Material Point Method For Metal And Soil Impact Dynamics Problems

The impact dynamics problems have broad and significant applications in the military and aerospace technologies. Numerical simulation is an important study approach for this kind of problems. Some physical phenomena, such as nonlinear wave propagation, friction and abrasion, large deformation, high strain rate, dynamic damage and fracture arise from the problems of impact dynamics. Compared with the Lagrangian and Eulerian mesh methods, meshfree methods have some advantages to solve the problems involving impact and penetration. Material point method (MPM) is a meshfree particle method. In MPM, each body is discretized by a set of particles, so that the material fragments can be efficiently simulated. MPM uses a predefined regular background grid to solve the momentum equations, so that the grid distortion and entanglement are completely avoided. MPM has been successfully applied to explosion problems and crack growth problems. In this study, the MPM simulations of the impact and penetration problems are carried out, especially for metal and soil material.Although MPM has been applied to hypervelocity problems, the small-scale MPM simulation is unable to obtain high-resolution results. The parallel MPM is developed using the shared memory OpenMP in this study. Two OpenMP parallel methods, the array expansion method and the domain decomposition method of background grid, are proposed to avoid data races in parallelizing MPM. The parallel MPM is applied to a large-scale simulation with 13 million particles for obtaining the high-resolution results of debris cloud in hypervelocity impact.The inherent non-slip contact constraint in the standard MPM creates a great penetration resistance. To overcome this deficiency, a contact MPM algorithm is presented and applied to the problems involving impact and penetration. A new method is proposed for the calculation of the normal vector of contact surface in the impact and penetration simulation. The mathematic description and numerical implementation of the contact algorithm are presented. The contact MPM algorithm is verified by some numerical examples. In the penetration simulations, the projectile's residual velocities obtained by the standard MPM are significantly lower than the experimental data. Whereas, the projectile's residual velocities obtained by the proposed contact MPM have agreements with the experimental results.A rigid-deformable contact MPM algorithm is proposed to simulate the contact between the rigid and deformable bodies. Some numerical examples are given to verify this rigid-deformable contact MPM algorithm. Using this contact algorithm, the Taylor bar impact on a rigid wall is simulated, and the water ball impact on a stair is also simulated.Because of avoiding mesh distortion, MPM can efficiently simulate the mechanical behavior of soft material, such as soil. In this paper, MPM is applied to the soil impact dynamics problems. The slope failure is simulated using MPM and Drucker-Prager material model. The collapse of granular layer under gravity is simulated by the rigid-deformable contact MPM algorithm. The computed final configurations of granular layer are in good agreement with the experimental results. Finally, the penetration process of a hemispherical shell into soil is simulated by MPM.