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Computational Mechanics
Erschienen in: Computational Mechanics 3/2022

21.01.2022 | Original Paper

Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua

verfasst von: Xiaozhe Ju, Rolf Mahnken, Yangjian Xu, Lihua Liang

Erschienen in: Computational Mechanics | Ausgabe 3/2022

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Abstract

We develop a goal-oriented finite element method for a class of micromorphic hyperelasticity problems, where size effects are taken into account by an enriched kinematics. Upon introducing a notion of generalized solutions, an abstract weak formulation that is convenient to error estimation is established along with its finite element discretization. Based on duality techniques, exact error representations aiming at a user-defined quantity of interest are derived. The dual problem is first introduced in a secant form, and subsequently linearized and discretized. The resulting discretizations of both primal and dual problem are shown to be consistent, thus theoretically ensuring an optimal convergence order. Some relevant numerical aspects are discussed in detail. In combination with a patch recovery technique avoiding nonlinear computations, an efficient error estimator is developed to guide a greedy adaptive mesh refinement algorithm. The effectiveness of the resulting algorithm is investigated by several numerical examples.
Vorheriger Artikel Crystal plasticity model of residual stress in additive manufacturing using the element elimination and reactivation method
Nächster Artikel A two-level macroscale continuum description with embedded discontinuities for nonlinear analysis of brick/block masonry

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Metadaten
Titel
Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua
verfasst von
Xiaozhe Ju
Rolf Mahnken
Yangjian Xu
Lihua Liang
Publikationsdatum
21.01.2022
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 3/2022
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-021-02117-y

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