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.

中文翻译：

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大变形超弹性固体与无限范围粘性声学流体之间非线性相互作用的隐式耦合方法

本文解决了研究高强度声波与大变形超弹性固体之间相互作用的挑战，其特点是超弹性材料的非线性、有限振幅声波和大变形流固界面。提出了一种隐式耦合方法来预测浸没在无限范围可压缩粘性流体中的大变形超弹性固体的非线性结构声学响应。开发了一种基于不分裂复频移完美匹配层方法的任意拉格朗日-欧拉 (ALE) 公式，用于长期模拟非线性声波传播，而不会表现出长期不稳定性。使用有限元方法对固体和声流体域进行离散化，并开发了用于非线性结构-声学相互作用的交错隐式耦合程序的两种不同选项。提供了隐式方法稳定性分析的理论公式。所提出方法的准确性、鲁棒性和收敛性通过基准问题（即与有限幅度声波相互作用的超弹性杆）进行评估。数值结果证实，本方法能够为非线性耦合超弹性固体和粘性声流体系统提供长时间稳态解，而不受小时间步长和长时间不稳定性的数值限制。该方法用于研究耦合超弹性椭圆环和声流体系统的非线性动力学行为。提供了对超弹性椭圆环的 2:1 和 4:2:1 内部共振以及系统结构和声学响应的倍周期分岔的物理见解。