Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures

Recently, novel and uniform deformation-induced pattern transformations have been found in periodic elastomeric cellular solids upon reaching a critical value of applied load Mullin, T., Deschanel, S., Bertoldi, K., Boyce, M.C., 2007. Pattern transformation triggered by deformation. Phys. Rev. Lett. 99, 084301; Boyce, M.C., Prange, S.M., Bertoldi, K., Deschanel, S., Mullin, T., 2008. Mechanics of periodic elastomeric structures. In: Boukamel, Laiarinandrasana, Meo, Verron (Eds.), Constitutive Models for Rubber, vol. V. Taylor & Francis Group, London, pp. 3–7]. Here, the mechanics of the deformation behavior of several periodically patterned two-dimensional elastomeric sheets are investigated experimentally and through numerical simulation. Square and oblique lattices of circular voids and rectangular lattices of elliptical voids are studied. The numerical results clearly show the mechanism of the pattern switch for each microstructure to be a form of local elastic instability, giving reversible and repeatable transformation events as confirmed by experiments. Post-deformation transformation is observed to accentuate the new pattern and is found to be elastic and to occur at nearly constant stress, resulting in a superelastic behavior. The deformation-induced transformations have been physically realized on structures constructed at the millimeter length scale. This behavior should also persist at the micro and nano length scales, providing opportunities for transformative photonic and phononic crystals which can switch in a controlled manner and also exploiting the phenomenon to imprint complex patterns.