On the mechanical modeling of the extreme softening/stiffening response of axially loaded tensegrity prisms

• We model the axial response of tensegrity prisms under large displacements.
• Thick prisms exhibit elastic softening in compression under low prestrains.
• Slender prisms need high prestress to show elastic softening in compression.
• Prisms featuring ordinary aspect ratios and rigid bases exhibit stiffening response.
• Experimental tests provide evidence of the versatile response of tensegrity prisms.

We study the geometrically nonlinear behavior of uniformly compressed tensegrity prisms through fully elastic and rigid-elastic models. The given models predict a variety of mechanical behaviors in the regime of large displacements, including an extreme stiffening-type response, already known in the literature, and a newly discovered, extreme softening behavior. The latter may lead to a snap buckling event producing an axial collapse of the structure. The switching from one mechanical regime to another depends on the aspect ratio of the structure, the magnitude of the applied prestress, and the material properties of the constituent elements. We discuss potential mechanical and acoustic applications of such behaviors, which are related to the design and manufacture of tensegrity lattices and innovative metamaterials.

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