Mechanics Governing Reprogrammable Thermal Expansion in Prestressed Multistable Metamaterials

The coefficient of thermal expansion (CTE) is traditionally regarded as an intrinsic material property governed by chemical composition, crystallographic arrangement, and intermolecular interactions. Here, we demonstrate that thermal expansion in prestressed multistable metamaterials can instead emerge as a reprogrammable, mechanically state-dependent response, with values determined by the instantaneous configuration of the elements within their interior architecture. We investigate a representative class of material architectures composed of prestressed wavy building blocks formed by bimaterial constituents with mismatched elastic moduli and distinct CTEs. At the level of a single unit, bistability arises from buckling-induced bifurcation governed by a symmetric nonlinear potential energy landscape and creates two stable geometric configurations that generate opposite axial length changes under thermal loading, thereby producing configuration-dependent effective CTEs. In stacked assemblies of interconnected units, a geometric gradient breaks configurational degeneracy and enforces a prescribed snapping sequence, thereby controlling the distribution of units among stable states, and in turn the macroscopic effective CTE of the structure. Reduced-order spring analogs elucidate the mechanisms of bistability and sequential snapping. Elastica theory, combined with classical thermal expansion relations, and finite element simulations quantify how prestress, geometry, and material contrast set the effective CTE, and experiments on 2D prototypes support the predicted state-dependent CTEs. This allows a single architecture to be mechanically reprogrammed to exhibit amplified positive, near-zero, or strongly negative thermal expansion without changes in material composition or remanufacturing. Finite element simulations of three-dimensional hierarchical lattices further predict a combinatorial scaling of the number of thermal expansion states, suggesting multidirectional, anisotropic responses with discrete reprogrammability. Together, these results show that reprogrammable thermal expansion emerges as a state-dependent property from mechanical instability and unit-cell topology in prestressed multistable metamaterials.