Physics

Metric (unit)

Mathematics

Mechanics

Optics

Statistical physics

Engineering

Liquid crystal

Gaussian

Composite material

Gaussian curvature

Compression (physics)

Materials science

Curvature

Operations management

Geometry

Computer science

Quantum mechanics

Anisotropy

Classical mechanics

Annual Review of Condensed Matter Physics

Liquid crystal elastomers and glasses suffer huge length changes on heating, illumination, exposure to humidity, etc. A challenge is to program these changes to give a complex mechanical response for micromachines and soft robotics. Also desirable can be strong response, where bend is avoided in favor of stretch and compression, even in the slender shells that are our subject. A new mechanics paradigm arises from such materials—spatially programmed anisotropy allows a spatially varying metric to develop upon stimulation, with evolving Gaussian curvature, topography changes, and superstrong actuation. We call this metric mechanics or topographical mechanics. Thus programmed, liquid crystalline solids meet the above aims. A frontier is the complete programming and control of topography, driving both Gaussian and mean curvature evolution. That, and smart shells, which sense and self-regulate, and exotic new realizations of anisotropic responsive structures, are our concluding themes.

Topographic Mechanics and Applications of Liquid Crystalline Solids