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Abstract This study computationally investigates the elastic interaction of two pressurized cylindrical cavities in a 2D hyperelastic medium. Unlike linear elasticity, where interactions are exclusively attractive, nonlinear material models (neo-Hookean, Mooney–Rivlin, Arruda–Boyce) exhibit both attraction and repulsion between the cavities. A critical pressure-shear modulus ratio governs the transition, offering a pathway to manipulate cavity configurations through material and loading parameters. At low ratios, the interactions are always attractive, while at high ratios, both attractive and repulsive regimes exist depending on the separation between the cavities. The effect of the strain-stiffening on these interactions is also analyzed. These insights bridge theoretical and applied mechanics, with implications for soft material design and subsurface engineering. 

Flexoelectricity in multilayer graphene (MLG) buckling can stimulate kink-shaped crinkle formation. In the process, the bifurcation becomes subcritical and the suspended-MLG’s crinkle curvature is localized to a narrow band of ∼2𝑛𝑚 width. We extend the study to flexoelectric layers bonded to a soft elastic substrate. Elastic substrates can guide the morphology of MLG and produce periodic patterns. We show that MLG’s flexoelectricity together with substrate elasticity can produce periodic crinkles, which qualitatively explains the grade-dependent mosaic spreading in highly oriented pyrolytic graphite (HOPG). Experimental measurements of HOPG’s surface-slope variations indeed confirm curvature localization at the crinkle valleys and ridges. 

Biofilms are aggregates of bacterial cells surrounded by an extracellular matrix. Much progress has been made in studying biofilm growth on solid substrates; however, little is known about the biophysical mechanisms underlying biofilm development in three-dimensional confined environments in which the biofilm-dwelling cells must push against and even damage the surrounding environment to proliferate. Here, combining single-cell imaging, mutagenesis, and rheological measurement, we reveal the key morphogenesis steps ofVibrio choleraebiofilms embedded in hydrogels as they grow by four orders of magnitude from their initial size. We show that the morphodynamics and cell ordering in embedded biofilms are fundamentally different from those of biofilms on flat surfaces. Treating embedded biofilms as inclusions growing in an elastic medium, we quantitatively show that the stiffness contrast between the biofilm and its environment determines biofilm morphology and internal architecture, selecting between spherical biofilms with no cell ordering and oblate ellipsoidal biofilms with high cell ordering. When embedded in stiff gels, cells self-organize into a bipolar structure that resembles the molecular ordering in nematic liquid crystal droplets. In vitro biomechanical analysis shows that cell ordering arises from stress transmission across the biofilm–environment interface, mediated by specific matrix components. Our imaging technique and theoretical approach are generalizable to other biofilm-forming species and potentially to biofilms embedded in mucus or host tissues as during infection. Our results open an avenue to understand how confined cell communities grow by means of a compromise between their inherent developmental program and the mechanical constraints imposed by the environment.