Details
| Original language | English |
|---|---|
| Pages (from-to) | 905-922 |
| Number of pages | 18 |
| Journal | Computational mechanics |
| Volume | 60 |
| Issue number | 6 |
| Publication status | Published - 20 Jul 2017 |
Abstract
The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.
Keywords
- Anisotropic material, Fiber-reinforced material, Finite element analysis, Inextensible fibers, Mixed finite element method
ASJC Scopus subject areas
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 60, No. 6, 20.07.2017, p. 905-922.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Fiber-reinforced materials
T2 - finite elements for the treatment of the inextensibility constraint
AU - Auricchio, Ferdinando
AU - Scalet, Giulia
AU - Wriggers, Peter
PY - 2017/7/20
Y1 - 2017/7/20
N2 - The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.
AB - The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.
KW - Anisotropic material
KW - Fiber-reinforced material
KW - Finite element analysis
KW - Inextensible fibers
KW - Mixed finite element method
UR - http://www.scopus.com/inward/record.url?scp=85025086020&partnerID=8YFLogxK
U2 - 10.1007/s00466-017-1437-9
DO - 10.1007/s00466-017-1437-9
M3 - Article
AN - SCOPUS:85025086020
VL - 60
SP - 905
EP - 922
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 6
ER -