An arbitrary Lagrangian-Eulerian method for nonlinear structural-acoustic interaction of hyperelastic solid and compressible viscous fluid

Li, Yapeng; Qu, Yegao; Xie, Fangtao; Meng, Guang

doi:10.1016/j.jcp.2022.111665

Cited by 7 publications

(11 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present analysis, the hydrostatic pressure of the fluid is ignored and only the time-varying part of the acoustic fluid traction is considered. The stress 𝛔 F in terms of the velocity potential and acoustic pressure of the fluid can be given as 8 :…”

Section: Preliminariesmentioning

confidence: 99%

“…Large-amplitude vibrational hyperelastic solids are considered, and nonlinear acoustic waves radiated from the solids are modeled in moving acoustic domains. An ALE frame of reference is adopted to accommodate the large movement of the acoustic fluid domain, and the governing equation in the ALE frame is given as 8 :…”

Section: Governing Equationsmentioning

confidence: 99%

“…The finite element method is adopted to discretize the nonlinear acoustic model of Equation (8) in space. This results in a first-order nonlinear system of equations.…”

Section: Finite Element Discretizationmentioning

confidence: 99%

“…Technical challenges exist for analyzing such interactions due to the geometrical and material nonlinearities of the hyperelastic solid, the nonlinear convection and pressure-density relation of the acoustic fluid, and the kinematic nonlinearity due to the large-deformable fluid-solid interface. [6][7][8] It is desirable to develop a computational method for predicting the interaction between a large-deformable hyperelastic solid and finite-amplitude acoustic waves.…”

Section: Introductionmentioning

confidence: 99%

“…Implicit or explicit direct integration schemes can be adopted to calculate the dynamic responses of hyperelastic solid and acoustic waves. 6,8,34 It is noted an explicit time integration scheme is efficient to calculate the responses in a time step but requires a restricted time step size to achieve stable numerical results. 35 On the contrary, implicit integration schemes can be unconditionally stable so that a large time step size can be adopted to achieve stable numerical results.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Implicit coupling methods for nonlinear interactions between a large‐deformable hyperelastic solid and a viscous acoustic fluid of infinite extent

Li,

Qu,

Meng

2023

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

This paper addresses the challenges in studying the interaction between high‐intensity sound waves and large‐deformable hyperelastic solids, which are characterized by nonlinearities of the hyperelastic material, the finite‐amplitude acoustic wave, and the large‐deformable fluid–solid interface. An implicit coupling method is proposed for predicting nonlinear structural‐acoustic responses of the large‐deformable hyperelastic solid submerged in a compressible viscous fluid of infinite extent. An arbitrary Lagrangian–Eulerian (ALE) formulation based on an unsplit complex‐frequency‐shifted perfectly matched layer method is developed for long‐time simulation of the nonlinear acoustic wave propagation without exhibiting long‐time instabilities. The solid and acoustic fluid domains are discretized using the finite element method, and two different options of staggered implicit coupling procedures for nonlinear structural‐acoustic interactions are developed. Theoretical formulations for stability analysis of the implicit methods are provided. The accuracy, robustness, and convergence properties of the proposed methods are evaluated by a benchmark problem, that is, a hyperelastic rod interacting with finite‐amplitude acoustic waves. The numerical results substantiate that the present methods are able to provide long‐time steady‐state solutions for a nonlinear coupled hyperelastic solid and viscous acoustic fluid system without numerical constraints of small time step sizes and long‐time instabilities. The methods are applied to investigate nonlinear dynamic behaviors of coupled hyperelastic elliptical ring and acoustic fluid systems. Physical insights into 2:1 and 4:2:1 internal resonances of the hyperelastic elliptical ring and period‐doubling bifurcations of the structural and acoustic responses of the system are provided.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

“…The finite element method is adopted to discretize the nonlinear acoustic model of Equation (8) in space. This results in a first-order nonlinear system of equations.…”

Section: Finite Element Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%