Abstract
Electromagnetic field propagation inside composite materials represents a challenge where fiber-scale simulation remains intractable using classical simulation methods. The present work proposes an original 3D simulation with a mesh resolution fine enough to resolve the fiber scale, thanks to the use of Proper Generalized Decomposition (PGD)-based space decomposition, which avoids the necessity of considering homogenized properties and considers the richest description of the involved physics from the solution of the Maxwell equations. This high-resolution simulation enables comparing the electromagnetic field propagation in a composite part, depending on the considered frequency and the fiber’s/wave polarization’s relative orientation. The electromagnetic fields are then post-processed to identify the heat generation terms and- the resulting induced thermal field. The results prove the ability of the PGD-based discretization to attain extremely high levels of resolution, the equivalent of 1010 finite-element degrees of freedom. The obtained results show an enhanced wave penetration when the electric field polarization coincides with the fiber orientation. On the contrary, when the electric field is polarized along the normal to the fiber orientation, both the penetration and the associated heating reduce significantly, compromising the use of homogenized models, rendering them unable to reproduce the observed behaviors.
Highlights
Electromagnetic wave propagation has always been tricky to model using the classical numerical methods, motivating new numerical schema proposals, as in [1], and used, for instance, in [2]
Microwave heating of composites adds a layer of complexity on top of the classical problems of electromagnetic wave propagation
High-performance composite materials are a heterogeneous combination of electrical conductors with a dielectric material, as considered in [3] when addressing composite materials and in [4] in the case of multi-layered composite materials
Summary
Electromagnetic wave propagation has always been tricky to model using the classical numerical methods, motivating new numerical schema proposals, as in [1], and used, for instance, in [2]. The simulation must take into consideration the discontinuity of the wave across elements of the mesh From this fact, classical simulations require the use of Nedelec discontinuous/continuous shape functions, as introduced in [1], with some applications addressed in [7,8]. Classical simulations require the use of Nedelec discontinuous/continuous shape functions, as introduced in [1], with some applications addressed in [7,8] Such elements are cumbersome in some cases. The fiber volume fraction is often much larger than 10% From this fact, the space-separated representation technique appears as an appealing approach to circumvent the problem and tackle the composite using a representation of the material without homogenization as considered in [28], with a more detailed description in [29]. Field polarization is proved to be of utmost importance with respect to the penetration depth and the associated heating, an effect unseen in materials simulated by considering homogenized properties
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