A generalized hybrid smoothed particle hydrodynamics–peridynamics algorithm with a novel Lagrangian mapping for solution and failure analysis of fluid–structure interaction problems

Abstract

Fluid–structure interaction problems (FSI) are omnipresent in a wide variety of engineering fields and includes highly non-linear physics such as violent free-surface flow, complex interfacial and inter-phase interactions, and deformable structures with the possibility of damage formations. Well-established mesh dependent approaches may suffer from dynamic mesh-refinement, special algorithms to track free surfaces and handle the interface and inter-phase physics. On the other hand, due to their inherent nature, particle based meshless methods, namely Smoothed Particle Hydrodynamics (SPH) and Peridynamics (PD), can lend themselves easily to tackling with the above-stated complex physics involved in the fluid and structure phases of the FSI problems, respectively. This study presents a novel hybrid algorithm to couple the SPH and PD in a robust and high-fidelity manner for modeling extreme FSI problems with and without multi-scale defects. The coupled methodology is integrated with a novel mapping strategy based on Lagrange polynomial interpolation, which allows for the solution procedure to utilize different particle resolutions for fluid and deformable structural media. The mapping strategy enables one to construct a higher-accuracy PD solver that can predict the dynamic behavior of solids and provide an ability to model and track the damage nucleation, propagation, and branching in the structure phase of FSI domains. The corrected weakly compressible SPH is used for pressure–velocity coupling in the fluid phase whereas the ordinary state based PD is utilized for modeling the deformable structure. The SPH and PD solvers of the algorithm are validated separately through solving several well-accepted benchmark test cases such as the collapse of a water column, large deformation of a cantilever beam, and damage propagation in a plate under impact loading (Kalthoff–Winkler experiment). After validating each solver, the hybrid coupled SPH–PD algorithm is applied to simulate various extreme FSI problems of literature such as the dam break with an elastic gate, collapse of the water column and its hydrodynamic impact on an elastic obstacle, and the entry of a V-shaped deformable beam on the free surface of water in a tank. A close agreement between the SPH–PD results and the literature data is achieved for each of the aforementioned cases. The algorithm is further applied to model the failure propagation in the elastic wall of a tank under hydrostatic pressure. A realistic failure behavior is recorded for the FSI setups with different initial states of the wall, i.e., the wall is assumed to be with and without initial defects of different geometrical orientations. In particular, this study proposes and implements a new perspective for coupling different particle methods to achieve high-fidelity and low-cost modeling of complex FSI problems, which may involve multi-scale defects (i.e., cracks and voids) and failure propagations.