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The simulation of the structural response for impact scenarios strongly requires an accurate simulation of both the impact event as well as the subsequent wave propagation. The numerical modeling of the impact event is intrinsically ill-posed due to the instantaneous changes of velocities in the contact area, leading to unbounded accelerations for decreasing time steps which causes oscillations in the contact stresses. These oscillations then propagate into the bulk material. Using a rate dependent material model, like concrete, they might lead to significant errors and a wrong prediction of the structural response. A regularization is thus required to avoid oscillations in the contact stresses. Another issue is related to the numerical computation of the contact conditions. In impact simulations, the nonlinear contact computation needs to be evaluated in every time step. A segmentation technique of the contact area is accurate but time consuming and may result in a bottleneck for the simulation and implementation, especially for 3D problems. The modeling of the subsequent wave propagation requires small time steps, which is primarily due to accuracy reasons. Implicit schemes are thus not affordable. Explicit time integration schemes are efficient only for diagonal mass matrices, as in this case no solution of a linear system is required. In this work, a coupled finite element - Non-Uniform Rational B-Spline (FE-NURBS) approach is applied to impact problems. The coupled approach uses an intermediate NURBS layer to compute the contact forces between the contacting bodies discretized by FEs. The advantages of a smooth isogeometric contact formulation are used to compute the contact forces. A segmentation of the contact area is avoided and an efficient element-based integration is used. The impact event is regularized using a mesh dependent nonlinear penalty approach. The penalty function is a polynomial which ensures a smooth transition between the noncontact and the contact state during the impact. For finer meshes, the penalty regularization becomes stiffer while still avoiding artificial oscillations in the contact stresses. Efficient higher order space and time discretizations are used to model the wave propagation. Explicit time integration is combined with higher order spectral element spatial discretization.
In the approval procedure of transport packages for radioactive materials, the competent authority mechanical and thermal safety assessment is carried out in Germany by BAM Federal Institute for Materials Research and Testing. The combination of experimental investigations and numerical calculations in conjunction with materials and components testing is the basis of the safety assessment concept of the BAM. Among other mechanical test scenarios, a 1 metre drop test onto a steel bar has to be considered for the application of the hypothetical accident conditions to Type B packages according to IAEA regulations. Within the approval procedure for the new German package design of the HLW cask CASTOR® HAW 28M, designed by GNS Gesellschaft für Nuklear-Service Germany, a puncture drop test was performed with a half-scale model of the cask at -40°C. For independent assessment and to control the safety analysis presented by the applicant, BAM developed a complex finite element (FE) model for a dynamical ABAQUS/ExplicitTM analysis. This paper describes in detail the use of the FE method for modelling the puncture drop test within an actual assessment strategy. At first, investigations of the behaviour of the steel bar were carried out. Different friction coefficients and the material law of the bar were analysed by using a 'rigid-body' approximation for the cask body. In the next step, a more detailed FE model with a more realistic material definition for the cask body was developed. The validation of calculated strains was carried out by comparison with the results of the strain gauges located at the relevant points of the cask model. The influence of the FE meshing is described. Finally, the validated FE half-scale model was expanded to full-scale dimension. Scaling effects were analysed. The model was used for safety assessment of the package to be approved.
Transport casks for radioactive materials have to withstand the 9 m drop test, 1 m puncture drop test and dynamic crush test with regard to the mechanical requirements according to the IAEA regulations. The safety assessment of the package can be carried out on the basis of experimental investigations with prototypes or models of appropriate scale, calculations, by reference to previous satisfactory safety demonstrations of a sufficiently similar nature or a combination of these methods. Computational methods are increasingly used for the assessment of mechanical test scenarios. However, it must be guaranteed that the calculation methods provide reliable results. Important quality assurance measures at the Federal Institute for Materials Research and Testing are given concerning the preparation, run and evaluation of a numerical analysis with reference to the appropriate guidelines. Hence, a successful application of the finite element (FE) method requires a suitable mesh. An analysis of the 1 m puncture drop test using successively refined FE meshes was performed to find an acceptable mesh size and to study the mesh convergence using explicit dynamic FE codes. The FE model of the cask structure and the puncture bar is described. At the beginning a coarse mesh was created. Then this mesh was refined in two steps. In each step the size of the elements was bisected. The deformation of the mesh and the stresses were evaluated dependent on the mesh size. Finally, the results were extrapolated to an infinite fine mesh or the continuous body, respectively. The uncertainty of the numerical solution due to the discretisation of the continuous problem is given. A safety factor is discussed to account for the uncertainty.