Analysis of Concrete Tensile Failure using Dynamic Particle Difference Method under High Loading Rates

•Numerical analysis for rate dependency of concrete using Particle Difference Method based on the strong formulation•Simulation of viscosity and softening in concrete by proportional damping algorithm and damage model.•Modeling of crack propagation shape by visibility criterion and extension of traction boundary.•Examining the relationship between the mass and stiffness professional damping effects and the rate dependency of concrete.•Checking the impact of rate dependency of concrete on crack propagation. This study presents the use of the dynamic particle difference method (PDM) to analyze tensile failure in concrete subjected to high loading rates. In general, strong form-based meshfree methods suffer from limitations pertaining to the material modeling of concrete because concrete exhibits both softening and damage behaviors that initiate crack growth under an impact load. These methods are generally based on the direct discretization of the governing equations, such as Navier's equation, which involves second-order differentiation. However, conventional material models are based on the first-order derivatives of displacement. The newly developed dynamic PDM can effectively address the limitations of material modeling using a combination of first-order derivative approximations. This circumvents the requirement for high-order derivative approximations, which are essential in strong formulations, such as the finite difference method and point collocation method. The strain rate effect caused by an extremely high loading speed was successfully modeled by accurately reflecting the energy dissipations that result from the cohesive property of the concrete and brittle cracking. Although the developed method incorporates the elastic constitutive relation, it enables the effective modeling of these nonlinear effects. In addition, it can reduce the computational effort. The proportional damping algorithm simulates the effect of velocity in the equation of motion and the cohesion effect in the concrete material. The damage model and the visibility criterion adequately handle crack initiation and propagation in the concrete member. Furthermore, it is noteworthy that the final discrete forms of the dynamic PDM are similar to the integrands of the weak form in the conventional finite element formulation. We ascertained that the stiffness and mass proportional damping effects are related to the inertia and strain of the material, respectively. It was confirmed that