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1
Content available Simulation of Lueders bands using regularized large strain elasto-plasticity
Mucha M., Wcisło B., Pamin J.
Archives of Mechanics
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2021
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Vol. 73, nr 1
83--117
EN
This paper deals with the numerical simulation of an instability phenomenon called Lueders bands with two regularized material models: viscoplasticity and gradient-enhanced plasticity. The models are based on large strain kinematics and temperature-dependence is incorporated. The Huber–Mises–Hencky yield condition and multi-branch hardening are employed. After a brief presentation of the constitutive description, test computations are performed using AceGen and AceFEM symbolic packages for Wolfram Mathematica. The first benchmark is a rectangular tensile plate in plane strain isothermal conditions. For the viscoplastic model, simulation results for different values of viscosity, loading duration and enforced displacement are compared. For the gradient model different internal lengths are used. Mesh sensitivity of the results and the influence of boundary conditions are also examined. Next to the Lueders-type response to a softening-hardening yield strength function, an additional softening stage leading to failure is also considered. The second example concerns a bone-shape sample under tension, for which, next to mesh sensitivity and the effect of regularization, the influence of heat conduction on simulation results is evaluated.
2
Content available Simulation of propagative instability in shear using gradient-enhanced and viscoplastic model
Mucha Marzena, Wcisło Balbina, Pamin Jerzy
Computer Methods in Materials Science
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2019
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Vol. 19, No. 2
57--63
EN
The research presented in this paper is focused on simulation of a propagative instability called Lueders bands using large strain plasticity with Huber-Mises-Hencky yield function. Two types of regularization are used: gradient-enhanced plasticity and viscoplasticity. Regularization is needed to avoid mesh sensitivity associated with the classical continuum description. A special sample is used to study Lueders band propagation in shear, its shape is motivated by experiments. The gradient-enhanced model used in computation provides a more reliable regularization than the viscoplastic model.
PL
W artykule zaprezentowano symulacje numeryczne propagujących się pasm lokalizacji odkształcenia nazywanych pasmami Luedersa wykorzystując model dużych deformacji z funkcją plastyczności Hubera-Mises-Hencky'ego. Użyto dwóch typów regularyzacji, gradientowej plastyczności oraz lepkoplastyczności. Regularyzacja jest niezbędna celem uniknięcia zależności wyników od gęstości siatki elementów skończonych. Do przeprowadzania obliczeń w warunkach czystego ścinania została użyta specjalna próbka, której kształt motywowany jest eksperymentami. Model gradientowy wykazał lepsze możliwości regularyzacyjne niż model lepkoplastyczny.
3
Content available remote Selection of slip systems in confined single crystal gradient plasticity: coupled effects of slip system orientations, latent hardening, and grain boundaries
Dequiedt J. L.
Archives of Mechanics
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2019
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Vol. 71, nr 3
207--238
EN
In crystal plasticity under prescribed deformation, the incremental material response is potentially non-unique owing to slip system redundancy for most of the crystalline structures. Following Petryk, energy minimizing considerations give the way to select one of these solutions and the set of active systems, which depend on their more or less favorable orientation and their mutual interactions (latent hardening). This variational approach is extended here to confined plasticity in a finite volume, simulating a single crystal embedded in an aggregate. A slip gradient enhanced framework and related micro-hard boundary conditions are considered, using two defect energies introduced by Gurtin and coworkers: the first one takes the slip system polar dislocation densities as internal state variables and the second one is a quadratic potential of the dislocation density tensor. In both cases, micro-hard conditions amount to null flow for the two former quantities. For the classical one dimensional case of a strip in simple shear, the two models yield substantially different solutions, the second one coupling the gradients on the different systems. These results emphasize the necessity for a physically motivated modeling of gradient effects in the vicinity of grain boundary interfaces.
4
Content available remote A minimal gradient-enhancement of the classical continuum theory of crystal plasticity. Part I: The hardening law
Petryk H., Stupkiewicz S.
Archives of Mechanics
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2016
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Vol. 68, nr 6
459--485
EN
A simple gradient-enhancement of the classical continuum theory of plasticity of single crystals deformed by multislip is proposed for incorporating size effects in a manner consistent with phenomenological laws established in materials science. Despite considerable efforts in developing gradient theories, there is no consensus regarding the minimal set of physically based assumptions needed to capture the slip-gradient effects in metal single crystals and to provide a benchmark for more refined approaches. In order to make a step towards such a reference model, the concept of the tensorial density of geometrically necessary dislocations generated by slip-rate gradients is combined with a generalized form of the classical Taylor formula for the flow stress. In the governing equations in the rate form, the derived internal length scale is expressed through the current flow stress and standard parameters so that no further assumption is needed to define a characteristic length. It is shown that this internal length scale is directly related to the mean free path of dislocations and possesses physical interpretation which is frequently missing in other gradient-plasticity models.
5
Content available remote A minimal gradient-enhancement of the classical continuum theory of crystal plasticity. Part II: Size effects
Stupkiewicz S., Petryk H.
Archives of Mechanics
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2016
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Vol. 68, nr 6
487--513
EN
In our previous paper, a simple gradient-enhancement of the classical continuum theory of plasticity of single crystals deformed by multislip has been proposed for incorporating size effects. A single internal length scale has been derived as an explicit function of the flow stress defined as the isotropic part of critical resolved shear stresses. The present work is focused on verification whether the simplifications involved are not too severe and allow satisfactory predictions of size effects. The model has been implemented in a finite element code and applied to three-dimensional simulations of fcc single crystals. We have found that the experimentally observed indentation size effect in a Cu single crystal is captured correctly in spite of the absence of any adjustable length-scale parameter. The finite element treatment relies on introducing non-local slip rates that average and smoothen on an element scale the corresponding local quantities. Convergence of the finite element solution to the analytical one is also verified for the one-dimensional problem of a boundary layer formed at a constrained interface.
6
Content available Computational modelling of localized deformations with regularized continuum models
Pamin J.
Mechanics and Control
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2011
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Vol. 30, no. 1
27-33
EN
The paper presents a short overview of selected problems related to the numerical analysis of localized deformations. After defining the localization phenomenon and the class of gradient models, two simulation examples are shown. They are applications of the plasticity theory with a Laplacian of the hardening parameter and of the damage theory with an additional averaging equation for an equivalent strain measure.
PL
Artykuł przedstawia krótki przegląd wybranych problemów analizy numerycznej deformacji zlokalizowanych. Po zdefiniowaniu zjawiska lokalizacji i klasy modeli gradientowych zwięźle opisano dwa przykładowe zastosowania teorii płynięcia plastycznego zawierającej laplasjan parametru wzmocnienia i teorii uszkodzenia z dodatkowym równaniem uśredniającym miarę odkształcenia w otoczeniu punktu.
7
Content available remote Numerical simulation of instabilities in one- and two-phase soil model based on CAM-CLAY plasticity
Pamin J., Stankiewicz A.
Czasopismo Techniczne. Środowisko
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2008
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R. 105, z. 3-Ś
81-91
EN
In the paper a two-phase gradient-dependent soil model which is an extension of the Modified Cam-Clay plasticity concept has been derived. A three field finite element with the discretization of displacements, plastic multiplier and excess pore pressure has been proposed for the analysis of instabilities in the consolidation problem of evolving deformations and pore pressures. A set of computations for the biaxial compression test have been performed.
PL
W artykule przedstawiono gradientowy model gruntu będący rozszerzeniem zmodyfikowanego modelu Cam-Clay dla ośrodka dwufazowego. Do opisu problemu konsolidacji i ewolucji odkształceń i ciśnień porowych użyto trójpolowego elementu skończonego, z aproksymacją pola przemieszczeń, mnożnika plastycznego i nadwyżki ciśnień porowych. Przedstawiono wyniki obliczeń dla testu dwuosiowego ściskania.
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