Time-independent harmonics dispersion relation for time-evolving nonlinear waves.

We present a theory for the dispersion of generated harmonics in a traveling nonlinear wave. The harmonics dispersion relation (HDR), derived by the theory, provides direct and exact prediction of the collective harmonics spectrum in the frequency–wave number domain and does so without prior knowledge of the = (, ) solution. It is valid throughout the evolution of a distorting unbalanced wave or the steady-steady propagation of a balanced wave with waveform invariance.

Soft Adaptive Mechanical Metamaterials.

Soft materials are inherently flexible and make suitable candidates for soft robots intended for specific tasks that would otherwise not be achievable (e.g., smart grips capable of picking up objects without prior knowledge of their stiffness).

Guided transition waves in multistable mechanical metamaterials.

Transition fronts, moving through solids and fluids in the form of propagating domain or phase boundaries, have recently been mimicked at the structural level in bistable architectures. What has been limited to simple one-dimensional (1D) examples is here cast into a blueprint for higher dimensions, demonstrated through 2D experiments and described by a continuum mechanical model that draws inspiration from phase transition theory in crystalline solids. Unlike materials, the presented structural analogs admit precise control of the transition wave's direction, shape, and velocity through spatially tailoring the underlying periodic network architecture (locally varying the shape or stiffness of the fundamental building blocks, and exploiting interactions of transition fronts with lattice defects such as point defects and free surfaces).