3,059 research outputs found
Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media
In the present paper we investigate the mechanics of systems of
affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry.
Certain physical applications are possible in modelling of molecular crystals,
granular media, and other physical objects. Particularly interesting are
dynamical models invariant under the group underlying geometry of degrees of
freedom. In contrary to the single body case there exist nontrivial potentials
invariant under this group (left and right acting). The concept of relative
(mutual) deformation tensors of pairs of affine bodies is discussed. Scalar
invariants built of such tensors are constructed. There is an essential novelty
in comparison to deformation scalars of single affine bodies, i.e., there exist
affinely-invariant scalars of mutual deformations. Hence, the hierarchy of
interaction models according to their invariance group, from Euclidean to
affine ones, can be considered.Comment: 50 pages, 4 figure
On Dislocations in a Special Class of Generalized Elasticity
In this paper we consider and compare special classes of static theories of
gradient elasticity, nonlocal elasticity, gradient micropolar elasticity and
nonlocal micropolar elasticity with only one gradient coefficient. Equilibrium
equations are discussed. The relationship between the gradient theory and the
nonlocal theory is discussed for elasticity as well as for micropolar
elasticity. Nonsingular solutions for the elastic fields of screw and edge
dislocations are given. Both the elastic deformation (distortion, strain,
bend-twist) and the force and couple stress tensors do not possess any
singularity unlike `classical' theories.Comment: 28 pages, to appear in: physica status solid
Wedge disclination in the field theory of elastoplasticity
In this paper we study the wedge disclination within the elastoplastic defect
theory. Using the stress function method we found exact analytical solutions
for all characteristic fields of a straight wedge disclination in a cylinder.
The elastic stress, elastic strain, elastic bend-twist, displacement and
rotation have no singularities at the disclination line. We found a modified
stress function for the wedge disclination.Comment: 11 pages, 3 figure
Reflection of plane waves from the flat boundary of a micropolar elastic halfspace
Microstructure effect on wave propagation, and plane wave reflection from stress free flat surface in micropolar elastic half-spac
Extension the Noether's theorem to Lagrangian formulation with nonlocality
A Lagrangian formulation with nonlocality is investigated in this paper. The
nonlocality of the Lagrangian is introduced by a new nonlocal argument that is
defined as a nonlocal residual satisfying the zero mean condition. The nonlocal
Euler-Lagrangian equation is derived from the Hamilton's principle. The
Noether's theorem is extended to this Lagrangian formulation with nonlocality.
With the help of the extended Noether's theorem, the conservation laws relevant
to energy, linear momentum, angular momentum and the Eshelby tensor are
determined in the nonlocal elasticity associated with the mechanically based
constitutive model. The results show that the conservation laws exist only in
the form of the integral over the whole domain occupied by body. The
localization of the conservation laws is discussed in detail. We demonstrate
that not every conservation law corresponds to a local equilibrium equation.
Only when the nonlocal residual of conservation current exists, can a
conservation law be transformed into a local equilibrium equation by
localization.Comment: 13 page
The connection between elastic scattering cross sections and acoustic vibrations of an embedded nanoparticle
Arbitrary waves incident on a solid embedded nanoparticle are studied. The
acoustic vibrational frequencies are shown to correspond to the poles of the
scattering cross section in the complex frequency plane. The location of the
poles is unchanged even if the incident wave is nonplanar. A second approach
approximating the infinite matrix as a very large shell surrounding the
nanoparticle provides an alternate way of predicting the mode frequencies. The
wave function of the vibration is also provided.Comment: Accepted for publication in physica status solidi (c) (C) (2003)
WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Proceedings of Phonons200
Micromorphic description of turbulent channel flow
AbstractThe simple microfluid theory of Eringen is employed to determine the velocity profile and microgyrations in a steady flow of viscous fluids between two parallel walls. The shearing stress, microrotations, microinertia and Reynold stresses are determined. The results are compared with the experimental work of Laufer
A mixture theory for geophysical fluids
International audienceA continuum theory is developed for a geophysical fluid consisting of two species. Balance laws are given for the individual components of the mixture, modeled as micropolar viscous fluids. The continua allow independent rotational degrees of freedom, so that the fluids can exhibit couple stresses and a non-symmetric stress tensor. The second law of thermodynamics is used to develop constitutive equations. Linear constitutive equations are constituted for a heat conducting mixture, each species possessing separate viscosities. Field equations are obtained and boundary and initial conditions are stated. This theory is relevant to an atmospheric mixture consisting of any two species from rain, snow and/or sand. Also, this is a continuum theory for oceanic mixtures, such as water and silt, or water and oil spills, etc
The gauge theory of dislocations: a nonuniformly moving screw dislocation
We investigate the nonuniform motion of a straight screw dislocation in
infinite media in the framework of the translational gauge theory of
dislocations. The equations of motion are derived for an arbitrary moving screw
dislocation. The fields of the elastic velocity, elastic distortion,
dislocation density and dislocation current surrounding the arbitrarily moving
screw dislocation are derived explicitely in the form of integral
representations. We calculate the radiation fields and the fields depending on
the dislocation velocities.Comment: 12 page
A higher order control volume based finite element method to prodict the deformation of heterogeneous materials
Materials with obvious internal structure can exhibit behaviour, under loading, that cannot be described by classical elasticity. It is therefore important to develop computational tools incorporating appropriate constitutive theories that can capture their unconventional behaviour. One such theory is micropolar elasticity. This paper presents a linear strain control volume finite element formulation incorporating micropolar elasticity. Verification results from a micropolar element patch test as well as convergence results for a stress concentration problem are included. The element will be shown to pass the patch test and also exhibit accuracy that is at least equivalent to its finite element counterpart
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