A semi-lagrangian strategy to predict the fiber orientation in the steady flows of reinforced thermoplastics

✍ Scribed by F. Chinesta; A. Poitou; R. Torres

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 348 KB
• Volume: 189
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(99)00325-4

✦ Synopsis

The equations governing the ®ber orientation of a short ®ber reinforced thermoplastic are hyperbolic (non-linear transport-type equation). The most accurate technique for the treatment of these equations is the method of characteristics. In the present paper, a ``semi-lagrangian'' strategy is proposed, which reduces drastically the CPU time associated with the integration of the orientation equation. This strategy combines an integration by characteristics into each element of a standard ®nite element mesh, with a polynomial interpolation of the gradient of deformation tensor on the mesh skeleton. Moreover when a linear approximation of the velocity ®eld is assumed in each element, then the integration by characteristics can be carried out with explicit formulae.