A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading

The material point method (MPM) takes advantages of both the Eulerian and Lagrangian methods, so it is capable of handling many challenging engineering problems, such as the dynamic responses of reinforced concrete (RC) subjected to blast and impact loadings. However, it is time-consuming to discretize the steel reinforcement bars (“rebars”) in RC by using MPM because the diameter of the steel bar is very small compared with the size of concrete. A hybrid finite element–material point (FEMP) method is proposed, in which the truss element in the traditional finite element method (FEM) is incorporated into the MPM to model the rebars. The proposed FEMP method is implemented in our three-dimensional material point method code, MPM3D®, and validated by several benchmark problems. Finally, it is applied to simulate the dynamic response of RC slab penetrated by projectile, and the numerical results are in good agreement with the experimental data reported in the literature. The proposed idea is applicable to incorporate other types of finite elements into MPM to take advantages of both FEM and MPM.