# Publications

to improve and optimize the physical response of the surfaces such as drag force, superhydrophobicity, and

adhesion. While the effect of the height and spacing of the textures have been extensively studied, the effect

of the shape of the textures has only been considered qualitatively. Here, a polynomial framework is proposed

to mathematically define the cross-sectional profiles of the textures and offer a quantitative measure for

comparing the physical response of the textured surfaces with various shapes. As a case study, textured surfaces

designed with this framework are tested for their hydrodynamic frictional response in the cylindrical Couette

flow regime in Taylor–Couette flows. With the reduction in torque as the objective, experimental and numerical

results confirm that textures with height-to-half-spacing ratios of lower and equal to unity with concave profiles

offer a lower torque compared to both smooth surfaces and triangular textures. In addition, across multiple

polynomial orders, textures defined by second-order polynomials offer a wide range of responses, eliminating

the need for considering polynomials of higher orders and complexity. While the case study here is focused on

the laminar flow regime and the frictional torque, the same type of analysis can be applied to other surface

properties and physical responses as we

Changes in the elastic properties of brain tissue have been correlated with injury, cancers, and neurodegenerative diseases. However, discrepancies in the reported elastic moduli of brain tissue are persistent, and spatial inhomogeneities complicate the interpretation of macroscale measurements such as rheology. Here we introduce needle induced cavitation rheology (NICR) and volume-controlled cavity expansion (VCCE) as facile methods to measure the apparent Young's modulus *E* of minimally manipulated brain tissue, at specific tissue locations and with sub-millimeter spatial resolution. For different porcine brain regions and sections analyzed by NICR, we found *E* to be 3.7 ± 0.7 kPa and 4.8 ± 1.0 kPa for gray matter, and white matter, respectively. For different porcine brain regions and sections analyzed by VCCE, we found *E* was 0.76 ± 0.02 kPa for gray matter and 0.92 ± 0.01 kPa for white matter. Measurements from VCCE were more similar to those obtained from macroscale shear rheology (0.75 ± 0.06 kPa) and from instrumented microindentation of white matter (0.97 ± 0.40 kPa) and gray matter (0.86 ± 0.20 kPa). We attributed the higher stiffness reported from NICR to that method's assumption of a cavitation instability due to a neo-Hookean constitutive response, which does not capture the strain-stiffening behavior of brain tissue under large strains, and therefore did not provide appropriate measurements. We demonstrate via both analytical modeling of a spherical cavity and finite element modeling of a needle geometry, that this strain stiffening may prevent a cavitation instability. VCCE measurements take this stiffening behavior into account by employing an incompressible one-term Ogden model to find the nonlinear elastic properties of the tissue. Overall, VCCE afforded rapid and facile measurement of nonlinear mechanical properties of intact, healthy mammalian brain tissue, enabling quantitative comparison among brain tissue regions and also between species. Finally, accurate estimation of elastic properties for this strain stiffening tissue requires methods that include appropriate constitutive models of the brain tissue response, which here are represented by inclusion of the Ogden model in VCCE.

*Rubber Chem. Technol.*, 1990,

**63**, 49–53]. Since then, the debate on the mechanisms that drive this failure process is ongoing. Using a high precision volume controlled cavity expansion procedure, this paper reveals the intimate relationship between cavitation and fracture. Combining a Griffith inspired formulation for crack propagation, and a Gent inspired formulation for cavity expansion, we show that despite the apparent complexity of the fracture patterns, the pressure–volume response follows a predictable path. In contrast to available studies, both the model and our experiments are able to track the entire process including the unstable branch, by controlling the volume of the cavity. Moreover, this minimal theoretical framework is able to explain the ambiguity in previous experiments by revealing the presence of metastable states that can lead to first order transitions at onset of fracture. The agreement between the simple theory and all of the experimental results conducted in PDMS samples with shear moduli in the range of 25–246 [kPa] confirms that cavitation and fracture work together in driving the expansion process. Through this study we also determine the fracture energy of PDMS and show its significant dependence on strain stiffening.