## Inducing curved metrics in materials gives new mechanics

Radically novel materials, liquid crystalline elastomers and glasses, change shape by 100 per cent following changes in temperature or illumination. Shape change, that is elongation along a particular direction, rather than simply change of volume, can be imaginatively arranged induce intrinsic curvature in initially flat spaces. The intimate connection between differential geometry and mechanics comes into play and suggests ways of exploiting light-induced curvature of space for new mechanics paradigms.

I will give, with many demonstrations, examples of the geometry arising. These solids can apparently solve the map-maker’s problem of resolving planes with curved space. I will say how this unique property might be exploited in strong actuation.

Deformations can be large. Hence in-plane, in-material trajectories, along with integral curves of the director field, are substantially advected and distorted with the change. Calculating these distortions of in-material lengths will specify the evolving topography - both forward from a given director field, and inversely giving the director field required to obtain a desired shape.