On the Implementation of Plane Stress in Computational Multiscale Modeling

Lillbacka, Robert; Larsson, Fredrik; Runesson, Kenneth

doi:10.1615/intjmultcompeng.v4.i5-6.110

Cited by 9 publications

(8 citation statements)

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“…Miehe and Koch [3], Temizer and Wriggers [11]. This approach was then formulated in a continuous variational setting by Larsson and Runesson [14], Lillbacka et al [15]. (ii) The novel ''dual approach" was proposed by Larsson and Runesson [14] in the very same continuous variational setting.…”

Section: Macroscale Ats-tensormentioning

confidence: 99%

Computational homogenization based on a weak format of micro-periodicity for RVE-problems

Larsson

Runesson

Saroukhani

et al. 2011

Computer Methods in Applied Mechanics and Engineering

103

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Section: Macroscale Ats-tensormentioning

confidence: 99%

Computational homogenization based on a weak format of micro-periodicity for RVE-problems

Larsson

Runesson

Saroukhani

et al. 2011

Computer Methods in Applied Mechanics and Engineering

103

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“…The pertinent model assumptions, discussed thoroughly by Lillbacka et al [5], are summarized briefly in what follows.…”

Section: Preliminariesmentioning

confidence: 99%

“…We note that two different options are available for computing the components ofL I,I : (i) The "primal approach" was originally proposed by Miehe and Koch [12] in a discrete format for 3D modeling. This approach was formulated in a continuous variational setting by Larsson and Runesson [11], Lillbacka et al [5]. (ii) The novel "dual approach" was proposed by Larsson and Runesson [11] in the continuous variational setting, and it is particularly attractive in conjunction with adaptive computations aiming for control of the subscale discretization error.…”

Section: Macro-scale Problemmentioning

confidence: 99%

“…Methods for estimating the model error have been developed by, for instance, Stein et al [6], Oden and Vemaganti [7], Braack and Ern [8] and Larsson and Runesson [9][10][11]. The purpose of this paper is to extend the results of Lillbacka et al [5] and of Larsson and Runesson [10] with the purpose to investigate the possibility of carrying out fully model-adaptive two-scale CMM computations under the specific assumption of macroscale plane stress. However, the chosen model hierarchy is quite restricted in the sense that only the error of adopting the Taylor assumption for the RVE kinematics is included.…”

Section: Introductionmentioning

confidence: 99%

“…A number of other model assumptions can be envisioned: For thin structures (such as metal sheets) it is possible to implement "plane stress" in different ways, c.f. Lillbacka et al [5]. Other assumptions regard the choice of substructure modeling, such as constitutive modeling of constituents, size of the RVE, discretization of the RVE, etc.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the adaptive use of the Taylor assumption in computational homogenization of thin metal sheets

Larsson

Lillbacka²,

Runesson

2009

Int J Mater Form

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A strategy for macroscale modeling adaptivity in fully nested two-scale computational (first order) homogenization based on assumed scale separation is proposed. The Representative Volume Element (RVE) for a quite complex substructure pertinent to Duplex Stainless Steel (DSS) is considered, whereby crystal plasticity is adopted for the subscale material modeling. The choice of the pertinent prolongation condition defining the deformation mapping from the macroto the subscale is the sole source of model error discussed here. Two common choices are (in hierarchical order): (1) "simplified" model based on homogeneous (macroscale) deformation within the RVE, i.e., the Taylor assumption, (2) "reference" model employing Dirichlet boundary conditions on the RVE.

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A numerical homogenisation method for sandwich plates based on a plate theory with thickness change

Helfen

Diebels

2012

Z Angew Math Mech

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Nowadays composite plates are widely used, especially in the transport industry. Their importance derives from their relatively low weight and good mechanical properties, but their behaviour is complex and cannot be obtained from a simple mixture rule properly. In the scope of this work, the considered composite plate is composed of a complex assembly of metal layers and carbon fibers reinforced polymers (CFRP) layers. Whereas the CFRP can be considered as anisotropic elastic, the metal layers have an elasto-plastic material behaviour. In this case, the possibility to use the classical plate theory is excluded, because the classical plate theory can only regard small deformations and linear material behaviour. For this reason, the modelling of the mechanical behaviour of the composite plate is based on a numerical homogenisation. The underlying principle is a numerical multi-scale consideration of the composite plate: on the one hand, the macroscale is considered as a Finite Element computation of a plate which is following a plate theory including a thickness change, i. e. a seven degrees of freedom approach. On the other hand, the mesoscale is obtained with a three-dimensional modelling which explicitly takes into account the stacking order and the material behaviour of the different layers. From each integration point of the macroscale, the deformations are projected on the boundaries of a Representative Volume Element (RVE) of the mesoscale. In this scale, a boundary value problem is solved, and the macroscopic forces, moments and shear forces are obtained as resultants from the mesoscopic stresses.

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On the Implementation of Plane Stress in Computational Multiscale Modeling

Cited by 9 publications

References 0 publications

Computational homogenization based on a weak format of micro-periodicity for RVE-problems

Computational homogenization based on a weak format of micro-periodicity for RVE-problems

On the adaptive use of the Taylor assumption in computational homogenization of thin metal sheets

A numerical homogenisation method for sandwich plates based on a plate theory with thickness change

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