A “Numerical Mesoscope” for the Investigation of Local Fields in Rate-Dependent Elastoplastic Materials at Finite Strain

Haddadi, H.; Teodosiu, Cristian; Héraud, S.; Allais, L.; Zaoui, A.

doi:10.1007/978-94-017-0297-3_28

Cited by 6 publications

(4 citation statements)

References 5 publications

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“…Some authors () have intended to do so by intercalating between the heterogeneous model of interest and the boundary conditions of a homogeneous medium, with the appropriate homogenized tensor. As the properties of the medium do not vary in space, the corresponding mesh does not need to be heavily refined, and the boundary conditions can therefore be pushed away in a cost‐effective manner.…”

Section: A New Methods For the Determination Of The Homogenized Tensormentioning

confidence: 99%

“…The idea of coupling the microstructure to a homogenized medium to limit the influence of the boundary conditions was already developed in and , but with three major differences: (1) the microstructure is here random, although it was deterministic (and heterogeneous) in the previous papers; (2) the coupling is here made over a volume rather than along a surface; and (3) the approach is coupled to an iterative scheme to identify the value of the effective tensor, although it was previously only used to perform direct computations, for a given value of the homogenized tensor.…”

Section: Introductionmentioning

confidence: 99%

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Numerical strategy for unbiased homogenization of random materials

Cottereau

2013

Numerical Meth Engineering

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International audienceThis paper presents a numerical strategy that allows to lower the costs associated to the prediction of the value of homogenized tensors in elliptic problems. This is done by solving a coupled problem, in which the complex microstructure is confined to a small region and surrounded by a tentative homogenized medium. The characteristics of this homogenized medium are updated using a self-consistent approach and are shown to converge to the actual solution. The main feature of the coupling strategy is that it really couples the random microstructure with the deterministic homogenized model, and not one (deterministic) realization of the random medium with a homogenized model. The advantages of doing so are twofold: (a) the influence of the boundary conditions is significantly mitigated, and (b) the ergodicity of the random medium can be used in full through appropriate definition of the coupling operator. Both of these advantages imply that the resulting coupled problem is less expensive to solve, for a given bias, than the computation of homogenized tensor using classical approaches. Examples of 1D and 2D problems with continuous properties, as well as a 2D matrix-inclusion problem, illustrate the effectiveness and potential of the method

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Section: A New Methods For the Determination Of The Homogenized Tensormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical strategy for unbiased homogenization of random materials

Cottereau

2013

Numerical Meth Engineering

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“…The total number of elements was 3050. This type of element is suitable for elastic-plastic materials (Haddadi and Teodosiu, 1999;Heraud et al, 1998;Haddadi et al, 2001;Salahouelhadj and Haddadi, 2010). As the shape of each grain was different on faces A and B (see Fig.…”

Section: Finite Element Analysismentioning

confidence: 99%

Applying the grid method and infrared thermography to investigate plastic deformation in aluminium multicrystal

Bădulescu

Grédiac

Haddadi

et al. 2011

Mechanics of Materials

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“…It could either neglect neighbour grain effects (ii)) or take them into account (iii)). Using the FE code CAST3M, it is possible to compute the shear stresses on the 12 slip systems owing to additional subroutines developed by Heraud [9]. One orientation is attributed to each grain using the EBSD data [4].…”

Section: Introductionmentioning

confidence: 99%

Influence of Crystalline Elasticity on the Stress Distribution at the Free Surface of an Austenitic Stainless Steel Polycrystal. Comparison with Experiments

Sauzay

Man

2007

MSF

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This numerical study focuses on the recent observations of Man et al. [4] showing welloriented grains presenting no Persistent Slip Marking even if PSMs are observed in 86% of the surface grains in 316L austenitic stainless steel cycled at room temperature up to 60% of fatigue life. Scanning Electron Microscopy (SEM) permits us to build Finite Element (FE) meshes of the observed aggregates and to assign to the modelled grains the crystallographic orientations measured by Electron Back Scattering Diffraction (EBSD). Then, 3D FE computations using crystalline elasticity allow the evaluation of mean grain stress tensors and resolved shear stresses. The results could explain qualitatively the anomalous behaviour of the studied well-oriented grains which is partly due to the particular orientations and shapes of the neighbour grains. This study highlights the influence of crystalline elasticity and neighbour grains in microplasticity and crack nucleation.

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A “Numerical Mesoscope” for the Investigation of Local Fields in Rate-Dependent Elastoplastic Materials at Finite Strain

Cited by 6 publications

References 5 publications

Numerical strategy for unbiased homogenization of random materials

Numerical strategy for unbiased homogenization of random materials

Applying the grid method and infrared thermography to investigate plastic deformation in aluminium multicrystal

Influence of Crystalline Elasticity on the Stress Distribution at the Free Surface of an Austenitic Stainless Steel Polycrystal. Comparison with Experiments

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