Intense surface eruptions are observed along the curved surface of a confined cylindrical film of hydrogel subject to laser-induced converging-diverging shock loading. Detailed numerical simulations are used to identify the dominant mechanisms causing mechanical instability. The mechanisms that produce surface instability are found to be fundamentally different from both acoustic parametric instability and shock-driven Richtmyer-Meshkov instability. The time scale of observed and simulated eruption formation is much larger than that of a single shock reflection, in stark contrast to previously studied shock-driven instabilities. Moreover, surface undulations are only found along external, as opposed to internal, soft solid boundaries. Specifically, classic bubble surface instability mechanisms do not occur in our experiments and here we comment only on the new surface undulations found along the outer boundary of solid hydrogel cylinders. Our findings indicate a new class of impulsively excited surface instability that is driven by cycles of internal shock reflections.

Recent experiments on hydrogels subjected to large elongations have shown elastic instabilities resulting in the formation of geometrically intricate fringe and fingering deformation patterns. In this paper, we present a robust numerical framework addressing the challenges that emerge in the simulation of this complex material response from the onset of instability to the post-bifurcation behavior. We observe that the numerical difficulties stem from the non-convexity of the strain energy density in the near-incompressible, large-deformation regime, which is responsible for the coexistence of multiple equilibrium paths with vastly-different, sinuous deformation patterns immediately after bifurcation. We show that these numerical challenges can be overcome by using sufficiently-high order of interpolation in the finite element approximation, an arc-length-based nonlinear solution procedure that follows the entire equilibrium path of the system, and an implementation enabling parallel, large-scale simulations. The resulting computational approach provides the ability to conduct highly-resolved, truly quasi-static simulations of complex elastic instabilities. We present numerical results illustrating the ability of the path-following approach to describe the full evolution of fringe and fingering instabilities observed experimentally in recent experiments of confined cylindrical specimens of soft hydrogels subject to tension. Importantly, we observe that the robustness of the static solution procedure enables complete access to the multiplicity of solutions occurring immediately after the onset of bifurcation, as well as to the settled post-bifurcation states.