Anomalous strain energy transformation pathways in mechanical metamaterials.

This discussion starts with a mechanics version of Parseval's energy theorem applicable to any discrete lattice material with periodic internal structure: a microtruss, grid, frame, origami or tessellation. It provides a simple relationship between the strain energy volumetric/usual and distributions in the reciprocal space. The spectral energy distribution leads directly to a spectral entropy of lattice deformation (Shannon's type), whose variance with a material coordinate represents the decrease of information about surface loads in the material interior.

Reprogramming Static Deformation Patterns in Mechanical Metamaterials.

This paper discusses an x-braced metamaterial lattice with the unusual property of exhibiting bandgaps in their deformation decay spectrum, and, hence, the capacity for reprogramming deformation patterns. The design of polarizing non-local lattice arising from the scenario of repeated zero eigenvalues of a system transfer matrix is also introduced. We develop a single mode fundamental solution for lattices with multiple degrees of freedom per node in the form of static Raleigh waves.

Negative extensibility metamaterials: Occurrence and design-space topology.

A negative extensibility material structure pulls back and contracts when the external tensile load reaches a certain critical level. In this paper, we reveal basic mathematical features of the nonlinear strain energy function responsible for this unusual mechanical property. A systematic discussion leads to a comprehensive phase diagram in terms of design parameters for a simple unit cell structure that provides a panoramic view of all possible nonlinear mechanical behaviors.