Displacement controlled arc length method for the lattice discrete particle model
Baixi Chen, Gianluca Cusatis, Alessandro Fascetti
Abstract
Many studies have demonstrated the Lattice Discrete Particle Model (LDPM) to be an accurate methodology for simulating the fracture behavior of quasi-brittle materials at the spatial scale of major heterogeneities, often referred to as mesoscale. Despite the availability of various solution schemes for LDPM, dedicated static solvers that allow for displacement controlled loading conditions are not available in the literature due to several challenges associated with enforcing convergence for highly complex 3-dimensional stress states at the mesoscopic level. To address this knowledge gap and enhance solution stability while mitigating time step sensitivity, this study presents a newly developed arc length-based static solver for LDPM capable of direct enforcement of displacement constraints. Both residual- and increment-based convergence criteria are integrated to facilitate numerical convergence, while adaptive strategies are introduced to ensure compatibility of the arc length equation with the LDPM framework. Two solution schemes are proposed, namely the consistent and non-consistent schemes. To achieve satisfactory convergence rates, modifications to the standard LDPM constitutive laws are proposed to ensure continuity in the transition between tensile and compressive stress states. Validation against three tests with distinct failure mechanisms demonstrates that the developed static solver achieves excellent accuracy and high stability, and robust convergence behavior with respect to different solver settings. A parametric investigation is also presented to quantify the effects of different parameter choices in the proposed arc length equation.