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A domain splitting method for heat conduction problems in composite materials

Friedrich Karl Hebeker (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a domain decomposition method for some unsteady heat conduction problem in composite structures. This linear model problem is obtained by homogenization of thin layers of fibres embedded into some standard material. For ease of presentation we consider the case of two space dimensions only. The set of finite element equations obtained by the backward Euler scheme is parallelized in a problem-oriented fashion by some noniterative overlapping domain splitting method, eventually enhanced...

A Dynamic Frictionless Contact Problem with Adhesion and Damage

Mohamed Selmani, Lynda Selmani (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We consider a dynamic frictionless contact problem for a viscoelastic material with damage. The contact is modeled with normal compliance condition. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness of the solution. The proofs are based on the theory of evolution equations with...

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