High‐order finite elements compared to low‐order mixed element formulations

Netz, Torben; Düster, Alexander; Hartmann, Stefan

doi:10.1002/zamm.201200040

Cited by 16 publications

(6 citation statements)

References 45 publications

(61 reference statements)

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“…The second strain-energy function under consideration is based on a split into an isochoric U(J) and unimodular W(IC, IIC) part see Hartmann and Neff [6] and Netz et al [7]. The principal invariants of the unimodular right Cauchy-Green tensor are given with…”

Section: Hyperelastic Materials Modelmentioning

confidence: 99%

A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

Schröder

Wick

Reese

et al. 2020

Arch Computat Methods Eng

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In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis’.

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Section: Hyperelastic Materials Modelmentioning

confidence: 99%

A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

Schröder

Wick

Reese

et al. 2020

Arch Computat Methods Eng

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“…In this example the h-version is clearly faster than the p-version finite element simulations. This cannot be generalized, however, as it depends on the mesh density of the p-version formulation, see [39].…”

Section: Cook's Membranementioning

confidence: 99%

“…Another possibility is to apply high-order finite elements with an appropriate higher polynomial degree. This approach employs hierarchical shape functions based on integrated Legendre polynomials [13,29,58] or [39] for the case of large deformations. This element formulation goes back to [55], see [12] as well.…”

Section: Introductionmentioning

confidence: 99%

Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p‐version finite elements

2014

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In this article the multiplicative decomposition of the deformation gradient into one part constrained in the direction of the axis of anisotropy and one part describing the directional deformation is proposed. This leads to a clear division of the deformation and stress states in the direction of anisotropy and a remaining part. The decomposition is explained in detail and a constitutive model of hyper-elasticity is proposed for the case of transversal isotropy, where the behavior of the model is investigated with the aid of simple analytical examples. The model is also investigated for inhomogeneous deformation states using high-order finite elements based on hierarchical shape functions showing the sensitivity of the accuracy of the results in the case of anisotropic media.

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“…Small and higher order elements are useful when the results change rapidly, and bigger size, loworder [18,19] elements are usable when the results are more constant [20].…”

Section: Introductionmentioning

confidence: 99%

Implementing model reduction to the JuliaFEM platform

Rapo¹,

Aho²,

Koivurova³

et al. 2018

RakMek

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JuliaFEM is an open source nite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper rst describes the JuliaFEM concept briey after which it presents the theory of model reduction, and nally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

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High‐order finite elements compared to low‐order mixed element formulations

Cited by 16 publications

References 45 publications

A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p‐version finite elements

Implementing model reduction to the JuliaFEM platform

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