ABSTRACT
There are in general two classes of time integration algorithms for dynamics problems, namely implicit and explicit methods. While explicit methods are conditionally stable and often require a very small time step, implicit algorithms are unconditionally stable and larger time steps can be used. In terms of memory usage, implicit algorithms require more memory as a system of equations needs to be solved one or several times per step for the solution to advance. Implicit methods are usually used to solved problems in which low frequency modes dominate. Nevertheless, one often faces convergence issues when the material behavior is highly nonlinear and explicit methods seem more appropriate in that case. In this study, the performance of the Lattice Discrete Particle Model (LDPM), newly implemented in the implicit solver CAST3M was investigated. LDPM is a mesoscale model developed to simulate concrete and other granular quasi-brittle materials. It incorporates complex nonlinear constitutive equations and for this reason, it is currently used within the dynamic explicit framework ABAQUS Explicit. This manuscript presents preliminary results on the comparison between explicit central difference algorithm and implicit average acceleration scheme for LDPM. For this purpose, a classical three-point bending test under quasi-static conditions was considered. Three different integration methods were used: dynamic explicit, dynamic implicit and static implicit. Load-displacement responses were obtained and discussed, along with the force imbalance at loading points to assess static equilibrium. For each simulation, the computational cost was also obtained. Results show that quasi-static simulations can be performed using dynamic explicit integration method if the effect of inertia is small enough. In addition, the computational cost for static and dynamic implicit simulations is much lower than for dynamic explicit calculations. Last but not least, the time step size in the dynamic implicit method needs to be chosen carefully to avoid spurious energy growth or higher modes due to time discretization.
