Elastica Catastrophe Machine and Configurational Forces in Dynamics

Seminar | February 4 | 4-5 p.m. | 3110 Etcheverry Hall

 Associate Professor Francesco Dal Corso, Department of Civil, Environmental and Mechanical Engineering; University of Trento, Italy

 Department of Mechanical Engineering (ME)

Abstract: Nonlinear structural mechanics breaks the limits of traditional linear elastic design, to create elements working much beyond the realm of linearized kinematics, fully inside the nonlinear range, so matching the strong requirements imposed by soft robotics, flexible locomotion devices, metastructures, architected structures for vibration mitigation, and morphable structures. Within this context, the following recent results are presented:

- The number of stable equilibrium configurations is disclosed for a planar stip with varying the kinematics conditions at its ends [1]. This result leads to the definition of a ‘universal snap surface’, collecting the sets of critical boundary conditions for which the system snaps;

- A catastrophe machine based on a continuous flexible element has been designed and realized [2]. In contrast to the classical Zeeman’s machine, the catastrophe locus of the elastica catastrophe machine may display a number of bifurcation points different than four and the convexity measure may significantly vary;

- The sudden release of a rod partially inserted into a frictionless sliding sleeve is shown to be strongly affected by the action of configurational forces [3]. During its motion, the elastic rod dances by alternatively slipping in and out from the sliding sleeve. The nonlinear dynamics eventually ends with the rod completely injected into or completely ejected from the constraint.

The presented structural systems are modelled as nonlinear elastic structures and solved analytically. Physical models have been designed, realized and tested, confirming the theoretical predictions. These results represent innovative concepts ready to be used for enhancing the efficiency of snapping devices and retractable/extensible soft actuators towards advanced technological applications.

[1] Cazzolli, A., Dal Corso, F. (2019). Snapping of elastic strips with controlled ends. International Journal of Solids and Structures, 162, 285-303. doi: http://dx.doi.org/10.1016/j.ijsolstr.2018.12.005

[2] Cazzolli, A., Misseroni, D., Dal Corso, F. (2020). Elastica catastrophe machine: theory, design and experiments. Journal of the Mechanics and Physics of Solids, in press. doi: https://doi.org/10.1016/j.jmps.2019.103735

[3] Armanini, C., Dal Corso, F., Misseroni, D., Bigoni, D. (2019). Configurational forces and nonlinear structural dynamics. Journal of the Mechanics and Physics of Solids, 130, 82-100. doi: https://doi.org/10.1016/j.jmps.2019.05.009

Biography: After earning a PhD in Materials and Structural Engineering at the University of Trento, Italy, Francesco Dal Corso had a postdoctoral fellowship at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. Dal Corso is currently an Associate Professor of Solid and Structural Mechanics in the Department of Civil, Environmental and Mechanical Engineering at the University of Trento, Italy.

Dal Corso’s research activity is devoted to the mechanical behaviour of Solid and Structures. In particular, he dealt with problems related to the localization of deformation, plasticity, large deformations, homogenization, higher-order continua, stress concentrations and singularities, contact mechanics, configurational mechanics and stability. He has co-authored more than 40 journal papers and has co-guest edited a Special Issue of the Journal of the Mechanics and Physics of Solids in 2020.

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