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Register a new userThird- and fourth-order constants of incompressible soft solids and the acousto-elastic effect
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Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third- and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for $rho v^2$, where $rho$ is the mass density and v the wave speed, in terms of the elongation $e$ of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: $rho v^2 = a + be + ce^2$, say, $a$ depends linearly on $mu$; $b$ on $mu$ and $A$; and $c$ on $mu$, $A$, and $D$, the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves.
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In the theory of weakly non-linear elasticity, Hamilton et al. [J. Acoust. Soc. Am. textbf{116} (2004) 41] identified $W = mu I_2 + (A/3)I_3 + D I_2^2$ as the fourth-order expansion of the strain-energy density for incompressible isotropic solids. Subsequently, much effort focused on theoretical and experimental developments linked to this expression in order to inform the modeling of gels and soft biological tissues. However, while many soft tissues can be treated as incompressible, they are not in general isotropic, and their anisotropy is associated with the presence of oriented collagen fiber bundles. Here the expansion of $W$ is carried up to fourth-order in the case where there exists one family of parallel fibers in the tissue. The results are then applied to acoustoelasticity, with a view to determining the second- and third-order nonlinear constants by employing small-amplitude transverse waves propagating in a deformed soft tissue.
We show that the electric field driven surface instability of visco-elastic films has two distinct regimes: (1) The visco-elastic films behaving like a liquid display long wavelengths governed by applied voltage and surface tension, independent of its elastic storage and viscous loss moduli, and (2) the films behaving like a solid require a threshold voltage for the instability whose wavelength always scales as ~ 4 x film thickness, independent of its surface tension, applied voltage, loss and storage moduli. Wavelength in a narrow transition zone between these regimes depends on the storage modulus.
A rigid cylinder placed on a soft gel deforms its surface. When multiple cylinders are placed on the surface, they interact with each other via the topography of the deformed gel which serves as an energy landscape; as they move, the landscape changes which in turn changes their interaction. We use a combination of experiments, simple scaling estimates and numerical simulations to study the self-assembly of cylinders in this elastic analog of the Cheerios effect for capillary interactions on a fluid interface. Our results show that the effective two body interaction can be well described by an exponential attraction potential as a result of which the dynamics also show an exponential behavior with respect to the separation distance. When many cylinders are placed on the gel, the cylinders cluster together if they are not too far apart; otherwise their motion gets elastically arrested.
The response to shear of the dense soft solids features a stress overshoot and a persistent shear banding before reaching a homogeneously flowing state. In 3D large scale simulations we analyze the time required for the onset of homogeneous flow, the normal stresses and structural signatures at different shear rates and in different flow geometries, finding that the stress overshoot, the shear band formation and its persistence are controlled by the presence of overconstrained microscopic domains in the initially solid samples. Being able to identify such domains in our model by prevalently icosahedrally packed regions, we show that they allow for stress accumulation during the stress overshoot and that their structural reorganization controls the emergence and the persistence of the shear banding.
Surface stress and surface energy are two fundamental parameters that determine the surface properties of any material. While it is commonly believed that the surface stress and surface energy of liquids are identical, the relationship between the two parameters in soft polymeric gels remains debatable. In this work, we measured the surface stress and surface energy of soft silicone gels with varying crosslinking densities in soft wetting experiments. Above a critical crosslink density, $k_0$, the surface stress is found to increase significantly with crosslinking density while the surface energy, by contrast, remains unchanged. In this regime, we can estimate a non-zero surface elastic modulus that also increases with the ratio of crosslinkers. By comparing the surface mechanics of the soft gels to their bulk rheology, the surface properties near the critical density $k_0$ are found to be closely related to the underlying percolation transition of the polymer networks.
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