  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, in the input (measured) variable, than a hydrostatic bulge test.
