Instabilities and dynamics of elastic rods in the presence of movable constraints

A new trend in the mechanical design of devices for advanced technologies, such as soft robotics and micro/nano mechanics, is the exploitation of structures undergoing large deflections, in an attempt of achieving superior performances. Within this framework, non-linear modelling becomes a fundamental tool for the design of compliant structures and deformable mechanism. Two structural systems are investigated, both based on the planar elastica and subject to movable and configurational constraints. These two structures disclose unforeseen behaviours when the values of the parameters defining the models are varied. The first structural system is an elastic rod constrained by a slowly rotating clamp, while the other end is loaded with a lumped mass weight. When this weight is lower than that corresponding to buckling, the edge of the rod describes a closed curve, behaving as an elastica compass. Differently, when the load is higher than that of buckling, a release of elastic energy is observed, leading to a snapback of the structure, so that the rod realizes an elastica catapult. The clamp in the above described structure is replaced by a frictionless and fixed sliding sleeve in the second system considered in this thesis. The rod is subject to a sudden release from the underformed configuration, providing dynamic effects on the system. By means of the variational approach, the presence of a configurational force at the exit of the sliding sleeve is proven within the dynamical setting, extending previous results restricted to the quasi-static assumption. The configurational force is found to strongly affect the dynamics of the structure. In particular, two different behaviours are observed, in which the rod may either completely penetrate in ("injection") or be expelled from ("ejection") the sliding sleeve. In both the above problems, the theoretical predictions are corroborated through the experimental validation on physical models, which have been ad hoc invented and designed. A new insight is obtained in the design of flexible devices, paving the way to applications in soft robotics.