Anti-Hertz bulging of actuated liquid crystal elastomers

We consider the ‘anti-Hertz’ elastic problem of inverse indentation, which happens when the surface of an elastic material is pressed down with a plate with a round hole to form a bulge. This classical problem takes on a new life when a polydomain nematic liquid crystal elastomer is used. In this case, the nematic director aligns with the leading principal direction of local stress distribution created by bulging. When the deformed material is crosslinked a second time, this alignment pattern and the resulting permanent protrusion are preserved as pressure is removed, creating a bulge that can be reversibly actuated from a flat surface upon cooling. Experimentally, we also observe a dimple ring around the bulge and a punt (indentation) underneath it at the bottom. Theoretically, we model the deformation by coupling linear elastic and anelastic deformations using non-monotonic nematic elasticity and the singular stress-order relation of the polydomain-monodomain transition. The theory is in excellent agreement with the experiments, and predicts the emergence of all observed features.