Tensegrity structures are prestressable truss structures, obtained by connecting compressive members (bars or struts) through pre-stretched tensile elements (cables or strings). The interest in such structures has been motivated by nature: Tensegrity concepts are ubiquitous and can be found, in every cell, from the microstructure of spider silk to the arrangement of bones and tendons, to name but a few examples. This course is aimed at illustrating the peculiar mechanical behavior of tensegrity systems in the large displacement regime and their application for the development of mechanical metamaterials, space structures, and mechanical models of biological systems.
The course will cover the following thematic blocks:
1. Basic concepts and calculation methods of tensegrity systems: tensegrity principles (classification and case studies), linear theory (force density method, self-stress), stiffness and stability (geometric stiffness, the stress matrix, prestress stability and superstability), form-finding problems and methods, static response, bistable regimes, basic concepts of tensegrity dynamics, tensegrity space structures (case study of a tensegrity ring for a deployable mesh reflector).
2. Tensegrity metamaterials and tensegrity-based mechanical systems: tensegrity metamaterials (basic concepts and casuistry), bandgap response (dispersion relation of tensegrity mass-spring chains, role of prestress), wave dynamics of stiffening-type tensegrity metamaterials (propagation of solitary compression waves), softening-type tensegrity metamaterials (propagation of rarefaction solitary waves), origami tensegrities (deployability, collapsibility and stiffness), seismic protection devices (displacement capacity, superelastic response, energy dissipation properties).
3. Tensegrity structures for space applications and 3D tensegrity metamaterials: post-buckling response of tensegrity planetary landers, 3D tensegrity metamaterials (unique properties in the post-buckling regime), reduced-order models for the dynamic and post-buckling behavior of tensegrity structures, computational implementation (modelling bars and cables, solution techniques for statics and dynamics), advanced Machine Learning (ML) methods for tensegrity.
4. Extremal mechanical properties of tensegrity metamaterials and structures: basic concepts of extremal mechanical properties of materials and structures, tensegrity meta-systems (discrete and continuum models), scale effects (identification of extremal mechanical properties of tensegrity systems in structural scales), 2D and 3D tensegrity modules and lattices with extremal properties.
5. Biotensegrities: overview of biotensegrities (tensegrities mimicking biology systems), biotensegrities mimicking the anatomy and physiology of living organisms, form-finding in the linear regime of self-equilibrated biotensegrities, mathematical modelling of the shape change of biotensegrities (initial, deformed, shape change, and target state), computational approaches and numerical examples.
6. Nonlinear biomechanical character of tensegrity: nonlinear biotensegrities (the role of structure in evolution, triangulation and trusses, non-linearity), soft matter mechanics in living organisms, the fascia connection (ubiquitous of the fascial connections, kinematic chains), muscles mechanics (internal vs external forces), biotensegrity dynamics (instability vs superstability, energy source and storage), mechanics of walking and running in a biotensegrity model. The course is addressed to doctoral students, young researchers, practicing engineers, medical doctors, and architects, interested in tensegrity systems.

This work was supported in part by the Italian Ministry of Foreign Affairs and International Cooperation, grant no. US23GR15.