A model of elastoplastic bodies with continuously distributed dislocations

Le, Khanh Chau; Stumpf, H.

doi:10.1016/s0749-6419(96)00022-8

Cited by 96 publications

(45 citation statements)

References 11 publications

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“…This is in contrast to other continuum proposals incorporating continuum measures of dislocation density, e.g. Naghdi and Srinivasa (1993 a, b), Le and Stumpf (1996), Menzel and Steinmann (2000), Gurtin (2001), where the free energy is itself modified by an explicit dependence on the local value of the dislocation density. Such theories have not been shown to reproduce the results of the elastic theory of continuously distributed dislocations.…”

Section: Uniqueness Of Dislocation Density Evolution Allowing Growthcontrasting

confidence: 62%

Driving forces and boundary conditions in continuum dislocation mechanics

Acharya

2003

Proc. R. Soc. Lond. A

141

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SummaryAs a guide to constitutive specification, driving forces for dislocation velocity and nucleation rates are derived for a field theory of dislocation mechanics and crystal plasticity proposed in Acharya (2001, J. Mech. Phys. Solids). A condition of closure for the theory in the form of a boundary condition for dislocation density evolution is also derived. The closure condition is generated from a uniqueness analysis in the linear setting for partial differential equations controlling the evolution of dislocation density. The boundary condition has a simple physical meaning as an inward flux over the dislocation inflow part of the boundary. Kinematical features of dislocation evolution like initiation of bowing of a pinned screw segment, and the initiation of cross-slip of a single screw segment are discussed. An exact solution representing the expansion of a polygonal dislocation loop is derived for a quasilinear system of governing partial differential equations. The representation within the theory of some physical features of dislocation mechanics and plastic deformation like local (dislocation level) Schmid and non-Schmid behavior, unloaded, stress free and steady microstructures, and yielding are also discussed.

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Section: Uniqueness Of Dislocation Density Evolution Allowing Growthcontrasting

confidence: 62%

Driving forces and boundary conditions in continuum dislocation mechanics

Acharya

2003

Proc. R. Soc. Lond. A

141

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“…(34) 2 and (35) as [3], Steinmann [32], Acharya and Bassani [33,73], Menzel and Steinmann [9], Bammann [34], Bassani [74], and Regueiro et al [39]. On the other hand, they are contradictory to the models of Teodosiu [1], Dillon and Kratochvil [5], Naghdi and Srinivasa [38,28], Le and Stumpf [30,31], Shizawa and Zbib [16,17], and Gurtin [13,36].…”

Section: Multiscale Balance Lawsmentioning

confidence: 99%

“…In many cases the higher order gradients are associated, upon invocation of differential-geometric arguments, with the density of ''geometrically necessary dislocations'' (GNDs) in single crystals (cf. [28][29][30][31][32][33][34][35][36][37]) and in polycrystals (cf. [38,16,17,9,39]).…”

Section: Introductionmentioning

confidence: 99%

A multiscale gradient theory for single crystalline elastoviscoplasticity

Clayton

McDowell

Bammann

2004

International Journal of Engineering Science

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“…In our context we define two other measures of inhomogeneities, A 0 and A, by means of curl and starting from Cartan-torsion [22], [18]. These measures are associated to the plastically deformed configuration, at any time t, starting from the formulae (14), (15) and using the identity,F T (Fv ×Fu) = detF(v × u),…”

Section: Moreovermentioning

confidence: 99%

Couple stresses and non-Riemannian plastic connection in finite elasto-plasticity

Cleja-Ţigoiu

2002

Z. angew. Math. Phys.

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In this paper we propose a macroscopic model for elasto-plastic materials with continuously distributed dislocations. The crystal is not homogeneous and the relaxed state is described by a plastic non-Riemannian metric connection. The dynamic balance equations involve non-symmetric Cauchy stresses and couple stresses. The crystalline body behaves as an elastic material element with respect to the relaxed state. The evolution equations for plastic distortion and its gradient have to be compatible with the requirement of a vanishing plastic curvature. Mathematics Subject Classification (2000). 74A30, 74E05,74C99.

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A model of elastoplastic bodies with continuously distributed dislocations

Cited by 96 publications

References 11 publications

Driving forces and boundary conditions in continuum dislocation mechanics

Driving forces and boundary conditions in continuum dislocation mechanics

A multiscale gradient theory for single crystalline elastoviscoplasticity

Couple stresses and non-Riemannian plastic connection in finite elasto-plasticity

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