a b s t r a c tComposite materials generally exhibit a highly anisotropic thermal behavior (due to the orientation of fibers), leading to strong difficulties to determine the thermal conductivity tensor. Two approaches can be developed for its evaluation. The first one is to carry out experimental measurements with one or several devices to get all the components of the tensor. The second one is to use predictive models based on homogenization theories from the properties and the arrangement at the microscopic scale of each component of the composite material.Following this second approach, a space-time homogenization based on the multi-scale asymptotic expansion method is first developed to model the transient heat conduction problem within periodic heterogeneous structures. The introduction of additional terms to correct the edge effects (i.e. close to the boundaries of the macroscopic domain) in the transient state is considered. We show how these transient correcting terms can be introduced and calculated, depending on the classical boundary conditions in conduction heat transfer problems. Moreover, we underline that correcting terms have also to be added to take into account "short time" effects. Furthermore, we propose to discuss numerical results of the heat transfer modeling in a Laser Flash experiment. We specifically show how the effective thermal diffusivity may be biased when edge effects are neglected in the homogenized model.
Floating offshore renewable energies (OREs), such as offshore floating wind turbines (wind energy) or wave power (wave and wave energy), are increasingly in demand. Submarine cables that transmit the energy produced from offshore farms all the way to onshore stations are critical structures that must be able to work perfectly over 20 years without any maintenance. In order to reduce the significant costs associated with electrical cables, it is important to optimize the dimensioning of the components of these cables, or to develop structural monitoring techniques that target zero and/or minimum maintenance over their lifespan. In this paper, we FEM of the impact of damage mechanisms of the conductor part of a submarine power phase on its mechanical, electrical, and thermal behavior. The main damage mechanisms are local plasticity and wire failure. The first mechanical study made it possible to obtain the elasto-plastic behavior of the conductor. The electrical study took into consideration the deformed geometry of the conductor in the elasto-plastic domain, as well as the non-homogeneous distribution of the electrical conductivity of the conductor. Their influence on the electrical resistance of the conductor was then analyzed. Finally, we studied the impact of plasticity and conductor failure on the thermal behavior of the phase. The temperature differences obtained in the numerical analysis of this work may be used further to help preventive and curative maintenance of the cables, for example, by using an optical fiber as sensor for structural health monitoring.
The homogenization theory is a powerful approach to determine the effective thermal conductivity ten-sor of heterogeneous materials such as composites, including thermoset matrix and fibers. Once the effect ive properties are calculated, they can be used to solve a heat conduction problem on the composite structure at the macroscop ic scale. This approach leads to good approximations of both the heat flux and temperat ure fields in the interior zone of the structure; however edge effects occur in the vicinity of the domain boundaries. In this paper, following an approach proposed for elasticity problems, it is shown how these edge effects can be accounted for. An additional asymptotic expansion term is introduced, which plays the role of a ''heat conduction boundary layer'' (HCBL) term. This expansion decreases exponentially and tends to zero far from the boundary. Moreover, the HCBL length can be determined from the solution of an eigenvalues problem. Numerical examples are considered for a standard multilayered material and for a unidirection al carbon-epoxy composite. The homogenized solutions computed with a finite element software, and corrected with the HCBL terms are compared to a heterogeneous finite element solution at the microscopic scale. The influences of the thermal contrast and the scale factor are illustr ated for different kind of boundary condit ions.
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