Summary.
This contribution is concerned with the consideration of material incompressibility at large strains and proposes various methods for the enforcement of the corresponding constraint into finite-rotation shell models. The incompressibility condition can be expressed in terms of displacement as well as strain variables and is considered by means of three different procedures in the numerical implementation. As kinematic hypothesis a quadratic assumption with respect to the thickness coordinate is used in which the corresponding directors are decomposed into two stretch parameters and a common inextensible unit vector. Various constitutive laws holding for incompressible isotropic hyperelasticity are considered and directly coupled with shell equations through a numerical thickness integration. A 4-node isoparametric shell element is developed parameterizing the inextensible shell director in terms of rotation variables in the framework of an up-dated rotation formulation. Finally, several examples are analysed to identify the most effective procedure for modelling isochoric deformations in thin-walled structures.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
In memory of Y. Başar, who passed away on August 30, 2002.
Rights and permissions
About this article
Cite this article
Başar, Y., Grytz, R. Incompressibility at large strains and finite-element implementation. Acta Mechanica 168, 75–101 (2004). https://doi.org/10.1007/s00707-003-0055-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-003-0055-0