The modeling and simulation of concrete structures at high-loading rates is an important topic in computational mechanics, as it can be relevant to improving the safety and durability of structures. High-loading rates on concrete structures may occur during explosions, or impacts. Mesh-based methods often encounter difficulties in these scenarios due to potentially high mesh distortion in these regions. However, the Material Point Method (MPM) is well-suited for modeling situations involving large deformations, as it uses a continuously reset computational mesh.

Additionally, modeling concrete that exhibits strain softening behavior requires regularization methods to solve strain localization and mesh dependency issues. One of the leading methods is implicit gradient enhancement, which is based on a nonlocal formulation, where an additional degree of freedom is introduced to be solved in the linearized system of equations.

In this work, the MPM is used with a regularized microplane damage material model at finite deformation to describe concrete behavior at high loading rates.