arXiv subjects

John Biggins

Publications and source records attributed to John Biggins.

2 recordsLinked to original sources

arXiv2024

Programming evolution of geometry in shape-morphing sheets via spatiotemporal activation

Shape-programmed sheets morph from one surface into another upon activation by stimuli such as illumination, and have attracted much interest for their potential engineering applications, especially in soft robotics. Complex shape changes can be achieved by patterning a simple local active deformation (e.g. isotropic swelling), to generate differential growth. Usually the material itself is designed $\unicode{x2014}$ for example by patterning a molecular director $\unicode{x2014}$ such that a particular shape change occurs upon exposure to a spatially uniform stimulus. A limitation of this paradigm is that typically only one target geometry can be attained as the stimulus is adjusted. Here we show that this limitation can be overcome by patterning the stimulus itself, thereby exercising spatiotemporal control over local deformation magnitudes. Thus a single physical sample can be induced to traverse a continuous family of target geometries, opening the door to precise shape adjustments, new functionalities, and designable non-reciprocal loops in shape space. We illustrate these possibilities with examples including active parabolic reflectors, chiral flow guides, and bending channels. Finding the necessary patterns of activation involves solving families of metric inverse problems; we solve these by reduction to ODEs in an axisymmetric setting, then present a novel numerical scheme to solve them in generality.

cond-mat.soft↗

arXiv2015

Finite wavelength surface-tension driven instabilities in soft solids, including instability in a cylindrical channel through an elastic solid

We deploy linear stability analysis to find the threshold wavelength ($\lambda$) and surface tension ($\gamma$) of Rayleigh-Plateau type "peristaltic" instabilities in incompressible neo-Hookean solids in a range of cylindrical geometries with radius $R_0$. First we consider a solid cylinder, and recover the well-known, infinite wavelength instability for $\gamma\ge6 \mu R_0$, where $\mu$ is the solid's shear modulus. Second, we consider a volume-conserving (e.g.\ fluid filled and sealed) cylindrical cavity through an infinite solid, and demonstrate infinite wavelength instability for $\gamma\ge 2 \mu R_0$. Third, we consider a solid cylinder embedded in a different infinite solid, and find a finite wavelength instability with $\lambda\propto R_0$, at surface tension $\gamma \propto \mu R_0$, where the constants depend on the two solids' modulus ratio. Finally, we consider an empty cylindrical channel (or filled with expellable fluid) through an infinite solid, and find an instability with finite wavelength, $\lambda \approx2 R_0$, for $\gamma\ge 2.543... \mu R_0$. Using finite-strain numerics, we show such a channel jumps at instability to a highly peristaltic state, likely precipitating it's blockage or failure. We argue that finite wavelengths are generic for elasto-capillary instabilities, with the simple cylinder's infinite wavelength being the exception rather than the rule.

cond-mat.soft↗