A macro-element for incompressible finite deformations based on a volume averaged deformation gradient

Boerner, Eiris F. I.; Wriggers, Peter

doi:10.1007/s00466-008-0250-x

Cited by 9 publications

(2 citation statements)

References 28 publications

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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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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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“…In this approach, an element is split into sub-triangles (sub-tetrahedra), and then on each sub-triangle the strain is approximated and combined to recover the strain field over the entire element. Similar constructions are also used in [13] to construct a three-dimensional brick element for nearly incompressible nonlinear elasticity problems and in [23,24,25,30] for triangular bending elements.…”

Section: Introductionmentioning

confidence: 99%

Stress‐hybrid virtual element method on quadrilateral meshes for compressible and nearly‐incompressible linear elasticity

Chen,

Sukumar

2023

Numerical Meth Engineering

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In this article, we propose a robust low‐order stabilization‐free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress‐hybrid principle. We refer to this approach as the stress‐hybrid virtual element method (SH‐VEM). In this method, the Hellinger–Reissner variational principle is adopted, wherein both the equilibrium equations and the strain‐displacement relations are variationally enforced. We consider small‐strain deformations of linear elastic solids in the compressible and near‐incompressible regimes over quadrilateral (convex and nonconvex) meshes. Within an element, the displacement field is approximated as a linear combination of canonical shape functions that are virtual. The stress field, similar to the stress‐hybrid finite element method of Pian and Sumihara, is represented using a linear combination of symmetric tensor polynomials. A 5‐parameter expansion of the stress field is used in each element, with stress transformation equations applied on distorted quadrilaterals. In the variational statement of the strain‐displacement relations, the divergence theorem is invoked to express the stress coefficients in terms of the nodal displacements. This results in a formulation with solely the nodal displacements as unknowns. Numerical results are presented for several benchmark problems from linear elasticity. We show that SH‐VEM is free of volumetric and shear locking, and it converges optimally in the norm and energy seminorm of the displacement field, and in the norm of the hydrostatic stress.

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Brick Elements for Finite Deformations Based on Macro-concepts and on Inhomogeneous Mode Enhancement

Wriggers

Mueller-Hoeppe

Löhnert

ECCOMAS Multidisciplinary Jubilee Symposium

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A macro-element for incompressible finite deformations based on a volume averaged deformation gradient

Cited by 9 publications

References 28 publications

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

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

Stress‐hybrid virtual element method on quadrilateral meshes for compressible and nearly‐incompressible linear elasticity

Brick Elements for Finite Deformations Based on Macro-concepts and on Inhomogeneous Mode Enhancement

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