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Metric generation for anisotropic mesh adaptation, with numerical applications to material forming simulation

Abstract : This work concerns simulation of viscoelastic compressible flows and applications in injection molding. Compressibility has been integrated in REM3D by considering a density evolution for the material, function of the pressure and temperature through the Tait law. Conservation of mass is written in terms of velocity, pressure and temperature, using the isothermal compressibility and dilatation material parameters. We are led to the Stokes compressible problem, which is solved using the Mixed Finite Element method. The linear system arising from the problem is non-linear and non-symmetrical. Thermal coupling is also taken into account, being the energy problem solved through the Space-Time Discontinuous Galerkin method. Extension of the compressible Stokes problem to a multi-domain configuration is given through the characteristic functions, computed by advection equations. Viscoelasticity is introduced using the Pom-Pom model. The extra-stress is considered function of microscopic properties of the material, such as molecular orientation and chain stretch. Elasticity is a perturbation in the mechanical problem. The presence of a solvent viscosity guarantees the ellipticity of the problem, and a stabilization scheme of the DEVSS type is adopted. Orientation and stretch are obtained solving evolution equations, of the hyperbolic type, through the Space-Time Discontinuous Galerkin method. Finally, a temperature equation for viscoelastic compressible models is derived. In what concerns injection molding applications, REM3D covers now all the main stages of the injection molding process, from filling to part ejection. Solidification and behavior of the polymer at the solid state are taken into account considering a very simple evolution. Compensation of the material's shrinkage is done using the material's compressible character. Anisotropy in the internal stresses remaining in the part affects its final mechanical, optical or dimensional properties and induce warpage once the part ejected. Comparison with the literature and experiments is performed, mainly to validate the post-filling stage, showing a good agreement.
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Submitted on : Tuesday, January 25, 2005 - 8:00:00 AM
Last modification on : Wednesday, November 17, 2021 - 12:28:17 PM
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  • HAL Id : pastel-00000989, version 1


Cyril Gruau. Metric generation for anisotropic mesh adaptation, with numerical applications to material forming simulation. Mathematics [math]. École Nationale Supérieure des Mines de Paris, 2004. English. ⟨NNT : 2004ENMP1230⟩. ⟨pastel-00000989⟩



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