On the role of higher-order conditions in distortion gradient plasticity

Panteghini, Andrea; Bardella, Lorenzo

doi:10.1016/j.jmps.2018.05.019

Cited by 28 publications

(21 citation statements)

References 52 publications

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“…Notice that, in the context of crystal gradient plasticity, non-uniqueness has been shown in [13] for the case of nonhomogeneous displacement boundary conditions, focussing on the simple shear of a constrained strip endowed with multiple slip systems. The same type of non-unqiueness results have been obtained also in [46,107,104].…”

Section: Perfect Gradient Plasticity With Spinsupporting

confidence: 78%

A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector

Ebobisse

Hackl

Neff

2019

Continuum Mech. Thermodyn.

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In this paper we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor Curl p giving rise to a non-symmetric nonlocal backstress, and isotropic hardening response only depending on the accumulated equivalent plastic strain. The model is fully isotropic and satisfies linearized gauge-invariance conditions, i.e., only true state-variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn's inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain ε p and standard isotropic hardening.

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Section: Perfect Gradient Plasticity With Spinsupporting

confidence: 78%

A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector

Ebobisse

Hackl

Neff

2019

Continuum Mech. Thermodyn.

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“…(a) Higher-order boundary conditions where × denotes the vector product and n is the outward unit vector normal to the boundary S of Ω. Equation (2.3) implies that not all components of γ have to be continuous [35].…”

Section: The (Distortion) Gradient Plasticity Frameworkmentioning

confidence: 99%

“…in which σ 0 > 0 denotes the yield stress and V(Ė p ) is a viscoplastic function that controls the material rate-sensitivity. On the basis of our previous investigations [17,35,37], we adopt:…”

Section: (B) Constitutive Assumptions For the Dissipative Stressesmentioning

confidence: 99%

“…The strip is discretized along its height with a column of 382 H(curl) 4-noded FEs (as in [35]). We present and discuss the results by focusing on the comparison between the purely recoverable HO formulation endowed with less-than-quadratic defect energy and the theory based on the novel HO plastic potential.…”

Section: (A) the Adopted Boundary Value Problemmentioning

confidence: 99%

“…In this work, we refer to the FE implementation presented in [35]. Here, we explain how to extend that FE code to include the new HO plastic potential, through an algorithm to provide the new HO stress ζ and its gradient dζ /dα.…”

Section: Appendix a Numerical Integrationmentioning

confidence: 99%

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A potential for higher-order phenomenological strain gradient plasticity to predict reliable response under non-proportional loading

2019

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We propose a plastic potential for higher-order (HO) phenomenological strain gradient plasticity (SGP), predicting reliable size-dependent response for general loading histories. By constructing the free energy density as a sum of quadratic plastic strain gradient contributions that each transitions into linear terms at different threshold values, we show that we can predict the expected micron-scale behaviour, including increase of strain hardening and strengthening-like behaviour with diminishing size. Furthermore, the anomalous behaviour predicted by most HO theories under non-proportional loading is avoided. Though we demonstrate our findings on the basis of Gurtin (Gurtin 2004

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Strain Gradient Plasticity: Theory and Implementation

Bardella

Niordson

2020

Mechanics of Strain Gradient Materials

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On the role of higher-order conditions in distortion gradient plasticity

Cited by 28 publications

References 52 publications

A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector

A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector

A potential for higher-order phenomenological strain gradient plasticity to predict reliable response under non-proportional loading

Strain Gradient Plasticity: Theory and Implementation

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