Davide Bigoni’s KEYNOTE seminar “Flutter instability, homogenization, and hypoelastic materials without a strain potential”

Davide_Bigoni_Jan_13_2021.pdf (pdf 155 kB)

Abstract. Flutter, divergence instabilities, and Hopf bifurcations may occur in elastic structures subject to nonconservative loads such as follower forces and forces acting on a fixed line. This was theoretically shown by [10, 1, 9], among many others (see the review [8]). However, the practical realization of these nonconservative forces was considered for sixty years very difficult and often declared impossible. In this talk we will show theoretically and experimentally how to obtain follower forces of the Ziegler type and related instabilities by exploiting Coulomb friction, a result which sheds light on the interplay between friction and instability [5]. The destabilizing effect of dissipation will be given an experimental proof [4]. We will introduce forces acting on a fixed line and explain how these can be realized to demonstrate instabilities [3]. It will be shown that flutter and divergence instabilities (including Hopf bifurcation and destabilizing effects connected to dissipation phenomena) can be obtained in structural systems loaded by conservative forces, as a consequence of the application of non-holonomic constraints. The motion of the structure produced by these dynamic instabilities may reach a limit cycle,a feature that can be exploited for soft robotics applications, especially for the realization of limbless locomotion [2]. Finally, it is shown as the previous results can be used to demonstrate, via a rigorous application of homogenization theory [7], how to design a hypoelastic material violating the concept of strain potential [6].

[1] Beck, Z. Angew. Math. Phys. 3, 225 (1952).
[2] Cazzolli, et al. J. Mech. Phys. Solids 138, 103919 (2020).
[3] Bigoni, et al. J. Mech. Phys. Solids, 134, 103741 (2020).
[4] Bigoni et al. J. Mech. Phys. Solids 116, 99 (2018)
[5] Bigoni et al. J. Mech. Phys. Solids 59, 2208-2226 (2011).
[6] Bordiga, et al. J. Mech. Phys. Solids, 158 (2022).
[7] Bordiga, et al. J. Mech. Phys. Solids 146, 104198 (2021).
[8] Elishakoff, et al.. Appl. Mech. Rev. 58, 117 (2005).
[9] Reut, Proc. Odessa Inst. of Civil and Comm. Eng. 1 (1939).
[10] Ziegler, Adv. Appl. Mech. 4, 351–403 (1956).