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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 91
Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros
Paper 273

Numerical Analysis of Coupled Problems with Discontinuities

J. Kruis1 and J. Madera2

1Department of Mechanics, 2Department of Materials Engineering and Chemistry,
Czech Technical University in Prague, Czech Republic

Full Bibliographic Reference for this paper
J. Kruis, J. Madera, "Numerical Analysis of Coupled Problems with Discontinuities", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 273, 2009. doi:10.4203/ccp.91.273
Keywords: interface discontinuity, coupled heat and moisture problem, domain decomposition method, parallel computing.

Real engineering problems usually contain several different materials. The interface between materials plays an important role in numerical analysis because many variables used for the model description are discontinuous there. The finite element method, which is the most universal numerical method at this time, has to be modified in order to describe the discontinuity at the material interfaces.

Examples of discontinuities on material interfaces can be found in many different areas. In the case of moisture transfer through a porous heterogeneous medium, the moisture content is discontinuous on the interface between two various materials. Such a discontinuity can be removed by using the relative humidity but there are tasks where this transformation cannot be done. An example is the coupled moisture and salt transfer where the moisture content is required. Another example of the discontinuity of a material interface is the interaction between the reinforcement and composite matrix where the perfect or imperfect bond is assumed. More details concerning this topic can be found in references [1,2].

There are several possibilities of how to deal with the discontinuities but some of them may cause additional difficulties. A typical example is the penalty method which generates very large contributions to the matrix of the system of the algebraic equations. These contributions lead to the cancellation of errors in direct methods or large numbers of iterations in iterative methods.

A suitable tool for the description of the domain or structure composed from several different materials is a nonoverlapping domain decomposition method. If each material region is assumed as one subdomain, the material interfaces coincide with the subdomain interfaces. Each material region can be split further into smaller subdomains. Each subdomain is covered by its own finite element mesh and the interface conditions enforce the coupling between them. In the case of the classical domain decomposition method, the interface conditions enforce the continuity while in the case of problems with discontinuities the interface conditions describe the prescribed discontinuities.

If a moisture transfer is assumed, and if the moisture content is required, then discontinuities occur on material interfaces. It is possible to compute the magnitude of the discontinuity with the help of sorption isotherms. The magnitude is then used in the interface conditions. The proposed approach is demonstrated using an example of moisture and heat transfer through a concrete wall with plaster on both sides. There are discontinuities on the interfaces between the concrete and the plaster.

J. Kruis, Z. Bittnar, "Reinforcement-Matrix Interaction Modelled by FETI Method", in "Proceedings of the XVII International Conference on Domain Decomposition Methods", U. Langer, et al., (Editors), Springer-Verlag Berlin, 567-574, 2007.
J. Kruis, P. Štemberk, "Modelling of Imperfect Bond using the FETI Method", in "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", B.H.V. Topping, (Editor), Civil-Comp Press, Stirlingshire, United Kingdom, paper 61, 2007. doi:10.4203/ccp.86.61

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