Integration efficiency for model reduction in micro-mechanical analyses

Tuijl, RA Rody van; Remmers, Jjc Joris; Geers, Mgd Marc

doi:10.1007/s00466-017-1490-4

Cited by 14 publications

(8 citation statements)

References 40 publications

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“…There are mainly two integration methods described in literature, which are Empirical Interpolation Methods (EIM) and Empirical Cubature Methods (ECM) [16], [46]. A numerical examination in comparing different approaches in the multiscale context can be found e.g.…”

Section: Hyper Integrationmentioning

confidence: 99%

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Efficient monolithic solution of FE2 problems

Lange

Hütter

Abendroth

et al. 2021

Proc Appl Math & Mech

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concurrent FE 2 -method is a very powerful and flexible computational tool for multi-scale problems. However the computational effort is very high. The conventional, staggered ("nested Newton") solution scheme solves the microscopic problem iteratively within each macroscopic Newton-Raphson (NR) iteration, although the macroscopic deformation gradients as boundary conditions at the micro scale are only estimates. In this contribution a monolithic FE 2 scheme is proposed, solving the displacements of both scales in a common NR loop, which proved being faster by saving expansive micro-scale iterations.

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Section: Hyper Integrationmentioning

confidence: 99%

“…A numerical examination in comparing different approaches in the multiscale context can be found e.g. in [46] and [44]. Tuijl et.al.…”

Section: Hyper Integrationmentioning

confidence: 99%

Efficient monolithic solution of FE2 problems

Lange

Hütter

Abendroth

et al. 2021

Proc Appl Math & Mech

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show abstract

“…In an attempt to reduce the numerical costs associated with the evaluation of microscale material models, Empirical Interpolation Methods [25][26][27] or Cubature Methods [28,29] make use of stress modes and a reduced set of quadrature points with optimised weights, respectively. The numerical error that is induced by these approximations has, however, been shown to significantly increase with increasing deformation for non-linear historydependent material behaviour, see [30].…”

Section: Introductionmentioning

confidence: 99%

An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics

2022

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Computational multiscale methods are highly sophisticated numerical approaches to predict the constitutive response of heterogeneous materials from their underlying microstructures. However, the quality of the prediction intrinsically relies on an accurate representation of the microscale morphology and its individual constituents, which makes these formulations computationally demanding. Against this background, the applicability of an adaptive wavelet-based collocation approach is studied in this contribution. It is shown that the Hill–Mandel energy equivalence condition can naturally be accounted for in the wavelet basis, (discrete) wavelet-based scale-bridging relations are derived, and a wavelet-based mapping algorithm for internal variables is proposed. The characteristic properties of the formulation are then discussed by an in-depth analysis of elementary one-dimensional problems in multiscale mechanics. In particular, the microscale fields and their macroscopic analogues are studied for microstructures that feature material interfaces and material interphases. Analytical solutions are provided to assess the accuracy of the simulation results.

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“…A possibility to reduce the cost of constructing the cubature was introduced in [29] together with the term Empirical Cubature (EC). The accuracy and efficiency of EC was compared to a variant of DEIM/Gappy POD used in [25] for homogenisation of elasto-viscoplastic materials in small strains [30].…”

Section: Introductionmentioning

confidence: 99%

Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods

Brands¹,

Davydov²,

Mergheim³

et al. 2019

MCA

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The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE 2 method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the micro-scale FE problems are replaced by POD reduced models of comparable accuracy. As these models do not deliver the required reductions in computational effort, they are combined with hyper-reduction methods like the Discrete Empirical Interpolation Method (DEIM), Gappy POD, Gauss–Newton Approximated Tensors (GNAT), Empirical Cubature (EC) and Reduced Integration Domain (RID). The goal of this work is the comparison of the aforementioned hyper-reduction techniques focusing on accuracy and robustness. For the application in the FE 2 framework, EC and RID are favourable due to their robustness, whereas Gappy POD rendered both the most accurate and efficient reduced models. The well-known DEIM is discarded for this application as it suffers from serious robustness deficiencies.

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Integration efficiency for model reduction in micro-mechanical analyses

Cited by 14 publications

References 40 publications

Efficient monolithic solution of FE2 problems

Efficient monolithic solution of FE2 problems

An adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanics

Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods

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