On the Geometrically Nonlinear Elastic Response of Class θ = 1 Tensegrity Prisms

Ida Mascolo,Luciano Feo,Fernando Fraternali,Giulio Zuccaro,Ada Amendola

doi:10.3389/fmats.2018.00016

Ida Mascolo, Luciano Feo + Show 3 more

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https://doi.org/10.3389/fmats.2018.00016

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Abstract

The present work studies the geometrically nonlinear response of class ϑ=1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables) or compression (bars), under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either 'standard' or 'expanded' configurations. An experimental validation of the predicted constitutive response is conducted with reference to a 'thick' and a 'slender' model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.

Highlights

The research area of mechanical metamaterials has recently paid considerable attention to structures alternating lumped masses and tensegrity units, which feature unconventional behaviors mainly derived from the geometry and the nonlinear response of the units in the large displacement regime (Skelton and de Oliveira, 2010; Fraternali et al, 2012, 2014, 2015a; Micheletti, 2012; Amendola et al, 2014; Davini et al, 2016; Carpentieri and Skelton, 2017; Cimmino et al, 2017; De Tommasi et al, 2017; Fraddosio et al, 2017; Magliozzi et al, 2017; Rimoli and Pal, 2017; Rimoli, 2018)
The elastic response of several tensegrity units can be strongly nonlinear, like, e.g., in the case of bistable systems (Micheletti, 2012), tensegrity prisms (Amendola et al, 2014; Fraternali et al, 2015a), and three-dimensional lattices endowed with truncated octahedron cells (Rimoli and Pal, 2017; Rimoli, 2018), just to name a few examples
In particular, that the elastic response of tensegrity prisms may progressively switch from stiffening to softening, through the tuning of mechanical, geometrical, and prestress variables (Amendola et al, 2014; Fraternali et al, 2014, 2015a)

Summary

Introduction

The research area of mechanical metamaterials has recently paid considerable attention to structures alternating lumped masses and tensegrity units, which feature unconventional behaviors mainly derived from the geometry and the nonlinear response of the units in the large displacement regime (Skelton and de Oliveira, 2010; Fraternali et al, 2012, 2014, 2015a; Micheletti, 2012; Amendola et al, 2014; Davini et al, 2016; Carpentieri and Skelton, 2017; Cimmino et al, 2017; De Tommasi et al, 2017; Fraddosio et al, 2017; Magliozzi et al, 2017; Rimoli and Pal, 2017; Rimoli, 2018). The elastic response of several tensegrity units can be strongly nonlinear, like, e.g., in the case of bistable systems (Micheletti, 2012), tensegrity prisms (Amendola et al, 2014; Fraternali et al, 2015a), and three-dimensional lattices endowed with truncated octahedron cells (Rimoli and Pal, 2017; Rimoli, 2018), just to name a few examples It has been shown, in particular, that the elastic response of tensegrity prisms may progressively switch from stiffening to softening, through the tuning of mechanical, geometrical, and prestress variables (Amendola et al, 2014; Fraternali et al, 2014, 2015a). Other innovative uses of lattice metamaterials can be found in Amendola et al (2017), Colombi et al (2017), Feo et al (2017), Genoese et al (2017), Jiang et al (2017), La Salandra et al (2017), Naddeo et al (2017a,b), Tallarico et al (2017), Yin et al (2017), Miniaci et al (2018), and references therein

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