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Critically elastic materials - those that are rigid with a single state ofself-stress - can be generated from parent systems with two states ofself-stress by the removal of one of many constraints. We show that the elasticmoduli of the resulting homogeneous and isotropic daughter systems areinterrelated by a universal functional form parametrized by properties of theparent. In simulations of both spring networks and packings of soft spheres,judicious choice of parent systems and bond removal allows for the selection ofa wide variety of moduli and Poisson's ratios in the critically elasticsystems, providing a framework for versatile deterministic selection ofmechanical properties.

Deterministic Interrelation Between Elastic Moduli in Critically Elastic Materials