Hybrid staggered grid finite element material point method (HSGFEMP) for reinforced concrete

It is of great significance to study numerical algorithms to simulate the response of reinforced concrete (RC) under explosion and impact loads. The material point method (MPM) is effective for simulating extreme problems such as fracture and large solid deformation, and the hybrid finite element material point method (HFEMP) improves the overall calculation efficiency in simulating RC by introducing the bar element of FEM to the MPM. However, similar to the MPM, the HFEMP also suffers several defects caused by the particle quadrature, including cell crossing noise, low accuracy, and low stability. Therefore, this paper develops a hybrid staggered grid finite element material point method (HSGFEMP) with higher accuracy by introducing the cell-center quadrature from the staggered material point method (SGMP) to the HFEMP. An auxiliary grid is generated to reconstruct variables at cell centers and map the updating variables at the particles and bar elements. When employing cell-center quadrature, the influence on the calculation result from the ratio between the size of the bar element and the grid element is also studied. Numerical examples verify that the HSGFEMP is more effective and accurate than the HFEMP in modeling the RC.