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Maxwell’s tape measure

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Tape-springs are thin, transversely curved strips, of which the carpenter’s tape measures is a familiar everyday example. When you bend a tape-spring, it initially deforms uniformly, before suddenly forming a highly curved “fold” region: an example of elastic localisation. The curvature in the fold and unfolded regions are governed by the Maxwell equal areas construction – familiar from thermodynamics – applied to the tape-spring moment-curvature relationship. In our recent work, we have introduced “tapered-springs”: tape-springs with varying cross-sectional geometry along their length. When bent, we observe novel spiral-shaped folds and “jumping” behaviour. Key to understanding this behaviour is the fact that the Maxwell equal-areas construction must be satisfied specifically on the propagating fronts of the fold

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