2,396 research outputs found
A dynamical interpretation of flutter instability in a continuous medium
Flutter instability in an infinite medium is a form of material instability
corresponding to the occurrence of complex conjugate squares of the
acceleration wave velocities. Although its occurrence is known to be possible
in elastoplastic materials with nonassociative flow law and to correspond to
some dynamically growing disturbance, its mechanical meaning has to date still
eluded a precise interpretation. This is provided here by constructing the
infinite-body, time-harmonic Green's function for the loading branch of an
elastoplastic material in flutter conditions. Used as a perturbation, it
reveals that flutter corresponds to a spatially blowing-up disturbance,
exhibiting well-defined directional properties, determined by the wave
directions for which the eigenvalues become complex conjugate. Flutter is shown
to be connected to the formation of localized deformations, a dynamical
phenomenon sharing geometrical similarities with the well-known mechanism of
shear banding occurring under quasi-static loading. Flutter may occur much
earlier than shear banding in a process of continued plastic deformation.Comment: 32 pages, 12 figure
Screw dislocations in the field theory of elastoplasticity
A (microscopic) static elastoplastic field theory of dislocations with moment
and force stresses is considered. The relationship between the moment stress
and the Nye tensor is used for the dislocation Lagrangian. We discuss the
stress field of an infinitely long screw dislocation in a cylinder, a dipole of
screw dislocations and a coaxial screw dislocation in a finite cylinder. The
stress fields have no singularities in the dislocation core and they are
modified in the core due to the presence of localized moment stress.
Additionally, we calculated the elastoplastic energies for the screw
dislocation in a cylinder and the coaxial screw dislocation. For the coaxial
screw dislocation we find a modified formula for the so-called Eshelby twist
which depends on a specific intrinsic material length.Comment: 19 pages, LaTeX, 2 figures, Extended version of a contribution to the
symposium on "Structured Media'' dedicated to the memory of Professor
Ekkehart Kr\"oner, 16-21 September 2001, Pozna\'n, Poland. to appear in
Annalen der Physik 11 (2002
Development of Stresses in Cohesionless Poured Sand
The pressure distribution beneath a conical sandpile, created by pouring sand
from a point source onto a rough rigid support, shows a pronounced minimum
below the apex (`the dip'). Recent work of the authors has attempted to explain
this phenomenon by invoking local rules for stress propagation that depend on
the local geometry, and hence on the construction history, of the medium. We
discuss the fundamental difference between such approaches, which lead to
hyperbolic differential equations, and elastoplastic models, for which the
equations are elliptic within any elastic zones present .... This displacement
field appears to be either ill-defined, or defined relative to a reference
state whose physical existence is in doubt. Insofar as their predictions depend
on physical factors unknown and outside experimental control, such
elastoplastic models predict that the observations should be intrinsically
irreproducible .... Our hyperbolic models are based instead on a physical
picture of the material, in which (a) the load is supported by a skeletal
network of force chains ("stress paths") whose geometry depends on construction
history; (b) this network is `fragile' or marginally stable, in a sense that we
define. .... We point out that our hyperbolic models can nonetheless be
reconciled with elastoplastic ideas by taking the limit of an extremely
anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps.
Philosophical Transactions A, Royal Society, submitted 02/9
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
The aim of this paper is to compare a hyperelastic with a hypoelastic model
describing the Eulerian dynamics of solids in the context of non-linear
elastoplastic deformations. Specifically, we consider the well-known
hypoelastic Wilkins model, which is compared against a hyperelastic model based
on the work of Godunov and Romenski. First, we discuss some general conceptual
differences between the two approaches. Second, a detailed study of both models
is proposed, where differences are made evident at the aid of deriving a
hypoelastic-type model corresponding to the hyperelastic model and a particular
equation of state used in this paper. Third, using the same high order ADER
Finite Volume and Discontinuous Galerkin methods on fixed and moving
unstructured meshes for both models, a wide range of numerical benchmark test
problems has been solved. The numerical solutions obtained for the two
different models are directly compared with each other. For small elastic
deformations, the two models produce very similar solutions that are close to
each other. However, if large elastic or elastoplastic deformations occur, the
solutions present larger differences.Comment: 14 figure
Macroelement modeling of shallow foundations
The paper presents a new macroelement model for shallow foundations. The
model is defined through a non-linear constitutive law written in terms of some
generalized force and displacement parameters. The linear part of this
constitutive law comes from the dynamic impedances of the foundation. The
non-linear part comprises two mechanisms. One is due to the irreversible
elastoplastic soil behavior: it is described with a bounding surface
hypoplastic model, adapted for the description of the cyclic soil response. An
original feature of the formulation is that the bounding surface is considered
independently of the surface of ultimate loads of the system. The second
mechanism is the detachment that can take place at the soil-footing interface
(foundation uplift). It is totally reversible and non-dissipative and can thus
be described by a phenomenological non-linear elastic model. The macroelement
is qualitatively validated by application to soil-structure interaction
analyses of simple real structures
Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations
Continuum mechanics with dislocations, with the Cattaneo type heat
conduction, with mass transfer, and with electromagnetic fields is put into the
Hamiltonian form and into the form of the Godunov type system of the first
order, symmetric hyperbolic partial differential equations (SHTC equations).
The compatibility with thermodynamics of the time reversible part of the
governing equations is mathematically expressed in the former formulation as
degeneracy of the Hamiltonian structure and in the latter formulation as the
existence of a companion conservation law. In both formulations the time
irreversible part represents gradient dynamics. The Godunov type formulation
brings the mathematical rigor (the well-posedness of the Cauchy initial value
problem) and the possibility to discretize while keeping the physical content
of the governing equations (the Godunov finite volume discretization)
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