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

Abstract

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.