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On scale invariance in anisotropic plasticity, gradient plasticity and gradient elasticity
International Journal of Engineering Science, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Gradient Nanomechanics: Plastic Flow in Nanopolycrystals
Materials Science Forum, 2010Gradient nanomechanics is a generalized continuum mechanics framework accounting for “bulk-surface” interactions in the form of gradient terms that enter in the evolution equations of the relevant constitutive variables and/or in the governing field equations.
Xu Zhang +2 more
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Strain gradients in plasticity
Acta Mechanica, 1977An analytical model of a plastically deforming solid is assumed to be a material where the second spatial gradients of strain are included in the constitutive equations. These constitutive equations are combined, in a one dimensional shearing problem, with the second law of thermodynamics and condition of thermodynamic stability. The results are that a
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A strain gradient theory of plasticity
International Journal of Solids and Structures, 1970Abstract A theory which includes first and second strain gradients is proposed as a model for plastic deformations. Heuristic arguments for including the gradients are also given. The main goal is to develop a logical framework in which behavior on a small scale can interact with the response on a larger one.
Dillon, O. W. jun., Kratochvil, J.
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A variational principle for gradient plasticity
International Journal of Solids and Structures, 1991We elaborate on a generalized plasticity model, which belongs to the class of gradient models. The generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher-order spatial gradients of the equivalent plastic strain in the yield condition.
Mühlhaus, H.-B., Aifantis, E. C.
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Gradient plasticity in isotropic solids
Mathematics and Mechanics of Solids, 2021We discuss a framework for the description of gradient plasticity in isotropic solids based on the Riemannian curvature derived from a metric induced by plastic deformation. This culminates in a flow rule in the form of a fourth-order partial differential equation for the plastic strain rate, in contrast to the second-order flow rules that have been ...
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Gradient-Enhanced Continuum Plasticity
, 2020 This book provides an expansive review of gradient-enhanced continuum plasticity from the initial stage to current research trends in experimental, theoretical, computational and numerical ...
Voyiadjis, George Z.
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Gradient Plasticity Formulations
2017A theoretical framework that has potential to cover a large range of gradient plasticity effects in isotropic materials is presented. Four classes of strain gradient plasticity theories are considered, aiming to span a wide domain of gradient plasticity formulations.
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On the role of moving elastic–plastic boundaries in strain gradient plasticity
Modelling and Simulation in Materials Science and Engineering, 2006Gradient plasticity theories which are used to describe size effects require nonstandard boundary conditions. We believe that the role of these boundary conditions in combination with a moving elastic–plastic boundary has so far not been well understood. In order to clarify the conditions which are required at such an internal boundary, semi-analytical
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Shakedown theorems for elastic–plastic solids in the framework of gradient plasticity
International Journal of Plasticity, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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