Metastructures based on graded tube inversion for arbitrarily prescribable force-displacement relationships

The force-displacement relationship is a fundamental mechanical property of materials, and the ability to inversely customize a prespecified relationship is useful for complex energy absorption systems, substrates of wearable electronics, and programmable vibration control. The recent development of mechanical metamaterials introduces graded strength into porous frameworks, which, however, can only achieve designable strain-hardening behavior. This is because the soft layers always deform prior to the hard layers due to the minimum energy gradient principle, regardless of the spatial arrangement of the component strength. Inspired by the “Domino effect” of tube inversion where its deformation sequence is governed by its kinematic compatibility, this paper introduces graded strength into a progressive and sequential tube inversion process, and correspondingly achieves arbitrarily prescribable force-displacement curves. Parametric study, numerical simulations for 9 different target curves, theoretical modeling leading to an inverse design framework, and experiments are carried out. This strategy paves the way for the inverse design of materials with arbitrary nonlinear mechanical responses essential for various novel applications.