A fluid--peridynamic structure model of deformation and damage of microchannels

TL;DR

This paper introduces a coupled fluid-peridynamic model for microchannels with soft walls, enabling simulation of deformation, wave dynamics, and failure scenarios under fluid flow, advancing understanding of microchannel stability and failure.

Contribution

It develops a novel nonlocal peridynamic model integrated with fluid dynamics to analyze deformation and failure in microchannels, capturing discontinuities and complex failure modes.

Findings

Wave propagation deviates from classical behavior with increased nonlocal influence.

A dividing curve predicts failure scenarios during transient and steady conditions.

The model reveals potential failure mechanisms under hydrodynamic loads.

Abstract

Soft-walled microchannels arise in many applications, ranging from organ-on-a-chip platforms to soft-robotic actuators. However, despite extensive research on their static and dynamic response, the potential failure of these devices has not been addressed. To this end, we explore fluid--structure interaction in microchannels whose compliant top wall is governed by a nonlocal mechanical theory capable of simulating both deformation and material failure. We develop a one-dimensional model by coupling viscous flow under the lubrication approximation to a state-based peridynamic formulation of an Euler--Bernoulli beam. The peridynamic formulation enables the wall to be modeled as a genuinely nonlocal beam, and the integral form of its equation of motion remains valid whether the deformation field is smooth or contains discontinuities. Through the proposed computational model, we explore the steady and time-dependent behaviors of this fluid--peridynamic structure interaction. We rationalize the wave and damping dynamics observed in the simulations through a dispersion (linearized) analysis of the coupled system, finding that, with increasing nonlocal influence, wave propagation exhibits a clear departure from classical behavior, characterized by a gradual suppression of the phase velocity. The main contribution of our study is to outline the potential failure scenarios of the microchannel's soft wall under the hydrodynamic load of the flow. Specifically, we find a dividing curve in the space spanned by the dimensionless Strouhal number (quantifying unsteady inertia of the beam) and the compliance number (quantifying the strength of the fluid--structure coupling) separating scenarios of potential failure during transient conditions from potential failure at the steady load.