Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

Abstract

Characterizing the elastic properties of soft materials through bulge testing relies on accurate measurement of deformation, which is experimentally challenging. To avoid measuring deformation, we propose a hydrodynamic bulge test for characterizing the material properties of thick, pre-stressed elastic sheets via their fluid-structure interaction with a steady viscous fluid flow. Specifically, the hydrodynamic bulge test relies on a pressure drop measurement across a rectangular microchannel with a deformable top wall. We develop a mathematical model using first-order shear-deformation theory of plates with stretching, and the lubrication approximation for Newtonian fluid flow. Specifically, a relationship is derived between the imposed flow rate and the total pressure drop. Then, this relationship is inverted numerically to yield estimates of the Young's modulus (given the Poisson ratio), if the pressure drop is measured (given the steady flow rate). Direct numerical simulations of two-way-coupled fluid-structure interaction are carried out in ANSYS to determine the cross-sectional membrane deformation and the hydrodynamic pressure distribution. Taking the simulations as "ground truth," a hydrodynamic bulge test is performed using the simulation data to ascertain the accuracy and validity of the proposed methodology for estimating material properties. An error propagation analysis is performed via Monte Carlo simulation to characterize the susceptibility of the hydrodynamic bulge test estimates to noise. We find that, while a hydrodynamic bulge test is less accurate in characterizing material properties, it is less susceptible to noise, than a hydrostatic bulge test, in the input (measured) variable.

Reduced modeling and global instability of finite-Reynolds-number flow in compliant rectangular channels

“…It is also worth mentioning that if the top wall is thin with γ 1, the elasticity problem is usually taken to be a plane stress problem, and a 1D engineering model is usually available for the displacement out of plane (i.e., u y here), such as the Kirchhoff-Love (Love, 1888;Timoshenko and Woinowsky-Krieger, 1959) and Reissner-Mindlin (Reissner, 1945;Mindlin, 1951) plate theories. However, this fact does not fundamentally contradict with our plane-strain reduction because the decoupling of the cross-sections remains true (Christov et al, 2018;Shidhore and Christov, 2018;Anand et al, 2020) due to the separation of scales, w . Moreover, the discussion above is only based on the balance of Cauchy stresses, and does not involve the boundary conditions either on the sides (i.e., at x = ±w/2) or at the upper surface of the wall (i.e., at ŷ = d or y = h 0 + d).…”

Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits

“…Importantly, when (22) can be resolved for ∆p in terms of q, then it is generally expected that the resulting soft hydraulic resistance R h = R h (∆p). Deriving analytical expressions for R h (∆p), and obtaining a "generalized Ohm's law" for soft resistors, has been the goal of a number of recent studies [100,114,53,115,106,108,116].…”

“…are negligible, has been justified by perturbation methods [100,108,116,109,106] within the long and shallow conduit scaling that leads to the lubrication approximation. Thus, unlike rigid pipes (figure 4), calculating the hydraulic resistance of a soft conduit requires the solution of a non-trivial elasticity problem (figure 7), in addition to the flow problem.…”

“…the parameters S 1 , S 2 and S 3 are known functions of the geometry (e.g., wall thickness t) [114,108], or potentially pre-stress in the wall [116]. The term outside of the bracket can be compared to figure 4 (row "two plates").…”

“…An earlier technique by Ozsun et al [232] was based on "constitutive pressure-deformation" curves, measured ahead of time, so that the axial pressure (and deformation) profiles could be inferred from a single pressure drop measurement across a microchannel. Similarly, Anand et al [116] demonstrated a "hydrodynamic bulge test" in silico for measuring the material properties of thin elastic films sealing a microchannel, from the pressure drop across the length of the channel. Once again, the key innovation of these methods is to harness the flow-induced deformation of a PDMS microchannel.…”