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Contribution à l’étude d’éléments finis de type coque sans degrés de liberté en rotation ou à formulation solide pour des simulations numériques de l’emboutissage et du retour élastique

Abstract : This thesis presents a methodology for developing under-integrated “solid-shell” finite elements for sheet forming simulations like deep drawing where these elements must offer a bending capability and sheet thinning conditions as well. Starting from 8-node elements endowing three degrees of freedom per node (three displacement components), a ninth node is added at the centre of the element. This extra node has just one degree of freedom: a displacement along the ‘thickness’ direction. Several integration points are distributed along this privileged direction (5 points, generally) but the in-plane reduced integration at the centre of the element decreases CPU costs compared to a full integration. A special care has been taken to control all zero-energy modes due to the reduced integration. This additional node allows a linear distribution of the normal strain. With fully-3D constitutive laws, these new solid-shell elements give similar bending results as those obtained with shell elements and a plane stress state hypothesis. This ninth node acts as an additional parameter for the quadratic interpolation of the displacement in the ‘thickness’ direction. The corresponding degree of freedom has a physical meaning and a force, equivalent to a normal pressure for instance, may be prescribed. In situations of a normal pressure and in the case of contact, the obtained normal stress is physically defined, which is not the case for many solid-shell elements found in the literature. The pinching (or the thinning) of sheets is properly modelled. To validate these elements, an apparatus for U-drawing tests with ironing or thinning on strip sheets has been built in the laboratory. The comparison between numerical and experimental punch force during sheet forming is pretty good as well as the geometry of blank after springback.
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Bruno Bassa. Contribution à l’étude d’éléments finis de type coque sans degrés de liberté en rotation ou à formulation solide pour des simulations numériques de l’emboutissage et du retour élastique. Autre. INSA de Lyon, 2011. Français. ⟨NNT : 2011ISAL0113⟩. ⟨tel-00716446⟩

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