@article{d1b5cbe079dd4a6aa82dbcd4ff594b23,
title = "p-FEM applied to finite isotropic hyperelastic bodies",
abstract = "In this article the p-version finite element method is applied to finite strain problems. In particular, the behaviour of high order finite elements is studied for an isotropic hyperelastic material in the case of near incompressibility. The question of robustness with respect to distortion and efficiency of anisotropic p-version elements for thin-walled or beam-like structures will be addressed. It will be shown that the p-version finite element approach is a promising method to compute geometrically highly non-linear structures.",
keywords = "Anisotropic finite elements, Finite strains, Hyperelasticity, P-FEM",
author = "Alexander D{\"u}ster and Stefan Hartmann and Ernst Rank",
note = "Funding Information: On the other hand, it has been shown by Suri [11] and Szab{\'o} and Babuska [12] in the case of small strains that beyond a certain polynomial order of the shape functions locking-free results are obtained. Furthermore, it was demonstrated in the case of small strains that high order elements are superior to the h-version, even when compared to adaptive state-of-the-art approaches. With regard to Reissner–Mindlin-type plates, for example, significant advantages of a uniform p-version over an adaptive h-version based on MITC4 elements can be observed [13,14] . Within the joint research project {\textquoteleft}Adaptive Finite-Element-Methods in Computational Mechanics{\textquoteright} undertaken by nine German University Institutes and supported by the German National Science Foundation (Deutsche Forschungsgemeinschaft DFG), several benchmark problems, tackled by all groups using different finite element strategies, were defined, computed and compared. Some of the results are set out in [15] . A detailed report on the behaviour of the p-version for three-dimensional thin-walled structures, based on a solid type of hexahedral element, can be found in [14,16] . This shows that the approach, which is also applied in this paper, yields a consistent and efficient strategy to analyse both thin and thick-walled, three-dimensional, curved structures with the same type of anisotropic hexahedral elements. The efficiency of the p-version also extends to non-linear problems, such as elastoplasticity. By comparing a uniform p-version to an adaptive strategy based on Q1P0 elements the superior behaviour of high order finite elements for the deformation theory of plasticity can be shown numerically, [17] . In the case of a physically more realistic elastoplastic model, based on the flow theory, the computation of both two and three-dimensional benchmark problems emphasizes the advantages of high order finite elements [15,16,18,19] . ",
year = "2003",
month = nov,
day = "21",
doi = "10.1016/j.cma.2003.07.003",
language = "English",
volume = "192",
pages = "5147--5166",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier B.V.",
number = "47-48",
}