of a rigid
coating plays the slab substance (lithosphere) and the upper mantle acts as a
soft substratum. Within the framework of this model we have obtained the
estimation of average values of stress in the upper mantle and Young's modulus
for the oceanic slab (lithosphere) and upper mantle.Comment: 9 pages, 7 figure
UPPER MANTLE CONVECTION RELATED TO SUBDUCTION ZONE AND APPLICATION OF THE MODEL TO INVESTIGATE THE CRETACEOUS-CENOZOIC GEODYNAMICS OF CENTRAL EAST ASIA AND THE ARCTIC
A geodynamic model of upper mantle convection related to the Pacific subduction zone is mathematically substantiated and applied to investigate the Cretaceous-Cenozoic evolution of Central East Asia (CEA) and the Arctic. We present a solution for the two-dimensional stationary problem of thermal convection in the upper mantle layer, considering different Rayleigh numbers and taking into account the influence of the subduction process and lithospheric movements along the upper mantle base. We describe the results of 3D modeling of nonstationary upper mantle convection in a subduction zone. Our data give grounds to propose explanations for the entire spectrum of tectonic-magmatic processes developing within CEA in the Cenozoic and the Arctic in the Upper Cretaceous and Cenozoic. We discuss the reasons why the lithosphere in CEA and the Arctic is generally shifting towards the Pacific subduction zone, considering the presence of separate magmatic provinces and rift zones. In our opinion, this is due to the existence of a large horizontally elongated convective cell, which interior is composed of smaller isometric cells. This long cell creates the effect of conveyor dragging of the lithosphere, while its internal cells produce the effect of upper mantle plumes
Nucleation and Bulk Crystallization in Binary Phase Field Theory
We present a phase field theory for binary crystal nucleation. In the
one-component limit, quantitative agreement is achieved with computer
simulations (Lennard-Jones system) and experiments (ice-water system) using
model parameters evaluated from the free energy and thickness of the interface.
The critical undercoolings predicted for Cu-Ni alloys accord with the
measurements, and indicate homogeneous nucleation. The Kolmogorov exponents
deduced for dendritic solidification and for "soft-impingement" of particles
via diffusion fields are consistent with experiment.Comment: 4 pages, 4 figures, accepted to PR
Dynamic ductile to brittle transition in a one-dimensional model of viscoplasticity
We study two closely related, nonlinear models of a viscoplastic solid. These
models capture essential features of plasticity over a wide range of strain
rates and applied stresses. They exhibit inelastic strain relaxation and steady
flow above a well defined yield stress. In this paper, we describe a first step
in exploring the implications of these models for theories of fracture and
related phenomena. We consider a one dimensional problem of decohesion from a
substrate of a membrane that obeys the viscoplastic constitutive equations that
we have constructed. We find that, quite generally, when the yield stress
becomes smaller than some threshold value, the energy required for steady
decohesion becomes a non-monotonic function of the decohesion speed. As a
consequence, steady state decohesion at certain speeds becomes unstable. We
believe that these results are relevant to understanding the ductile to brittle
transition as well as fracture stability.Comment: 10 pages, REVTeX, 12 postscript figure
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