Bending of bilayers with general initial shapes

TL;DR

This paper introduces a simple discrete formula for the elastic energy of bilayers with arbitrary initial shapes, enabling rapid computation of equilibrium configurations and analysis of diverse bending behaviors.

Contribution

It provides a novel, efficient method for modeling bilayer bending with general initial shapes, supported by analytical and computational validation.

Findings

Good agreement with analytical solutions for rectangular bilayers

Identification of typical bending patterns in complex shapes

Observation of curvature intensification and conical bending zones

Abstract

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.