The penetration into sand is one of the most challenging problems in soil mechanics and its numerical simulation, particularly by the widely-used finite element method (FEM), still poses a great challenge. In order to overcome the problems associated with the classical Lagrangian and Eulerian formulations of FEM, an arbitrary LagrangianEulerian (ALE) method particularly suitable for plane and axisymmetric penetration into sand is developed in this thesis based upon the theoretical foundations. The developed ALE method applies an operator-split which breaks up solution of the governing equations over a time step into a Lagrangian step, a mesh regularization step, and a transport step. The operator-split makes implementation into existing Lagrangian FE codes possible, which is shown using the example of ANSYS. A unique feature of the ALE method is its combination with an advanced hypoplastic rate constitutive equation for sand which enables realistic prediction of stress and density changes within the soil even at large deformations. In addition, an optimization-based algorithm for mesh regularization is developed in order to smooth out the non-convexly distorted mesh regions that occur below a penetrator. The ALE method is verified and validated by benchmarks, basic initial boundary value problems, and by specifically conducted penetration tests in chambers filled with sand.

P. Granet

Papers

Response of fast-reactor core subassemblies to pressure transients