Energy-based non-local plasticity models for deformation patterning, localization and fracture

Lancioni, Giovanni
Yalçınkaya, Tuncay
Cocks, Alan
This paper analyses the effect of the form of the plastic energy potential on the (heterogeneous) distribution of the deformation field in a simple setting where the key physical aspects of the phenomenon could easily be extracted. This phenomenon is addressed through two different (rate-dependent and rate-independent) non-local plasticity models, by numerically solving two distinct one-dimensional problems, where the plastic energy potential has different non-convex contributions leading to patterning of the deformation field in a shear problem, and localization, resulting ultimately in fracture, in a tensile problem. Analytical and numerical solutions provided by the two models are analysed, and they are compared with experimental observations for certain cases.


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Bulutay, C; Tanatar, B (IOP Publishing, 1998-09-01)
We study the short-range correlations in a quasi-one-dimensional electron gas within the dynamical version of the self-consistent field theory. The static structure factor exhibits a peak structure at low densities. The zero-frequency limit of the dynamic local-field factor has structure not encountered in the previous applications of the present method. The large oscillations at low densities observed in the pair-correlation function indicates a transition to a partially ordered state.
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Tiryaki, Aydın; Celebi, AO (Institute of Mathematics, Czech Academy of Sciences, 1998-01-01)
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Ikot, A. N.; Okorie, U. S.; Sever, Ramazan; Rampho, G. J. (Springer Science and Business Media LLC, 2019-08-12)
Within the framework of non-relativistic quantum mechanics via the Nikiforov-Uvarov (NU) method, we obtained the energy eigenvalues and the corresponding normalized eigenfunctions of a newly proposed screened Kratzer potential for lithium hydride (LiH) and hydrogen chloride (HCl) diatomic molecules. With the help of the Hellman-Feynman theorem, the expressions for the expectation values of the square of inverse of position, r(-2), inverse of position, r(-1), kinetic energy, T, and square of momentum, p(2), ...
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Pierce, D (Duke University Press, 2004-12-01)
This paper concerns the basic model-theory of fields of arbitrary characteristic with operators. Simplified geometric axioms are given for the model-companion of the theory of fields with a derivation. These axioms generalize to the case of several commuting derivations. Let a D-field be a field with a derivation or a difference-operator, called D. The theory of D-fields is companionable. The existentially closed D-fields can be characterized geometrically without distinguishing the two cases in which D can...
Citation Formats
G. Lancioni, T. Yalçınkaya, and A. Cocks, “Energy-based non-local plasticity models for deformation patterning, localization and fracture,” PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, pp. 0–0, 2015, Accessed: 00, 2020. [Online]. Available: