Geometric localization in supported elastic struts

T.C.T. Michaels, R. Kusters, A.J. Dear, C. Storm, J.C. Weaver, L. Mahadevan (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

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 languageEnglish
Article number20190370
Number of pages12
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume475
Issue number2229
DOIs
Publication statusPublished - 11 Sep 2019

Fingerprint

struts
Struts
Filament
shear
filaments
Localized Structures
Morphogenesis
Materials Science
Scaling laws
Continuum Limit
Scaling Laws
Materials science
materials science
Conformation
Mechanical Systems
scaling laws
Mechanics
Conformations
Texture
Theoretical Analysis

Keywords

  • Elasticity
  • Localization
  • Pattern formation

Cite this

Michaels, T.C.T. ; Kusters, R. ; Dear, A.J. ; Storm, C. ; Weaver, J.C. ; Mahadevan, L. / Geometric localization in supported elastic struts. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2019 ; Vol. 475, No. 2229.
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Geometric localization in supported elastic struts. / Michaels, T.C.T.; Kusters, R.; Dear, A.J.; Storm, C.; Weaver, J.C.; Mahadevan, L. (Corresponding author).

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, No. 2229, 20190370, 11.09.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Geometric localization in supported elastic struts

AU - Michaels, T.C.T.

AU - Kusters, R.

AU - Dear, A.J.

AU - Storm, C.

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AB - 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.

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