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GRALE2D – An Explicit Finite Element Code For Two-dimensional Plane And Axi-symmetric Multi-material ALE Simulations


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L. Olovsson & A. Helte


This paper describes the Euler-Lagrange coupling in GRALE2D, an explicit finite element code for two-dimensional plane and axi-symmetrical multi-material ALE simulations, which is being developed at the Swedish Defence Research Agency (FOI). A brief overview of the functionalities of the code is followed by a description of the implemented method for Euler-Lagrange coupling together with a numerical example demonstrating the performance of the code in a typical ballistic application. Since GRALE2D works with selectively reduced integrated elements, hourglass stabilization is not necessary for the treatment of materials with shear strength. 1 Introduction GRALE2D is an explicit multi-material ALE finite element software for twodimensional plane and axi-symmetric problems developed at the Swedish Defense Research Agency. The main objective with the software is to simulate the mechanics of warheads, with special emphasis on liner collapse and jet formation of shaped charges and projectile formation of EFP warheads. However, the software is general and can be used for other purposes as well. Most commercially available software are focused on three-dimensional problems while there is a lack of wellsupported two-dimensional hydro codes. This was the motivation for our group to develop a hydro code supporting Lagrangian and Eulerian elements as well as Euler-Lagrange coupling. The only implemented element type is a four node, selectively reduced integrated, iso-parametric, bi-linear quadrilateral. That is, there are no zero energy