Abstract
Localized deformation patterns are a common motif in morphogenesis and are increasingly finding applications in materials science and engineering, in such instances as mechanical memories. Here, we describe the emergence of spatially localized deformations in a minimal mechanical system by exploring the impact of growth and shear on the conformation of a semi-flexible filament connected to a pliable shearable substrate. We combine numerical simulations of a discrete rod model with theoretical analysis of the differential equations recovered in the continuum limit to quantify (in the form of scaling laws) how geometry, mechanics and growth act together to give rise to such localized structures in this system. We find that spatially localized deformations along the filament emerge for intermediate shear modulus and increasing growth. Finally, we use experiments on a 3D-printed multi-material model system to demonstrate that external control of the amount of shear and growth may be used to regulate the spatial extent of the localized strain texture.
Original language | English |
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Article number | 20190370 |
Number of pages | 12 |
Journal | Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences |
Volume | 475 |
Issue number | 2229 |
DOIs | |
Publication status | Published - 11 Sept 2019 |
Funding
Data accessibility. This article does not contain any additional data. Authors’ contributions. T.C.T.M. and R.K. contributed equally to this work. R.K. and C.S. performed numerical simulations. T.C.T.M., A.J.D. and L.M. developed the mathematical analysis. T.C.T.M. and J.C.W. performed the experiments. T.C.T.M., R.K. and L.M. wrote the paper, with input from the other authors. L.M. conceived of research, formulated the mathematical models, designed the experiments and supervised the work. Competing interests. We declare we have no competing interests. Funding. We acknowledge financial support from the Swiss National Science foundation (T.C.T.M.), the Netherlands Organization for Scientific Research (NWO-FOM) within the program ‘Barriers in the Brain: the Molecular Physics of Learning and Memory’ (no. FOM-E1012M, R.K. and C.S.), the Schiff Foundation and
Keywords
- Elasticity
- Localization
- Pattern formation
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Supplementary material from "Geometric localization in supported elastic struts"
Michaels, T. C. T. (Contributor), Kusters, R. (Contributor), Dear, A. J. (Contributor), Storm, C. (Contributor), Weaver, J. C. (Contributor) & Mahadevan, L. (Contributor), The Royal Society, 19 Sept 2019
DOI: 10.6084/m9.figshare.c.4643474, https://rs.figshare.com/collections/Supplementary_material_from_Geometric_localization_in_supported_elastic_struts_/4643474 and 2 more links, https://rs.figshare.com/collections/Supplementary_material_from_Geometric_localization_in_supported_elastic_struts_/4643474/1, https://rs.figshare.com/collections/Supplementary_material_from_Geometric_localization_in_supported_elastic_struts_/4643474/2 (show fewer)
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