Finite strain discrete dislocation plasticity in a total Lagrangian setting

Irani, Nilgoon; Remmers, Jjc Joris; Deshpande, V.S.

doi:10.1016/j.jmps.2015.06.013

Cited by 13 publications

(9 citation statements)

References 31 publications

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“…These effects can be significant in the bending of relatively small specimens. Thus, we also investigate the bending of single crystals using the finite strain discrete dislocation plasticity framework [32,33]. Analogous to the small strain DDP method, the finite strain DDP framework assumes that (1) lattice strains remain small away from the dislocation cores, and (2) the elastic properties are unaffected by slip.…”

Section: Finite Strain Discrete Dislocation Plasticitymentioning

confidence: 99%

“…Compared to the small strain formulation, the finite strain DDP formulation is less established, and thus we present this method more elaborately; nevertheless, readers are referred to Ref. [32] for further details.…”

Section: Finite Strain Discrete Dislocation Plasticitymentioning

confidence: 99%

“…Unlike the small strain formulation, this complimentary problem for the (ˆ) field is nonlinear and needs to be solved iteratively as explained in Ref. [32].…”

Section: Finite Strain Discrete Dislocation Plasticitymentioning

confidence: 99%

“…To address this question we shall employ the recently developed finite strain DDP formulation of Irani et al [32]. The outline of the paper is as follows: First, the small strain and finite strain DDP formulations are briefly described.…”

Section: Introductionmentioning

confidence: 99%

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Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

2017

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Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations. B Vikram S. Deshpande

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Section: Finite Strain Discrete Dislocation Plasticitymentioning

confidence: 99%

Section: Finite Strain Discrete Dislocation Plasticitymentioning

confidence: 99%

“…Unlike the small strain formulation, this complimentary problem for the (ˆ) field is nonlinear and needs to be solved iteratively as explained in Ref. [32].…”

Section: Finite Strain Discrete Dislocation Plasticitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

2017

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“…We also note the finite deformation discrete dislocation plasticity formulation presented in the works of [DNVdG03,IRD15]. The latter work attempts to address the violation of the hypoelastic constitutive equation for stress of the dislocation fields in the computational implementation of the model proposed in [DNVdG03].…”

Section: Introductionmentioning

confidence: 99%

Dislocation pattern formation in finite deformation crystal plasticity

Arora

Acharya

2020

International Journal of Solids and Structures

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Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters beyond the requirements of standard classical crystal plasticity theory. The dislocation microstructures shown are decoupled from deformation microstructures, and emerge without any consideration of latent hardening or constitutive assumptions related to crossslip. Crystal orientation effects on the pattern formation and mechanical response are also demonstrated. The manifest irrelevance of the necessity of a multiplicative decomposition of the deformation gradient, a plastic distortion tensor, and the choice of a reference configuration in our model to describe the micromechanics of plasticity as it arises from the existence and motion of dislocations is worthy of note.

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Relationship between element-level and contact-level parameters of micromechanical and upscaled plasticity models for granular soils

Liu

Chang

2020

Acta Geotech.

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Finite strain discrete dislocation plasticity in a total Lagrangian setting

Cited by 13 publications

References 31 publications

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Dislocation pattern formation in finite deformation crystal plasticity

Relationship between element-level and contact-level parameters of micromechanical and upscaled plasticity models for granular soils

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