Geometry and physics in the deformations of crystalline caps.

Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic regimes. Based on the revealed quasi-conformal ordering, we discover the partial but uniform screening of the substrate curvature by the induced curvature underlying the inhomogeneous lattice. This scenario is fundamentally different from the conventional screening mechanism based on topological defects. In the plastic regime, the yield of highly stressed caps leads to fractures with featured morphologies not found in planar systems. We also demonstrate the strategy of engineering stress and fractures by vacancies. These results advance our general understanding of the organization and adaptivity of the geometrically frustrated crystalline order.