An efficient static solver for the lattice discrete particle model

The lattice discrete particle model (LDPM) has been proven to be one of the most appealing computational tools to simulate fracture in quasi-brittle materials. Despite tremendous advancements in the definition and implementation of the method, solution strategies are still limited to dynamic algorithms, resulting in prohibitive computational costs and challenges related to solution accuracy for quasi-static conditions. This study presents a novel static solver for LDPM, introducing fundamental innovation: (1) LDPM constitutive laws are modified to provide continuous response through all possible strain/stress states; (2) an adaptive arc-length method is proposed in combination with a criterion to select the sign of the iterative load factor; (3) an adaptive limit-unloading–reloading path switch algorithm is proposed to restrict oscillations in the global stiffness matrix. Extensive validation of the proposed approach is presented. Numerical results demonstrate that the static solver exhibits satisfactory convergence rates, significantly outperforming available dynamic solutions in computational efficiency.