Homogenization of origami-based truss lattices

Abstract

An origami-based truss lattice inherits the deployability of the corresponding origami with the effective stiffness depending on the stiffness of bars, folded configuration and internal prestress. This paper presents a singular-continuum, namely, singum, homogenization framework that treats the Wigner–Seitz cell of each lattice node as a continuum particle and maps the forces and displacements at bar-cutting points to work-conjugate singum stress and strain. We provide closed-form effective stiffness of a three-dimensional origami-based truss lattice by the variation of the truss lattice configuration. Using a multi-layer Miura-ori-based lattice as an example, we show that the model captures both the deployable zero-energy mode and finite stiffness against constrained deformation modes. The effective stiffness depends on folding angle and stretch ratio of bars, and exhibits anisotropic and asymmetric features in prestressed configurations. The analytical formulation is verified by the representative volume element (RVE)-based finite-element simulations constructed from the same truss lattice under displacement-controlled perturbations on the boundary. This paper establishes a systemic approach from an origami-based truss lattice to a homogenized continuum with an effective stiffness in the current configuration.