Nearly-constrained transversely isotropic linear elasticity: energetically consistent anisotropic deformation modes for mixed finite element formulations
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...
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| Published in | International journal of solids and structures Vol. 202; pp. 166 - 183 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Elsevier Ltd
01.10.2020
Elsevier BV |
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| Online Access | Get full text |
| ISSN | 0020-7683 1879-2146 |
| DOI | 10.1016/j.ijsolstr.2020.05.011 |
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| 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. |
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| AbstractList | 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. |
| Author | Marino, Michele Wriggers, Peter |
| Author_xml | – sequence: 1 givenname: Michele orcidid: 0000-0002-4323-3061 surname: Marino fullname: Marino, Michele email: m.marino@ing.uniroma2.it organization: Department of Civil Engineering and Computer Science, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy – sequence: 2 givenname: Peter surname: Wriggers fullname: Wriggers, Peter email: wriggers@ikm.uni-hannover.de organization: Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstr. 11, 30167 Hannover, Germany |
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| Cites_doi | 10.1016/j.cma.2016.06.029 10.1016/j.cma.2018.10.016 10.1098/rspa.1984.0008 10.1016/j.compositesa.2013.06.001 10.1007/s00033-014-0421-x 10.1002/nme.5972 10.1007/BF00276073 10.1023/A:1010835316564 10.1016/j.camwa.2016.04.022 10.1177/1081286509105591 10.1016/0045-7825(85)90033-7 10.1007/s00466-017-1437-9 10.1016/j.cma.2016.10.032 10.1002/nme.1620330803 10.1002/nme.1620371805 10.1016/j.compositesa.2008.03.014 10.1016/S0045-7825(99)00261-3 10.1016/j.ijsolstr.2005.04.014 10.1177/1081286514550576 10.1177/1081286518810741 10.1016/S0065-2156(08)70332-6 10.1186/s40323-016-0079-3 10.1023/B:ELAS.0000005582.52534.2d 10.1007/BF00043417 |
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| Keywords | Mixed finite element method Nearly-inextensible fibers Variational principles Near-incompressibility Anisotropic materials |
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| SubjectTerms | Accuracy Anisotropic materials Deformation Elasticity Energy requirements Finite element method Incompressibility Isotropic material Kinematics Locking Material properties Mixed finite element method Near-incompressibility Nearly-inextensible fibers Robustness (mathematics) Two dimensional models Variational methods Variational principles |
| Title | Nearly-constrained transversely isotropic linear elasticity: energetically consistent anisotropic deformation modes for mixed finite element formulations |
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