Abstract
Abstract Many elastic systems localize under applied displacement, precipitating into regions of lower and higher strain; further displacement is accommodated by growth of the high strain region at a constant load. Such systems can be studied as propagating instabilities, focusing on the work required to propagate the high strain region, or as two-phase energy minimization problems. It is shown that the Maxwell “equal-areas” construction, and the related common tangent construction, provide the solution to either approach. A new, graphical, proof of the Maxwell equal-areas construction using total strain energy diagrams is presented. Tape-springs are investigated as a case study, with localization presenting as the formation of elastic folds—developable regions with high curvature. One notable property of tape-spring folds is that the fold radius is approximately equal to the initial transverse radius. This result was first proven by Rimrott, and later improved by Calladine and Seffen. A further improvement is obtained here by application of the common tangent construction, and all solutions are shown to be approximations to the Maxwell equal-areas construction in the limit of zero thickness.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
