On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials

Download

index.pdf

Date

2019-03-01

Author

Gueltekin, Osman
Dal, Hüsnü
Holzapfel, Gerhard A.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

135
views

81
downloads

Quasi-incompressible behavior is a desired feature in several constitutive models within the finite elasticity of solids, such as rubber-like materials and some fiber-reinforced soft biological tissues. The Q1P0 finite element formulation, derived from the three-field Hu-Washizu variational principle, has hitherto been exploited along with the augmented Lagrangian method to enforce incompressibility. This formulation typically uses the unimodular deformation gradient. However, contributions by Sansour (Eur J Mech A Solids 27:28-39, 2007) and Helfenstein et al. (Int J Solids Struct 47:2056-2061, 2010) conspicuously demonstrate an alternative concept for analyzing fiber reinforced solids, namely the use of the (unsplit) deformation gradient for the anisotropic contribution, and these authors elaborate on their proposals with analytical evidence. The present study handles the alternative concept from a purely numerical point of view, and addresses systematic comparisons with respect to the classical treatment of the Q1P0 element and its coalescence with the augmented Lagrangian method by means of representative numerical examples. The results corroborate the new concept, show its numerical efficiency and reveal a direct physical interpretation of the fiber stretches.

Subject Keywords

Mechanical Engineering, Computational Theory and Mathematics, Applied Mathematics, Ocean Engineering, Computational Mathematics, Finite element analysis, Augmented Lagrangian method, Hyperelasticity, Quasi-incompressibility, Fiber-reinforced materials, Soft biological tissues

URI

https://hdl.handle.net/11511/46054

Journal

COMPUTATIONAL MECHANICS

DOI

https://doi.org/10.1007/s00466-018-1602-9

Collections

Department of Mechanical Engineering, Article

Suggestions

OpenMETU
Core

Computational modeling of passive myocardium Göktepe, Serdar; Wong, Jonathan; Kuhl, Ellen (Wiley, 2011-01-01) This work deals with the computational modeling of passive myocardial tissue within the framework ofmixed, non-linear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscle. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy-Green deformation tensors and structural tensors of the corresponding material symmetry group. This model...
Characterization of fracture processes by continuum and discrete modelling KALISKE, M.; Dal, Hüsnü; FLEISCHHAUER, R.; JENKEL, C.; NETZKER, C. (Springer Science and Business Media LLC, 2012-09-01) A large number of methods to describe fracture mechanical features of structures on basis of computational algorithms have been developed in the past due to the importance of the topic. In this paper, current and promising numerical approaches for the characterization of fracture processes are presented. A fracture phenomenon can either be depicted by a continuum formulation or a discrete notch. Thus, starting point of the description is a micromechanically motivated formulation for the development of a loc...
Hybrid finite element for analysis of functionally graded beams Sarıtaş, Afşin; Soydas, Ozan (2017-01-01) A hybrid finite element model is presented, where stiffness and mass distributions over a beam with functionally graded material (FGM) are accurately modeled for both elastic and inelastic material responses. Von Mises and Drucker-Prager plasticity models are implemented for metallic and ceramic parts of FGM, respectively. Three-dimensional stress-strain relations are solved by a general closest point projection algorithm, and then condensed to the dimensions of the beam element. Numerical examples and veri...
Fracture mechanical behaviour of visco-elastic materials: application to the so-called dwell-effect NAESER, Bastian; KALISKE, Michael; Dal, Hüsnü; NETZKER, Christiane (Wiley, 2009-08-01) The material force approach is an efficient, elegant, and accepted means to compute the J-integral as a fracture mechanical parameter for elastic and inelastic materials. With the formulation of a multiplicative split of the deformation gradient at hand, rate-dependent (visco-elastic) materials described for example by the physically based Bergstrom-Boyce model can be investigated. For these investigations, the so-called material volume forces have to be computed in order to separate the driving forces acti...
Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation Demirci, Nagehan; Tönük, Ergin (2014-01-01) Purpose: During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoelastic behavior obtained from experiments. Although integer order models may yield comparably accurate results, non...

Citation Formats

O. Gueltekin, H. Dal, and G. A. Holzapfel, “On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials,” COMPUTATIONAL MECHANICS, pp. 443–453, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46054.