A direct displacement smoothing meshfree particle formulation for impact failure modeling

Abstract A direct displacement smoothing meshfree particle formulation is introduced to the material failure modeling of concrete and steel materials due to blast and high velocity impact loadings. A Lagrangian smoothing form of the shape function is developed for the direct displacement smoothing meshfree particle formulation, which is subsequently employed to discretize the variational equation of motion. The weak form is integrated nodally, which maintains the particle characteristics of the meshfree formulation and enables the formulation to track the impact debris evolution naturally. To model the failure process of concrete and steel physically, the physics-based material constitutive laws for these two materials are discussed as well. The computational implementation of the discrete equations is illustrated in detail particularly for the concrete constitutive equations. Numerical results show very favorable agreement with the available experimental data, as demonstrated that the present direct displacement smoothing meshfree particle formulation can effectively model the impact material failure. Moreover, the debris evolution can be efficiently simulated by the proposed meshfree particle formulation as well if the material constitutive law provides a physical means to indicate the damage and failure of the material.