Nearly-constrained transversely isotropic linear elasticity

energetically consistent anisotropic deformation modes for mixed finite element formulations

authored by: Michele Marino, Peter Wriggers
Abstract: Strong anisotropies and/or near-incompressibility properties introduce internal constraints in material deformation. Numerical simulations comprising such a constrained behaviour show an overstiff structural response, referred to as element locking. Implementations based on mixed variational methods can heal locking but available solutions in the state-of-the-art are still non-optimal for anisotropic materials. This paper addresses this issue, by proposing a novel decomposition of anisotropic deformation modes on the basis of kinematic and energy requirements. Theoretical results exploit the Walpole's formalism. The proposed kinematic split allows to introduce a new class of variational principles, referred to as energetically decoupled, for nearly-constrained transversely isotropic materials in linear elasticity. Low-order mixed finite element models are thus derived for treating near-inextensibility and/or near-incompressibility. Two-dimensional benchmark tests reproducing pure-bending and Cook's membrane problems are conducted. Numerical results show that the accuracy of energetically decoupled formulations is high and robust with respect to variations of material properties, while the accuracy of non-energetically decoupled formulations is more sensitive.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Tor Vergata University of Rome
Type: Article
Journal: International Journal of Solids and Structures
Volume: 202
Pages: 166-183
No. of pages: 18
ISSN: 0020-7683
Publication date: 01.10.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Materials Science(all), Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.ijsolstr.2020.05.011 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{a8fd7c654612434fb92e70e01f5bd9fe,
title = "Nearly-constrained transversely isotropic linear elasticity: energetically consistent anisotropic deformation modes for mixed finite element formulations",
abstract = "Strong anisotropies and/or near-incompressibility properties introduce internal constraints in material deformation. Numerical simulations comprising such a constrained behaviour show an overstiff structural response, referred to as element locking. Implementations based on mixed variational methods can heal locking but available solutions in the state-of-the-art are still non-optimal for anisotropic materials. This paper addresses this issue, by proposing a novel decomposition of anisotropic deformation modes on the basis of kinematic and energy requirements. Theoretical results exploit the Walpole's formalism. The proposed kinematic split allows to introduce a new class of variational principles, referred to as energetically decoupled, for nearly-constrained transversely isotropic materials in linear elasticity. Low-order mixed finite element models are thus derived for treating near-inextensibility and/or near-incompressibility. Two-dimensional benchmark tests reproducing pure-bending and Cook's membrane problems are conducted. Numerical results show that the accuracy of energetically decoupled formulations is high and robust with respect to variations of material properties, while the accuracy of non-energetically decoupled formulations is more sensitive.",
keywords = "Anisotropic materials, Mixed finite element method, Near-incompressibility, Nearly-inextensible fibers, Variational principles",
author = "Michele Marino and Peter Wriggers",
note = "Funding Information: M. Marino acknowledges that this work has been funded partially by the Masterplan SMART BIOTECS (Ministry of Science and Culture of Lower Saxony, Germany) and partially by the Rita Levi Montalcini Program for Young Researchers (Ministry of Education, University and Research, Italy). P. Wriggers gratefully acknowledges the support of the German Research foundation within the Priority Program SPP 1748 under the project WR19/50-2.",
year = "2020",
month = oct,
day = "1",
doi = "10.1016/j.ijsolstr.2020.05.011",
language = "English",
volume = "202",
pages = "166--183",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Ltd.",
}