Finite strain elastoplastic and solid-solid contact problems with the Smoothed Particle Hydrodynamics

Abstract

The Smoothed Particle Hydrodynamics (SPH) is a numerical scheme in which the domain is discretized into Lagrangian particles in the context of continuum mechanics. It has been widely used for fluid dynamics problems, and recently it has also been applied to solid mechanics with reasonable success. In this work, we present a total Lagrangian SPH (TL-SPH) for the application of solid mechanics and contact problems. Total Langrangian stands for the usage of the reference configuration to calculate the spatial derivatives. As a consequence, all particles maintain a perfect distribution, which, in turns, results in highly accurate calculations. In this way, the method is able to eliminate any problem related to tensile instability, which is one of the main shortcomings of SPH. Here, we introduce a simple, yet robust, way to include finite strain elastoplasticity into the TL-SPH method based on the logarithmic strain. Then, the elastic part can be easily defined with the Hencky elastic model, and the plastic part with any yield criteria such as Drucker-Prager. In addition, we develop a contact algorithm capable of simulating solid-solid contact problems. In this way, the simulation of different objects becomes a mix of continuous and discontinuous problems. Finally, we show the applicability of the method with several simple tests to validate the accuracy of the TL-SPH for simulating the elastoplastic solid material, as well as for contact problems including direct impact and friction effects. REFERENCES [1] Morikawa D.S. Toward robust landslide simulations from initiation to post-failure using the Smoothed Particle Hydrodynamics. Kyushu University PhD thesis (2022).