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Using a geometric formalism of elasticity theory we develop a systematictheoretical method for controlling and manipulating the mechanical response ofslender solids to external loads. We formally express global mechanicalproperties associated with non-euclidean thin sheets, and interpret theexpressions as inverse problem for designing desired mechanical properties. Weshow that by wisely designing geometric frustration, extreme mechanicalproperties can be encoded into a material using accessible experimentaltechniques. To test the methodology we derive a family of geometries thatresult with anomalous mechanical behavior such as tunable, an-harmonic, andeven vanishing rigidities. The presented formalism can be discretized and thusopens a new pathway for the design of both continuum and discrete solids andstructures.

Geometric approach to mechanical design principles in continuous elastic sheets