A finite deformation brick element with inhomogeneous mode enhancement

Mueller-Hoeppe, Dana; Löhnert, Stefan; Wriggers, Peter

doi:10.1002/nme.2523

Cited by 35 publications

(28 citation statements)

References 31 publications

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“…Remark The center evaluation is, eg, used in . A possible alternative is the use of the average deformation gradient

{boldF}_{a v g} = \frac{1}{V} \int_{{normalΩ}_{e}} {boldF}^{h, e} normald V

within an element with volume V as eg done in, the works . However, differences between using the average value and the evaluation at the element centroid are very small in usual problems without localization of strains (see Section 3.7).…”

Section: Enhanced Assumed Strain Methodsmentioning

confidence: 99%

On transformations and shape functions for enhanced assumed strain elements

Pfefferkorn

Betsch

2019

Numerical Meth Engineering

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Summary We summarize several previously published geometrically nonlinear EAS elements and compare their behavior. Various transformations for the compatible and enhanced deformation gradient are examined. Their effect on the patch test is one main concern of the work, and it is shown numerically and with a novel analytic proof that the improved EAS element proposed by Simo et al in 1993 does not fulfill the patch test. We propose a modification to overcome that drawback without losing the favorable locking‐free behavior of that element. Furthermore, a new transformation for the enhanced field is proposed and motivated in a curvilinear coordinate frame. It is shown in numerical tests that this novel approach outperforms all previously introduced transformations.

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“…Remark The center evaluation is, eg, used in . A possible alternative is the use of the average deformation gradient

{boldF}_{a v g} = \frac{1}{V} \int_{{normalΩ}_{e}} {boldF}^{h, e} normald V

Section: Enhanced Assumed Strain Methodsmentioning

confidence: 99%

On transformations and shape functions for enhanced assumed strain elements

Pfefferkorn

Betsch

2019

Numerical Meth Engineering

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“…Higher-order interpolations may suffer less from this problem, but the displacement solution is still of low order accuracy [52][53][54]. In this work, the classical Q1P0 method is employed where the displacement and pressure are the primary unknowns.…”

Section: Gel In Micropore Of Hcpmentioning

confidence: 99%

Multiscale hydro-thermo-chemo-mechanical coupling: Application to alkali–silica reaction

Temizer¹,

Wriggers²

2014

Computational Materials Science

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a b s t r a c tAlkali-Silica Reaction (ASR) is a complex chemical process that affects concrete structures and so far various mechanisms to account for the reaction at the material level have already been proposed. The present work adopts a simple mechanism, in which the reaction takes place at the micropores of concrete, with the aim of establishing a multiscale framework to analyze the ASR induced failure in the concrete. For this purpose, 3D micro-CT scans of hardened cement paste (HCP) and aggregates with a random distribution embedded in a homogenized cement paste matrix represent, respectively, the microscale and mesoscale of concrete. The analysis of the deterioration induced by ASR with the extent of the chemical reaction is initialized at the microscale of HCP. The temperature and the relative humidity influence the chemical extent. The correlation between the effective damage due to ASR and the chemical extent is obtained through a computational homogenization approach, enabling to build the bridge between microscale damage and macroscale failure. A 3D hydro-thermo-chemo-mechanical model based on a staggered method is developed at the mesoscale of concrete, which is able to reflect the deterioration at the microscale due to ASR.

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“…The stabilization matrix can also be derived in a similar way as stabilization techniques for underintegrated and stabilized finite element formulations. The approach was suggested by Reese and Wriggers [17] and further developed in [18] and in [14]. There have been several approaches where the original EAS formulation is combined with other proven approaches in order to improve stability of EAS elements.…”

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confidence: 99%

An improved EAS brick element for finite deformation

2010

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A new enhanced assumed strain brick element for finite deformations in finite elasticity and plasticity is presented. The element is based on an expansion of shape function derivatives using Taylor series and an extended set of orthogonality conditions that have to be satisfied for an hourglassing free EAS formulation. Such approach has not been applied so far in the context of large deformation threedimensional problems. It leads to a surprisingly well-behaved locking and hourglassing free element formulation. Major advantage of the new element is its shear locking free performance in the limit of very thin elements, thus it is applicable to shell type problems. Crucial for the derivation of the residual and consistent tangent matrix of the element is the automation of the implementation by automatic code generation.

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A finite deformation brick element with inhomogeneous mode enhancement

Cited by 35 publications

References 31 publications

On transformations and shape functions for enhanced assumed strain elements

On transformations and shape functions for enhanced assumed strain elements

Multiscale hydro-thermo-chemo-mechanical coupling: Application to alkali–silica reaction

An improved EAS brick element for finite deformation

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