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Transient filling modelling at meso-level for RTM process using a single phase LSM

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Abstract

A single phase level set method for capturing the propagating front within textile unit-cells is presented. The computational domain is embedded within an artificial Cartesian grid in order to avoid the difficulties associated with the meshing step. The flow is modelled by using the Stokes/Brinkman equations. Hence, the necessity of describing the yarn boundaries is avoided. The propagating front is represented by using a level set formulation where the extra step of reinitialization is avoided. The flow equations are solved only in the filled part of the domain. The velocity in the unfilled part is obtained through a harmonic continuation. Numerical tests on simple configurations in 2D and 3D space are presented in order to demonstrate the proposed method.

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Notes

  1. Although this statement is, in general, true, the LSM is notorious for not conserving the mass. A simple approach to improve this is to chose a different level set to represent the front based on whether mass is gained or lost. This approach however requires to reconstruct the flow front

  2. It has to be noted here that the chosen finite element space is not in general appropriate to discretize the flow equations within the porous yarn, see for example [39] and references therein. The reason is that the ellipticity condition required to have a well posed saddle-point problem breaks down. Nonetheless, we do not address this point herein.

  3. We remark here that \(\mathbf {u}_{h}\) is divided with the porosity of the yarn if the element has been categorized as a porous element, sub-section “Flow equations and approximation of geometry”.

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  1. Division of Materials, Mechanics and Structures, Faculty of Engineering, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    A. Giavaras & E. Boateng

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  1. A. Giavaras
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  2. E. Boateng
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Correspondence to A. Giavaras.

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Giavaras, A., Boateng, E. Transient filling modelling at meso-level for RTM process using a single phase LSM. Int J Mater Form 8, 197–210 (2015). https://doi.org/10.1007/s12289-013-1160-9

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  • DOI: https://doi.org/10.1007/s12289-013-1160-9

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