Lihong Zhang

New Solid-Shell Finite Element Based on EAS and ANS Concepts for Sheet Metal Forming

We present in this paper a new eight node solid-shell finite element called SSH3D (Three Dimensional Solid-Shell). This element is currently implemented in the frame of the in-house research code called LAGAMINE. Here the Enhanced Assumed Strain (EAS) technique based on the Hu-Washizu variational principle, described in [1] and [2], is used to cure the volumetric locking occurring when the material shows nearly incompressible behavior and Poisson’s thickness locking caused by the high aspect ratio of the finite element. In the proposed element, the EAS technique can be combined with the Assumed Natural Strain (ANS) [3-5] concept to treat shear locking caused by the transverse shear strain and curvature thickness locking caused by the transverse normal strain. Different schemes for the ANS concept are implemented while the number of integration points and the number of EAS modes are element parameters (the element uses four integration points in the plane of the element and at least two integration points through the thickness direction in a single element layer). These features must be adjusted by the user according to the studied process (geometry and loading) so as to avoid locking and limit the calculation time. This element was successfully tested and the numerical remedies were verified using several kinds of patch tests. A double sided contact problem is modeled in order to investigate the performance and accuracy of the developed element and to validate the suggested approach.

Out-of-plane displacement derivative measurement: comparison of results obtained by a shearographic interferometer using the separation of the polarization states and the finite element method

An original experimental setup for shearography with metrological applications is presented herein. The simplicity and the efficiency of the setup are provided by a shearing device, a prism that separates the TE and TM polarization modes with a coating and a thin glass plate attached on its face. The temporal phase shifting method is applied through the use of a liquid crystal variable retarder. The use of this shearing device enables an in-line and almostcommon path configuration for the shearing interferometer, a path that leads to high stability of the interferometer and a low sensitivity to external disturbances. In order to prove the efficiency and the accuracy of this speckle shearing interferometer, the out-of-plane displacement derivative relative to the shearing interferometry direction of a centrally loaded steel plate has been measured by the shearographic interferometer and then compared with the out-of-plane displacement derivative computed from the displacement field provided by the finite element method. The results are in good agreement.