Animating metamaterials with non-reciprocity

Complex material responses can be achieved by engineering the interactions between a material’s internal components and the geometry that organizes them. Yet even the most sophisticated designed materials remain limited compared to the adaptive, far-from-equilibrium behavior observed in living systems. This thesis explores how materials can be endowed with dynamical and autonomous behavior by embedding non-reciprocal interactions—forces that violate action-reaction symmetry—directly into their structure.
This thesis explores the interplay between non-reciprocity and nonlinearity in active elastic metamaterials, which leads to emergent behaviors such as unidirectional soliton propagation, self-spontaneous locomotion, and cyclical shape changes. These effects arise not from external programming or centralized control, but from structured internal asymmetries and feedback.
First, we uncover new classes of driven-dissipative solitons, including both topological and breathing solitons. Then, we focus on limit cycle dynamics in odd elastic metamaterials that generate robotic functionalities such as locomotion. We demonstrate how their vibrational spectra exhibit active phonon gaps which depend on the material's geometry. Finally, we uncover wave coarsening, a synchronization mechanism for waves mediated by the momentum-conserving nature of non-reciprocal and non-pairwise interactions.
Taken together, this thesis offers a framework for designing active solids—materials that respond actively to deformations, mimicking certain aspects of biological autonomy such as locomotion and shape changing. This points toward a new generation of active matter that blurs the line between material and machine, capable of movement, adaptation, and decision-making.