Finite element calculation of the stability behaviour of hyperelastic solids with the enhanced strain method

authored by: S. Reese, Peter Wriggers
Abstract: The stability behaviour of hyperelastic solids is characterized by two different kinds of instabilities. First, there are structural instabilities which occur under compressive stresses for moderate strains but large displacements. Structural instabilities depend only quantitatively on the chosen material law. In contrast to this, material instabilities can be observed only for certain constitutive relations (qualitative dependence). They occur under tensile stresses for large strains. To investigate the stability behaviour of hyperelastic solids, it is necessary to take into account geometncal as well as material non-linearities. This can be done by a numerical method. Here, the finite element method is used. Rubber represents a nearly incompressible material. Additionally, bending dominated secondary deformation states occur. In these situations standard displacement element formulations show extreme locking behaviour, i.e., the calculated displacements are much too small. To overcome this problem, the enhanced strain method is used, with which locking-free elements can be obtained.
External Organisation(s): Technische Universität Darmstadt
Type: Article
Journal: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume: 76
Pages: 415-416
No. of pages: 2
ISSN: 0044-2267
Publication date: 1996
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Applied Mathematics
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{6f8931481e584326a9e8c91f3359b0b9,
title = "Finite element calculation of the stability behaviour of hyperelastic solids with the enhanced strain method",
abstract = "The stability behaviour of hyperelastic solids is characterized by two different kinds of instabilities. First, there are structural instabilities which occur under compressive stresses for moderate strains but large displacements. Structural instabilities depend only quantitatively on the chosen material law. In contrast to this, material instabilities can be observed only for certain constitutive relations (qualitative dependence). They occur under tensile stresses for large strains. To investigate the stability behaviour of hyperelastic solids, it is necessary to take into account geometncal as well as material non-linearities. This can be done by a numerical method. Here, the finite element method is used. Rubber represents a nearly incompressible material. Additionally, bending dominated secondary deformation states occur. In these situations standard displacement element formulations show extreme locking behaviour, i.e., the calculated displacements are much too small. To overcome this problem, the enhanced strain method is used, with which locking-free elements can be obtained.",
author = "S. Reese and Peter Wriggers",
year = "1996",
language = "English",
volume = "76",
pages = "415--416",
journal = "ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik",
issn = "0044-2267",
publisher = "Wiley-VCH Verlag",
number = "SUPPL. 5",
}