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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Bespoke extensional elasticity through helical lattice systems.

Maximillian D X Dixon1, Matthew P O'Donnell1, Alberto Pirrera1

  • 1Bristol Composites Institute (ACCIS), Department of Aerospace Engineering, University of Bristol, Bristol BS8 1TR, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
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Summary
This summary is machine-generated.

Designing with nonlinear structural behavior is challenging. This study presents a tunable system of helical lattices that systematically creates desired nonlinear responses, approximating any continuous function for robust engineering applications.

Keywords:
anisotropybespoke stiffnesslatticemetamaterialsmulti-stabilitynonlinear spring

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Area of Science:

  • Engineering and Materials Science
  • Applied Mathematics
  • Computational Mechanics

Background:

  • Traditional linear design paradigms limit the exploration of complex structural behaviors.
  • Designing reliable nonlinear systems is difficult due to challenges in intuitive behavior description.
  • Nonlinear structural mechanics offers advanced functionalities not achievable with linear models.

Purpose of the Study:

  • To develop a systematic and understandable approach for designing bespoke nonlinear structural responses.
  • To construct a tunable, effectively one-dimensional system capable of approximating continuous energy functions.
  • To overcome the intuitive description challenges in nonlinear system design.

Main Methods:

  • Construction of a system using parallel helical lattices acting as one-dimensional nonlinear springs.
  • Development of an algorithm to tune lattice geometry, stiffness, and pre-strain for desired behavior.
  • Utilizing the Weierstrass approximation theorem to demonstrate energy function approximation capabilities.

Main Results:

  • The system's energy can approximate any polynomial, thus any continuous function, within a specified tolerance (epsilon).
  • Demonstrated systematic tuning of lattice parameters to achieve specific nonlinear behaviors.
  • Exhibited complex behaviors including deformation-dependent stiffness, snap-through buckling, and multi-stability.

Conclusions:

  • The proposed helical lattice system provides a systematic and intuitive method for designing complex nonlinear structural behaviors.
  • This approach expands the design space for robust and reliable nonlinear structures.
  • Enables the creation of bespoke material responses for advanced engineering applications.