Bending of bilayers with general initial shapes. (English) Zbl 1431.74083

Summary: We present a simple discrete formula for the elastic energy of a bilayer. The formula is convenient for rapidly computing equilibrium configurations of actuated bilayers of general initial shapes. We use maps of principal curvatures and minimum-curvature direction fields to analyze configurations. We find good agreement between the computations and an approximate analytical solution for the case of a rectangular bilayer. For more general shapes (simple polyiamonds), we find a range of typical bending behaviors: overall bending directions along longest and shortest dimensions, inward bending at corners, curvature intensification near boundaries, and conical bending and partitioned bending zones in some cases.


74K99 Thin bodies, structures
74E30 Composite and mixture properties
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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