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

This report summarizes activities undertaken during FY08-FY10 for the LDRD Peridynamics as a Rigorous Coarse-Graining of Atomistics for Multiscale Materials Design. The goal of our project was to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. The goal of our project is to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. Our coarse-graining overcomes the intrinsic limitation of coupling atomistics with classical continuum mechanics via the FEM (finite element method), SPH (smoothed particle hydrodynamics), or MPM (material point method); namely, that classical continuum mechanics assumes a local force interaction that is incompatible with the nonlocal force model of atomistic methods. Therefore FEM, SPH, and MPM inherit this limitation. This seemingly innocuous dichotomy has far reaching consequences; for example, classical continuum mechanics cannot resolve the short wavelength behavior associated with atomistics. Other consequences include spurious forces, invalid phonon dispersion relationships, and irreconcilable descriptions/treatments of temperature. We propose a statistically based coarse-graining of atomistics via peridynamics and so develop a first of a kind mesoscopic capability to enable consistent, thermodynamically sound, atomistic-to-continuum (AtC) multiscale material simulation. Peridynamics (PD) is a microcontinuum theory that assumes nonlocal forces for describing long-range material interaction. The force interactions occurring at finite distances are naturally accounted for in PD. Moreover, PDs nonlocal force model is entirely consistent with those used by atomistics methods, in stark contrast to classical continuum mechanics. Hence, PD can be employed for mesoscopic phenomena that are beyond the realms of classical continuum mechanics and atomistic simulations, e.g., molecular dynamics and density functional theory (DFT). The latter two atomistic techniques are handicapped by the onerous length and time scales associated with simulating mesoscopic materials. Simulating such mesoscopic materials is likely to require, and greatly benefit from multiscale simulations coupling DFT, MD, PD, and explicit transient dynamic finite element methods FEM (e.g., Presto). The proposed work fills the gap needed to enable multiscale materials simulations.

An enhanced ISPH–SPH coupled method for simulation of incompressible fluid–elastic structure interactions

Solving fluid–structure interaction (FSI) problems using traditional methods poses significant challenges in the field of numerical simulation. The multiphysics coupling library precise code interaction coupling environment (preCICE), renowned for its robust multiphysics coupling capabilities, offers a promising solution for FSI problems. It supports various open/closed source software and commercial computational fluid dynamics solvers in a black box manner. However, preCICE currently mainly supports coupling schemes of mesh-based methods as well as few meshless methods. This paper proposes a critical grid interpolation (CGI) method as an intermediate medium to enable the particle method to interface with preCICE. The CGI method leverages particles and critical meshes to interpolate displacement and force, thereby allowing the pure Lagrangian smoothed particle hydrodynamics (SPH) method to solve FSI problems. The critical mesh serves as a coupling interface between particles and meshes, theoretically resolving the mesh mismatch issue inherent in particle methods when connecting to preCICE. To validate the performance of the proposed CGI method, we conducted experiments where the fluid and the structure were discretized using SPH and the finite element method, respectively. The results demonstrate the effectiveness of the CGI method in solving FSI problems. Additionally, we have made our source code for the SPH fluid adapter open-source and available on (https://github.com/terrylongsifan/AdapterSPH), facilitating further development of preCICE compatibility with more meshless methods. This study significantly advances the application of SPH in FSI problems by integrating it with preCICE, thereby expanding the versatility and applicability of multiphysics simulations.

In this contribution, we discuss the pros and cons of using the Smoothed Particle Hydrodynamics (SPH) method in providing support to multiphysics simulations. The Lagrangian SPH method is proposed to address a fluid-structure interaction (FSI) problem in which the response of a flexible baffle with elastic behavior is solved by using three modeling strategies: I) a dynamic structural solver of 3D bonded rigid bodies with rotations, based on a Lumped-Parameter Method (LPM); II) a non-linear Finite Element Method structural solver (FEM), based on the Euler-Bernoulli beam model; and III) a unified SPH-based for continuum mechanics based on a Total Lagrangian formulation. The present work uses the open-source code DualSPHysics as the fluid solver and different options now available in this code to represent flexible structures. The FSI simulated process starts with a gravity-driven fluid mass that hits a flexible plate experiences wide motion excursions (comparable to its length) in a relatively short time. The fluid phase is consistently solved with a weakly compressible SPH-based solver, whereas the three solution strategies are used to model the flexibility of the solid element. By discussing the the computational performance, and the solvers particle resolution sensitivity, the outcome of this research enables understanding the requirements of each software implementation to optimize the performance scalability.

A smoothed particle element method (SPEM) for modeling fluid–structure interaction problems with large fluid deformations

Improved element-particle coupling strategy with δ-SPH and particle shifting for modeling sloshing with rigid or deformable structures

Analysis of wave-induced crack propagation through a coupling algorithm of the peridynamics and isogeometric analysis

In this work, a novel Smoothed Particle Hydrodynamics (SPH) implementation to model the pneumatic power take-off (PTO) system of floating oscillating water column (OWC) devices is presented. The working principle of an OWC relies on the compression and decompression of the air pocket formed by a water column oscillation in its chamber, which in turns generates an air flow that activates a turbine. Usually, for practical reasons, instead of simulating the full power train, an orifice plate is employed to replicate its effect [1], both numerically and experimentally. Previous work has analyzed the air–water interaction in the chamber of a floating OWC by means of mesh-based or mesh-less two-phase simulations [2,3]. This research, instead, focuses on the influence of the varying air pressure on water inside the chamber using a single-phase SPH technique [4], implemented by coupling a “chamber model” to the SPH scheme within the DualSPHysics software. Such approach estimates the air pressure depending on the air flux through the OWC orifice and on a damping coefficient depending on the orifice size. In terms of numerical modeling, the air pressure is directly added to the SPH momentum equation at the chamber free surface. In addition, a novel six DOF volume tracking algorithm, which works both in 2D and 3D, is implemented to identify the water volume inside the floating OWC chamber at every integration time step. It relies on detecting a fictitious chamber inside the SPH one by defining some reference points and updating their position according to the roto-translations of the floating body. By knowing the volume occupied by the fluid particles in the chamber, the air pressure inside the device is obtained and applied to the water free surface to mimic the behavior of the OWC. Simulations of a catenary moored dual-pontoon OWC device and a tension leg-moored one, are performed respectively in 2D and 3D to validate the methodology against experimental results and prove the accuracy of this implementation. Such a methodology is potentially applicable to various marine devices, since, in principle, the model chamber reference points can be defined for any arbitrary geometry. Moreover, to the authors’ knowledge, this work represents the first attempt at simulating free floating OWCs in a single-phase framework exploiting the coupling with an analytical model, hence improving the computational efficiency with respect to the analogous SPH two-phase simulations. [1] M. Morris-Thomas, et al. (2017). “An investigation into the hydrodynamic efficiency of an oscillating water column,” Journal of Offshore Mechanics and Arctic Engineering-transactions of The Asme - J OFFSHORE MECH ARCTIC ENG, vol. 129, 11. [2] Y. Zhang, et al., (2025). “A multi-phase SPH model for simulating the floatingowc-breakwater integrated systems,” Coastal Engineering, vol. 197, p.104658. [3] A. Elhanafi, et al. (2017). “Experimental and numerical investigations on the hydrodynamic performance of a floating–moored oscillating water column wave energy converter,” Applied Energy, vol. 205, pp. 369–390. [4] G. Zhu, et al. (2020). “Hydrodynamics of onshore oscillating water column devices: A numerical study using smoothed particle hydrodynamics,” Ocean Engineering, vol. 218, p.108226.

A scalable parallel computing SPH framework for predictions of geophysical granular flows

Smoothed particle hydrodynamics (SPH) is a Lagrangian meshless particle method. It is one of the best method for simulating violent free surface flows in fluids and solving large fluid deformations. Dam breaking is a typical example of these problems. The basis of SPH was reviewed, including some techniques for governing equation resolution, such as the stepping method and the boundary handling method. Then numerical results of a dam breaking simulation were discussed, and the benefits of concepts like artificial viscosity and position correction were analyzed in detail. When compared with dam breaking simulated by the volume of fluid (VOF) method, the wave profile generated by SPH had good agreement, but the pressure had only reasonable agreement. Improving pressure results is clearly an important next step for research.

We propose a non-intrusive numerical coupling method for transient fluid-structure interaction (FSI) problems simulated by means of different discretization methods: smoothed particle hydrodynamics (SPH) and finite element (FE) methods for the fluid and the solid sub-domains, respectively. As a partitioned coupling method, the present algorithm can ensure a zero interface energy during the whole period of numerical simulation, even in the presence of large interface motion. In other words, the time integrations of the two sub-domains (second order Runge---Kutta scheme for fluid and Newmark integrator for solid) are synchronized. Thanks to this energy-conserving feature, one can preserve the minimal order of accuracy in time and the numerical stability of the FSI simulations, which are validated with a 1D and a 2D trivial numerical test cases. Additionally, some other 2D FSI simulations involving large interface motion have also been carried out with the proposed SPH---FE coupling method. Finally, an example of aquaplaning problem is given in order to show the feasibility of such coupling method in multi-dimensional applications with complicated structural geometries.

An artificial damping method for total Lagrangian SPH method with application in biomechanics

With the increasing demand for the performance and design refinement of steel structures (including houses, bridges, and infrastructure), many structures have adopted ultimate bearing capacity in service. The design service lives of steel building structures are generally more than 50 years, and most of them contain bolted connections, which suffer from extreme conditions such as fire (high temperature) during service. When the structure contains defects or cracks and bolt holes, it is easy to produce stress concentration at the defect location, which leads to crack nucleation and crack propagation, reduces the bearing capacity of the structure, and causes the collapse of the structure and causes disasters. In the process of structural damage and crack propagation, the traditional method has some disadvantages, such as stress singularity, the mesh needing to be redivided, and the crack being restricted to mesh; however, the integral method of peridynamics (PD) can completely avoid these problems. Therefore, in this paper, the constitutive equation of PD in high temperature is derived according to the variation law of steel material properties when changed by temperature increase and peridynamics parameters; the damage and crack expansion characteristics of Q345 steel specimens with bolt holes and a central double-crack at 20 °C, 200 °C, 400 °C, and 600 °C were analyzed to clarify the structural damage and failure mechanism. This study is helpful for providing theoretical support for the design of high-temperature steel structures, improving the stability of the structure, and ensuring the bearing capacity of the structure and the safety of people’s lives and property.

Peridynamic micromechanical modeling of plastic deformation and progressive damage prediction in dual-phase materials

Numerical simulations of water entries based on a three-dimensional parallelized Smoothed Particle Hydrodynamics (SPH) model developed by Ecole Centrale Nantes are presented. The aim of the paper is to show how such SPH simulations of complex 3D problems involving a free surface can be performed on a super computer like the IBM Blue Gene/L with 8,192 cores of Ecole polytechnique fédérale de Lausanne. The present paper thus presents the different techniques which had to be included into the SPH model to make possible such simulations. Memory handling, in particular, is a quite subtle issue because of constraints due to the use of a variable-h scheme. These improvements made possible the simulation of test cases involving hundreds of million particles computed by using thousands of cores. Speedup and efficiency of these parallel calculations are studied. The model capabilities are illustrated in the paper for two water entry problems, firstly, on a simple test case involving a sphere impacting the free surface at high velocity; and secondly, on a complex 3D geometry involving a ship hull impacting the free surface in forced motion. Sensitivity to spatial resolution is investigated as well in the case of the sphere water entry, and the flow analysis is performed by comparing both experimental and theoretical reference results.