A hyperelastic oscillatory Couette system

TL;DR

This paper presents analytical solutions for a visco-hyperelastic solid layer between oscillating fluids, providing insights into elasto-hydrodynamic coupling with applications in biomechanics and a benchmark for numerical methods.

Contribution

It offers the first semi-analytical solutions for coupled fluid-hyperelastic systems and introduces an interactive tool and open-source code for further exploration.

Findings

Derived rigorous analytical solutions for coupled fluid-hyperelastic systems

Identified key parameters influencing elasto-hydrodynamic behavior

Provided benchmark cases for numerical solver validation

Abstract

We report (semi-)analytical solutions of a problem involving a visco-hyperelastic solid material layer sandwiched between two fluid layers, in turn confined by two long planar walls that undergo oscillatory motion. The resulting system dynamics are rationalized, based on fluid viscosity and solid elasticity, via wave and boundary-layer theory. This allows for physical interpretation of elasto-hydrodynamic coupling, potentially connecting to a broad set of biophysical phenomena and applications, from synovial joint mechanics to elastometry. Further, obtained solutions are demonstrated to be rigorous benchmarks for testing coupled incompressible fluid--hyperelastic solid and multiphase numerical solvers, towards which we highlight challenging parameter sets. Finally, we provide an interactive, online sandbox to build physical intuition, and open-source our code-base.