Active and robotic materials: from self-amplified waves to self-sustained deformations*

Active materials denote materials in which local active forces generate work. They correspond to many biological systems in which local chemical reactions trigger cyclic or feedback-based self-deformations. The recent development of robotics now enables the integration of such paradigm in artificial materials, which offers new ways for materials to interact with their environment. So far, in many of these systems, it remains difficult to predict which mechanical properties emerge from the presence of local active forces. Here, we use structured model experiments combining passive elasticity and local active forces to develop models predicting the mechanical properties of such active materials and demonstrate how the interplay between dissipation, restoring forces and active forces controls their dynamics. For small amplitudes of active forces, these active materials are characterized by new elastic moduli and wave phenomena, such as spatially asymmetric standing waves at all frequencies. For larger amplitudes of the active forces, waves are self-amplified, which destabilizes the material. Yet, for the right balance of each force in presence, active materials can stabilize in a state of self-deformation emerging from nonlinear self-sustained work cycles. We harness these inherently nonlinear cycles to power and control processes such as impact control and locomotion. Beyond distributed robotics, our work suggests how these nonlinear work cycles and associated functionalities can emerge as solutions of the non-conservative dynamics of active and biological materials.