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Partitioned procedures are appealing for solving complex fluid-structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added-mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin-Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection-based incompressible CFD and finite element-based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid-structure interfaces embedded in structured non-body-conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex-dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie, f , on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler-Bernoulli beam interacting with a two-dimensional incompressible inviscid flow. Both studies reveal a trade-off between stability and accuracy: smaller values of f tend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value of f that optimizes this trade-off is derived and discussed.KEYWORDS embedded boundary method, fluid-structure interaction, numerical added-mass effect, partitioned procedure, Robin-Neumann transmission conditions 578

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Understanding the response of solid materials to shock loading is important for mitigating shock-induced damages and failures, as well as advancing the beneficial use of shock waves for material modifications. In this paper, we consider a representative brittle material, BegoStone, in the form of cylindrical bodies and submerged in water. We present a computational study on the causal relationship between the prescribed shock load and the resulting elastic waves and damage in the solid material. A recently developed three-dimensional computational framework, FIVER, is employed, which couples a finite volume compressible fluid solver with a finite element structural dynamics solver through the construction and solution of local, one-dimensional fluid-solid Riemann problems. The material damage and fracture are modeled and simulated using a continuum damage mechanics model and an element erosion method. The computational model is validated in the context of shock wave lithotripsy and the results are compared with experimental data. We first show that after calibrating the growth rate of microscopic damage and the threshold for macroscopic fracture, the computational framework is capable of capturing the location and shape of the shock-induced fracture observed in a laboratory experiment. Next, we introduce a new phenomenological model of shock waveform, and present a numerical parametric study on the effects of a single shock load, in which the shock waveform, magnitude, and the size of the target material are varied. In particular, we vary the waveform gradually from one that features non-monotonic decay with a tensile phase to one that exhibits monotonic decay without a tensile phase. The result suggests that when the length of the shock pulse is comparable to that of the target material, the former waveform may induce much more significant damage than the latter one, even if the two share the same magnitude, duration, and acoustic energy.