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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 61

Modelling of Imperfect Bond using the FETI Method

J. Kruis1 and P. Štemberk2

1Department of Mechanics
2Department of Concrete and Masonry Structures
Czech Technical University in Prague, Czech Republic

Full Bibliographic Reference for this paper
J. Kruis, P. Štemberk, "Modelling of Imperfect Bond using the FETI Method", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 61, 2007. doi:10.4203/ccp.86.61
Keywords: composite materials, imperfect bond, FETI method.

Summary
Composite materials basically consist of a composite matrix and a reinforcement usually created by fibres. An interaction between the reinforcement and composite matrix has significant influence on the overall properties of the composite material. Perfect bond between reinforcement and composite matrix can be assumed under service conditions while an imperfect bond occurs under limit state conditions.

The perfect bond between the reinforcement and the composite matrix can be simply modelled by matching meshes of the both constituents. In such a case, the finite element method enforces the same displacements on the interface. The imperfect bond is more complicated and appropriate choice of a numerical model can considerably influence the numerical behaviour.

The classical primal formulation of the interaction of reinforcement and the composite matrix is replaced by the dual formulation. The main difference between these two approaches is based on unknowns used. While the primal formulation deals with unknown displacements, the dual formulation eliminates displacements and it deals with stresses. This is basic idea of the FETI method, a non-overlapping domain decomposition method [1].

Each piece of reinforcement can be modelled as one subdomain and the composite matrix can be described as one large subdomain even it can be split into several subdomains. Perfect bond between reinforcement and matrix is studied in [2]. This contribution generalises the previous work and it takes into account debonding effect.

The FETI method is designed for perfect bond because the original domain is fictitiously decomposed to subdomains and then they are merged together. No slip among subdomains is permitted and the FETI method enforces it by compatibility condition. Generalisation for imperfect bond consists in modification of the compatibility condition. The mentioned generalization lead to small modifications in the coarse problem. In the case of constant slip between two subdomains, only additional term on the right hand side occurs. In the case of linear law between slip and acting force, a diagonal or a nearly diagonal matrix is added to the system of equations and the classical FETI solver can be used.

The modifications of the FETI method necessary for description of imperfect bond are simply implementable and existing computer codes can be used. Second advantage of the proposed approach is simple parallelization of the problem. The composite matrix can be decomposed to smaller subdomains and each piece of reinforcement can be modelled as a subdomain.

The proposed generalisation of the method is presented on several examples. Especially, a pull-out test is simulated and several types of bonding and debonding effects are described.

References
1
J. Kruis, "Domain Decomposition Methods for Distrubuted Computing", Saxe-Coburg Publications, Kippen, Stirling, Scotland, UK, 2006.
2
J. Kruis and P. Štemberk, "Modelling of Interaction between Reinforcement and Matrix Using the FETI Method", in Proceedings of The Eighth International Conference on Computational Structures Technology, B.H.V. Topping, G. Montero and R. Montenegro, (Editors), Civil-Comp Press, Stirlingshire, United Kingdom, paper 133, 2006. doi:10.4203/ccp.83.133

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