Simulating the dynamics of actuated thin elastic sheets

We develop a method to simulate the dynamics of thin elastic sheets under time-dependent external or internal forces, e.g. contact forces, temperature change, or chemical reactions within the sheet. The dynamics are difficult to simulate efficiently due to numerical stiffness resulting from the in-plane stretching term in the elastic energy. We present a semi-implicit time discretization that allows the dynamics to be simulated stably with essentially no time-step constraint, allowing for fast simulations. We show examples for thin sheets, bilayers, and models of active gel materials, using different spatial geometries and different types of spatial discretizations.