99 research outputs found
Inelastic deformation during sill and laccolith emplacement: Insights from an analytic elastoplastic model
Numerous geological observations evidence that inelastic deformation occurs
during sills and laccoliths emplacement. However, most models of sill and
laccolith emplacement neglect inelastic processes by assuming purely elastic
deformation of the host rock. This assumption has never been tested, so that
the role of inelastic deformation on the growth dynamics of magma intrusions
remains poorly understood. In this paper, we introduce the first analytical
model of shallow sill and laccolith emplacement that accounts for
elasto-plastic deformation of the host rock. It considers the intrusion's
overburden as a thin elastic bending plate attached to an
elastic-perfectly-plastic foundation. We find that, for geologically realistic
values of the model parameters, the horizontal extent of the plastic zone lp is
much smaller than the radius of the intrusion a. By modeling the quasi-static
growth of a sill, we find that the ratio lp/a decreases during propagation, as
1/ \sqrt a 4 P , with P the magma overpressure. The model
also shows that the extent of the plastic zone decreases with the intrusion's
depth, while it increases if the host rock is weaker. Comparison between our
elasto-plastic model and existing purely elastic models shows that plasticity
can have a significant effect on intrusion propagation dynamics, with e.g. up
to a doubling of the overpressure necessary for the sill to grow. Our results
suggest that plasticity effects might be small for large sills, but conversely
that they might be substantial for early sill propagation.
Memory in random bouncing ball dynamics
The bouncing of an inelastic ball on a vibrating plate is a popular model
used in various fields, from granular gases to nanometer-sized mechanical
contacts. For random plate motion, so far, the model has been studied using
Poincar{\'e} maps in which the excitation by the plate at successive bounces is
assumed to be a discrete Markovian (memoryless) process. Here, we investigate
numerically the behaviour of the model for continuous random excitations with
tunable correlation time. We show that the system dynamics are controlled by
the ratio of the Markovian mean flight time of the ball and the mean time
between successive peaks in the motion of the exciting plate. When this ratio,
which depends on the bandwidth of the excitation signal, exceeds a certain
value, the Markovian approach is appropriate; below, memory of preceding
excitations arises, leading to a significant decrease of the jump duration; at
the smallest values of the ratio, chattering occurs. Overall, our results open
the way for uses of the model in the low excitation regime, which is still
poorly understood.Comment: Final published version, 5 pages, 4 figure
Understanding fast macroscale fracture from microcrack post mortem patterns
Dynamic crack propagation drives catastrophic solid failures. In many
amorphous brittle materials, sufficiently fast crack growth involves
small-scale, high-frequency microcracking damage localized near the crack tip.
The ultra-fast dynamics of microcrack nucleation, growth and coalescence is
inaccessible experimentally and fast crack propagation was therefore studied
only as a macroscale average. Here, we overcome this limitation in
polymethylmethacrylate, the archetype of brittle amorphous materials: We
reconstruct the complete spatio-temporal microcracking dynamics, with
micrometer / nanosecond resolution, through post mortem analysis of the
fracture surfaces. We find that all individual microcracks propagate at the
same low, load-independent, velocity. Collectively, the main effect of
microcracks is not to slow down fracture by increasing the energy required for
crack propagation, as commonly believed, but on the contrary to boost the
macroscale velocity through an acceleration factor selected on geometric
grounds. Our results emphasize the key role of damage-related internal
variables in the selection of macroscale fracture dynamics.Comment: 9 pages, 5 figures + supporting information (15 pages
Role of friction-induced torque in stick-slip motion
We present a minimal quasistatic 1D model describing the kinematics of the
transition from static friction to stick-slip motion of a linear elastic block
on a rigid plane. We show how the kinematics of both the precursors to
frictional sliding and the periodic stick-slip motion are controlled by the
amount of friction-induced torque at the interface. Our model provides a
general framework to understand and relate a series of recent experimental
observations, in particular the nucleation location of micro-slip instabilities
and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure
Adhesion in soft contacts is minimum beyond a critical shear displacement
The most direct measurement of adhesion is the pull-off force, i.e. the
tensile force necessary to separate two solids in contact. For a given
interface, it depends on various experimental parameters, including separation
speed, contact age and maximum loading force. Here, using smooth contacts
between elastomer spheres and rigid plates, we show that the pull-off force
also varies if the contact is sheared prior to separation. For shear
displacements below a critical valueabout 10% of that necessary to yield gross
sliding, the pull-off force steadily decreases as shear increases. For larger
shear, the pull-off force remains constant, at a residual value 10%--15% of its
initial value. Combining force measurements and in situ imaging, we show how
the unloading path leading to contact separation is modified by the initial
shear. In particular, we find that the residual pull-off force prevails if the
contact reaches full sliding during unloading. Based on those observations, a
first modeling attempt of the critical shear displacement is proposed,involving
a competition between jump instability and transition to sliding. Overall,
those results offer new insights into the interplay between adhesion and
friction, provide new constraints on adhesion measurements and challenge
existing adhesive models. They will be useful wherever soft contacts undergo
both normal and shear stresses, including tire grip, soft robotics, haptics and
animal locomotion
Experimental evidence of non-Amontons behaviour at a multicontact interface
We report on normal stress field measurements at the multicontact interface
between a rough elastomeric film and a smooth glass sphere under normal load,
using an original MEMS-based stress sensing device. These measurements are
compared to Finite Elements Method calculations with boundary conditions
obeying locally Amontons' rigid-plastic-like friction law with a uniform
friction coefficient. In dry contact conditions, significant deviations are
observed which decrease with increasing load. In lubricated conditions, the
measured profile recovers almost perfectly the predicted profile. These results
are interpreted as a consequence of the finite compliance of the multicontact
interface, a mechanism which is not taken into account in Amontons' law
The role of fingerprints in the coding of tactile information probed with a biomimetic sensor
In humans, the tactile perception of fine textures (spatial scale <200
micrometers) is mediated by skin vibrations generated as the finger scans the
surface. To establish the relationship between texture characteristics and
subcutaneous vibrations, a biomimetic tactile sensor has been designed whose
dimensions match those of the fingertip. When the sensor surface is patterned
with parallel ridges mimicking the fingerprints, the spectrum of vibrations
elicited by randomly textured substrates is dominated by one frequency set by
the ratio of the scanning speed to the interridge distance. For human touch,
this frequency falls within the optimal range of sensitivity of Pacinian
afferents, which mediate the coding of fine textures. Thus, fingerprints may
perform spectral selection and amplification of tactile information that
facilitate its processing by specific mechanoreceptors.Comment: 25 pages, 11 figures, article + supporting materia
Finite deformations govern the anisotropic shear-induced area reduction of soft elastic contacts
Solid contacts involving soft materials are important in mechanical
engineering or biomechanics. Experimentally, such contacts have been shown to
shrink significantly under shear, an effect which is usually explained using
adhesion models. Here we show that quantitative agreement with recent high-load
experiments can be obtained, with no adjustable parameter, using a non-adhesive
model, provided that finite deformations are taken into account. Analysis of
the model uncovers the basic mechanisms underlying shear-induced area
reduction, local contact lifting being the dominant one. We confirm
experimentally the relevance of all those mechanisms, by tracking the
shear-induced evolution of tracers inserted close to the surface of a smooth
elastomer sphere in contact with a smooth glass plate. Our results suggest that
finite deformations are an alternative to adhesion, when interpreting a variety
of sheared contact experiments involving soft materials.Comment: Version accepted at J. Mech. Phys. Solids. It includes Supplementary
Informatio
1D model of precursors to frictional stick-slip motion allowing for robust comparison with experiments
We study the dynamic behaviour of 1D spring-block models of friction when the
external loading is applied from a side, and not on all blocks like in the
classical Burridge-Knopoff-like models. Such a change in the loading yields
specific difficulties, both from numerical and physical viewpoints. To address
some of these difficulties and clarify the precise role of a series of model
parameters, we start with the minimalistic model by Maegawa et al. (Tribol.
Lett. 38, 313, 2010) which was proposed to reproduce their experiments about
precursors to frictional sliding in the stick-slip regime. By successively
adding (i) an internal viscosity, (ii) an interfacial stiffness and (iii) an
initial tangential force distribution at the interface, we manage to (i) avoid
the model's unphysical stress fluctuations, (ii) avoid its unphysical
dependence on the spatial resolution and (iii) improve its agreement with the
experimental results, respectively. Based on the behaviour of this improved 1D
model, we develop an analytical prediction for the length of precursors as a
function of the applied tangential load. We also discuss the relationship
between the microscopic and macroscopic friction coefficients in the model.Comment: 13 pages, 14 figures, accepted in Tribology Letter
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