On the torsion of isotropic elastoplastic Cosserat circular cylinders

Ghiglione, Flavien; Forest, Samuel

doi:10.1142/s2424913021420078

Cited by 2 publications

(2 citation statements)

References 37 publications

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“…In the present work, no such decomposition is introduced for curvature, for the sake of simplicity following [12,28]. The Hehlmholtz free energy density function ψ(e ∼ e , κ ∼ ) is here assumed to depend on elastic deformation and total curvature.…”

Section: Constitutive Equationsmentioning

confidence: 99%

Size Effects in Cosserat Crystal Plasticity

Forest

Ghiglione

2023

Advanced Structured Materials

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Some Cosserat elastoplasticity models for single crystals are reviewed in the present chapter. Their size-dependent response is evaluated in the case of a simple one-dimensional shear test involving one single slip system and vanishing microrotation prescribed at the boundaries of a material strip of width 2L. The inhomogeneous distribution of slip in the channel mimics the piling-up of dislocations against the boundaries. The free energy density function depends on the elastic strain and Cosserat curvature tensors. Two types of potentials are examined with respect to the curvature tensor, namely a quadratic function of its norm, on the one hand, and the norm itself, on the second hand. The first model is very often used but turns out to be non-physical since, according to physical metallurgy, the stored energy is proportional to the dislocation density (here the density of geometrically dislocations) rather than its square. The scaling laws predicted by these models are shown to be L −2 or L −1 , respectively. The latter scaling is reminiscent of Orowan's law of yielding [17]. The chapter ends with the combination of both quadratic and rank one contributions in a unified formulation applied to grain boundary modelling.

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Section: Constitutive Equationsmentioning

confidence: 99%

Size Effects in Cosserat Crystal Plasticity

Forest

Ghiglione

2023

Advanced Structured Materials

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“…12b. Sizedependent torsion of cylinders has been simulated recently using Cosserat isotropic plasticity in [77] and using strain gradient crystal plasticity in [78]. The torsion test is used here as a benchmark for 3D finite element simulations at large strains.…”

Section: Torsionmentioning

confidence: 99%

Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

Abatour¹,

Forest²,

Ammar³

et al. 2022

Acta Mech

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Strain gradient plasticity has been the subject of extensive research in the past forty years in order to model size effects in metal plasticity, on the one hand, and provide finite width shear bands in the simulation of localization phenomena, on the other hand. However, the use of the emerging models is still limited to academic applications and has not yet been adopted by industry practitioners. The present paper systematically reviews the pros and the cons of gradient plasticity at finite strains based on gradient of scalar plastic variables, in particular gradient of the cumulative plastic strain. It proposes benchmark tests addressing both size effect modeling and plastic strain localization simulation. It includes new analytical solutions for validation of FE implementation. It focuses on the micromorphic approach to gradient plasticity, as a convenient method for implementation in FE codes. New features of the analysis include the comparison of three distinct formulations of rate-independent gradient plasticity at finite deformations, based on the multiplicative decomposition of the deformation gradient and on quadratic potentials with respect to gradient terms. The performance of micromorphic and Lagrange-multiplier based strain gradient plasticity models is evaluated for various monotonic and cyclic loading conditions including confined plasticity in simple glide and tension, bending and torsion at large deformations. Limitations are pointed out in the case of bending and torsion, which can be overcome for instance by the use of the gradient of equivalent plastic strain model.

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On the torsion of isotropic elastoplastic Cosserat circular cylinders

Cited by 2 publications

References 37 publications

Size Effects in Cosserat Crystal Plasticity

Size Effects in Cosserat Crystal Plasticity

Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

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