Stimuli-responsive shell theory

Soft matter mechanics generally involve finite deformations and instabilities of structures in response to a wide range of mechanical and non-mechanical stimuli. Modeling plates and shells is generally a challenge due to their geometrically nonlinear response to loads; however, non-mechanical loads further complicate matters as it is often not clear how they modify the shell's energy functional. In this work, we demonstrate how to form a mechanical interpretation of these non-mechanical stimuli, in which the standard shell strain energy can be augmented with potentials corresponding to how a non-mechanical stimulus acts to change the shell's area and curvature via the natural stretch and curvature. As a result, the effect of non-mechanical stimuli to deform shells is transformed into effective external loadings, and this framework allows for the application of analytical and computational tools that are standard within the mechanics community. Furthermore, we generalize the effect of mass change during biological growth to account for its effect on the stress constitution. The theory is formulated based on a standard, stress-free reference configuration which is known a priori, meaning it can be physically observed, and only requires the solution of a single-field equation, the standard mechanical momentum or equilibrium equation, despite capturing the effects of non-mechanical stimuli. We validate the performance of this model by several benchmark problems, and finally, we apply it to complex examples, including the snapping of the Venus flytrap, leaf growth, and the buckling of electrically active polymer plates. Overall, we expect that mechanicians and non-mechanicians alike can use the approach presented here to quickly modify existing computational tools with effective external loadings calculated in this novel theory to study how various types of non-mechanical stimuli impact the mechanics and physics of thin shell structures.