Details
| Original language | English |
|---|---|
| Pages (from-to) | 166-183 |
| Number of pages | 18 |
| Journal | International Journal of Solids and Structures |
| Volume | 202 |
| Early online date | 11 Jun 2020 |
| Publication status | Published - 1 Oct 2020 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Materials Science(all)
- General Materials Science
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal of Solids and Structures, Vol. 202, 01.10.2020, p. 166-183.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Nearly-constrained transversely isotropic linear elasticity
T2 - energetically consistent anisotropic deformation modes for mixed finite element formulations
AU - Marino, Michele
AU - Wriggers, Peter
N1 - 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.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - 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.
AB - 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.
KW - Anisotropic materials
KW - Mixed finite element method
KW - Near-incompressibility
KW - Nearly-inextensible fibers
KW - Variational principles
UR - http://www.scopus.com/inward/record.url?scp=85086995679&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2020.05.011
DO - 10.1016/j.ijsolstr.2020.05.011
M3 - Article
AN - SCOPUS:85086995679
VL - 202
SP - 166
EP - 183
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
SN - 0020-7683
ER -