In this work, an innovative model is proposed as a design tool to predict both the inner and outer radii in rolled structures based on polydimethylsiloxane bilayers. The model represents an improvement of Timoshenko's formula taking into account the friction arising from contacts between layers arising from rolling by more than one turn, hence broadening its application field towards materials based on elastomeric bilayers capable of large deformations. The fabricated structures were also provided with surface topographical features that would make them potentially usable in different application scenarios, including cell/tissue engineering ones. The bilayer design parameters were varied, such as the initial strain (from 20 to 60%) and the bilayer thickness (from 373 to 93 µm). The model matched experimental data on the inner and outer radii nicely, especially when a high friction condition was implemented in the model, particularly reducing the error below 2% for the outer diameter while varying the strain. The model outperformed the current literature, where self-penetration is not excluded, and a single value of the radius of spontaneous rolling is used to describe multiple rolls. A complex 3D bioinspired hierarchical elastomeric microstructure made of seven spirals arranged like a hexagon inscribed in a circumference, similar to typical biological architectures (e.g., myofibrils within a sarcolemma), was also developed. In this case also, the model effectively predicted the spirals' features (error smaller than 18%), opening interesting application scenarios in the modeling and fabrication of bioinspired materials.
Keywords: bilayer; bioinspired materials; microfabrication; polydimethylsiloxane; programmable deformation; self-rolling.