2,583 research outputs found
The mechanics of a chain or ring of spherical magnets
Strong magnets, such as neodymium-iron-boron magnets, are increasingly being
manufactured as spheres. Because of their dipolar characters, these spheres can
easily be arranged into long chains that exhibit mechanical properties
reminiscent of elastic strings or rods. While simple formulations exist for the
energy of a deformed elastic rod, it is not clear whether or not they are also
appropriate for a chain of spherical magnets. In this paper, we use
discrete-to-continuum asymptotic analysis to derive a continuum model for the
energy of a deformed chain of magnets based on the magnetostatic interactions
between individual spheres. We find that the mechanical properties of a chain
of magnets differ significantly from those of an elastic rod: while both
magnetic chains and elastic rods support bending by change of local curvature,
nonlocal interaction terms also appear in the energy formulation for a magnetic
chain. This continuum model for the energy of a chain of magnets is used to
analyse small deformations of a circular ring of magnets and hence obtain
theoretical predictions for the vibrational modes of a circular ring of
magnets. Surprisingly, despite the contribution of nonlocal energy terms, we
find that the vibrations of a circular ring of magnets are governed by the same
equation that governs the vibrations of a circular elastic ring
Multiscale Modeling of Structurally-Graded Materials Using Discrete Dislocation Plasticity Models and Continuum Crystal Plasticity Models
A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response
Relaxation of Wobbling Asteroids and Comets. Theoretical Problems. Perspectives of Experimental Observation
A body dissipates energy when it freely rotates about any axis different from
principal. This entails relaxation, i.e., decrease of the rotational energy,
with the angular momentum preserved. The spin about the major-inertia axis
corresponds to the minimal kinetic energy, for a fixed angular momentum. Thence
one may expect comets and asteroids (as well as spacecraft or cosmic-dust
granules) stay in this, so-called principal, state of rotation, unless they are
forced out of this state by a collision, or a tidal interaction, or cometary
jetting, or by whatever other reason. As is well known, comet P/Halley,
asteroid 4179 Toutatis, and some other small bodies exhibit very complex
rotational motions attributed to these objects being in non-principal states of
spin. Most probably, the asteroid and cometary wobble is quite a generic
phenomenon. The theory of wobble with internal dissipation has not been fully
developed as yet. In this article we demonstrate that in some spin states the
effectiveness of the inelastic-dissipation process is several orders of
magnitude higher than believed previously, and can be measured, by the
presently available observational instruments, within approximately a year
span. We also show that in some other spin states both the precession and
precession-relaxation processes slow down considerably. (We call it
near-separatrix lingering effect.) Such spin states may evolve so slowly that
they can mimic the principal-rotation state.Comment: 2 figure
Field experience and the long-term durability of reinforced concrete structures
For reinforced concrete structures the conventional wisdom is that after some years of exposure to marine conditions reinforcement corrosion is inevitable. Much attention is paid in the literature to the rate of ingress of chlorides through the concrete cover to the reinforcing bars and to ensuring highly impermeable cover and/or deeper cover, to try top prevent chloride-induced or carbonation-induced corrosion initiation. Actual field experience shows that there are many reinforced concrete structures that have survived remarkably well for many decades despite having very high chloride concentrations next to the reinforcing bars. Even with very modest concrete cover by modern standards, exhumation often finds bars free from corrosion. Detailed investigations of a number of such cases showed no corrosion if the concrete pH levels are above about 9. On the other hand, very severe reinforcement corrosion was observed in the few cases where the concrete had cracked right through the cover to the bars. Often there was no external evidence or signs of interior corrosion, including longitudinal cracking. The implications of these findings for practice are discussed
On the distribution of surface extrema in several one- and two-dimensional random landscapes
We study here a standard next-nearest-neighbor (NNN) model of ballistic
growth on one- and two-dimensional substrates focusing our analysis on the
probability distribution function of the number of maximal points
(i.e., local ``peaks'') of growing surfaces. Our analysis is based on two
central results: (i) the proof (presented here) of the fact that uniform
one--dimensional ballistic growth process in the steady state can be mapped
onto ''rise-and-descent'' sequences in the ensemble of random permutation
matrices; and (ii) the fact, established in Ref. \cite{ov}, that different
characteristics of ``rise-and-descent'' patterns in random permutations can be
interpreted in terms of a certain continuous--space Hammersley--type process.
For one--dimensional system we compute exactly and also present
explicit results for the correlation function characterizing the enveloping
surface. For surfaces grown on 2d substrates, we pursue similar approach
considering the ensemble of permutation matrices with long--ranged
correlations. Determining exactly the first three cumulants of the
corresponding distribution function, we define it in the scaling limit using an
expansion in the Edgeworth series, and show that it converges to a Gaussian
function as .Comment: 25 pages, 12 figure
On the dynamics of planetesimals embedded in turbulent protoplanetary discs with dead zones
(abridged) Accretion in protoplanetary discs is thought to be driven by [...]
turbulence via the magnetorotational instability (MRI). Recent work has shown
that a planetesimal swarm embedded in a fully turbulent disc is subject to
strong excitation of the velocity dispersion, leading to collisional
destruction of bodies with radii R_p < 100 km. Significant diffusion of
planetesimal semimajor axes also arises, leading to large-scale spreading of
the planetesimal population throughout the inner regions of the protoplanetary
disc, in apparent contradiction of constraints provided by the distribution of
asteroids within the asteroid belt. In this paper, we examine the dynamics of
planetesimals embedded in vertically stratified turbulent discs, with and
without dead zones. Our main aims are to examine the turbulent excitation of
the velocity dispersion, and the radial diffusion, of planetesimals in these
discs. We employ three dimensional MHD simulations [...], along with an
equilibrium chemistry model [...] We find that planetesimals in fully turbulent
discs develop large random velocities that will lead to collisional
destruction/erosion for bodies with sizes below 100 km, and undergo radial
diffusion on a scale \sim 2.5 au over a 5 Myr disc life time. But planetesimals
in a dead zone experience a much reduced excitation of their random velocities,
and equilibrium velocity dispersions lie between the disruption thresholds for
weak and strong aggregates for sizes R_p < 100 km. We also find that radial
diffusion occurs over a much reduced length scale \sim 0.25 au over the disc
life time, this being consistent with solar system constraints. We conclude
that planetesimal growth via mutual collisions between smaller bodies cannot
occur in a fully turbulent disc. By contrast, a dead zone may provide a safe
haven in which km-sized planetesimals can avoid mutual destruction through
collisions.Comment: 18 pages, 13 figures, 3 tables, MNRAS in press, minor corrections to
match the published versio
2nd International Workshop on Physics-Based Modelling of Material Properties and Experimental Observations with special focus on Fracture and Damage Mechanics: Book of Abstracts
This report covers the book of abstracts of the 2nd International Workshop on Physics Based Modelling of Material Properties and Experimental Observations, with special focus on Fracture and Damage Mechanics. The workshop is organized in the context of European Commission’s Enlargement and Integration Action, by the Joint Research Centre in collaboration with the TOBB University of Economics and Technology (TOBB ETU) on 15th-17th May 2013 in Antalya, Turkey.
The abstracts of the keynote lectures and all the technical presentations are included in the book.
This workshop will give an overview of different physics-based models for fracture and degradation of metallic materials and how they can be used for improved understanding and more reliable predictions. Models of interest include cohesive zones to simulate fracture processes, ductile-brittle transition for ferritic steels, ductile fracture mechanisms such as void growth or localized shear, fatigue crack initiation and short crack growth, environmental assisted cracking. Experimental studies that support such models and case studies that illustrate their use are also within the scope. The workshop is also an opportunity for scientists and engineers from EU Member States and target countries to discuss research activities that could be a basis for future collaborations.JRC.F.4-Nuclear Reactor Integrity Assessment and Knowledge Managemen
- …