1,945 research outputs found
Riemann-Cartan Geometry of nonlinear dislocation mechanics
We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold – where the body is stress free – is a Weitzenbock manifold, i.e. a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan’s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance
The relaxed linear micromorphic continuum: well-posedness of the static problem and relations to the gauge theory of dislocations
In this paper we consider the equilibrium problem in the relaxed linear model
of micromorphic elastic materials. The basic kinematical fields of this
extended continuum model are the displacement and the
non-symmetric micro-distortion density tensor . In
this relaxed theory a symmetric force-stress tensor arises despite the presence
of microstructure and the curvature contribution depends solely on the
micro-dislocation tensor . However, the relaxed model is able
to fully describe rotations of the microstructure and to predict non-polar
size-effects. In contrast to classical linear micromorphic models, we allow the
usual elasticity tensors to become positive-semidefinite. We prove that,
nevertheless, the equilibrium problem has a unique weak solution in a suitable
Hilbert space. The mathematical framework also settles the question of which
boundary conditions to take for the micro-distortion. Similarities and
differences between linear micromorphic elasticity and dislocation gauge theory
are discussed and pointed out.Comment: arXiv admin note: substantial text overlap with arXiv:1308.376
Multi-Phase Equilibrium of Crystalline Solids
A continuum model of crystalline solid equilibrium is presented in which the
underlying periodic lattice structure is taken explicitly into account. This
model also allows for both point and line defects in the bulk of the lattice
and at interfaces, and the kinematics of such defects is discussed in some
detail. A Gibbsian variational argument is used to derive the necessary bulk
and interfacial conditions for multi-phase equilibrium (crystal-crystal and
crystal-melt) where the allowed lattice variations involve the creation and
transport of defects in the bulk and at the phase interface. An interfacial
energy, assumed to depend on the interfacial dislocation density and the
orientation of the interface with respect to the lattices of both phases, is
also included in the analysis. Previous equilibrium results based on nonlinear
elastic models for incoherent and coherent interfaces are recovered as special
cases for when the lattice distortion is constrained to coincide with the
macroscopic deformation gradient, thereby excluding bulk dislocations. The
formulation is purely spatial and needs no recourse to a fixed reference
configuration or an elastic-plastic decomposition of the strain. Such a
decomposition can be introduced however through an incremental elastic
deformation superposed onto an already dislocated state, but leads to
additional equilibrium conditions. The presentation emphasizes the role of
{configurational forces} as they provide a natural framework for the
description and interpretation of singularities and phase transitions.Comment: 32 pages, to appear in Journal of the Mechanics and Physics of Solid
Dislocation constriction and cross-slip in Al and Ag: an ab initio study
A novel model based on the Peierls framework of dislocations is developed.
The new theory can deal with a dislocation spreading at more than one slip
planes. As an example, we study dislocation cross-slip and constriction process
of two fcc metals, Al and Ag. The energetic parameters entering the model are
determined from ab initio calculations. We find that the screw dislocation in
Al can cross-slip spontaneously in contrast with that in Ag, which splits into
partials and cannot cross-slip without first being constricted. The dislocation
response to an external stress is examined in detail. We determine dislocation
constriction energy and critical stress for cross-slip, and from the latter, we
estimate the cross-slip energy barrier for the straight screw dislocations
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