Analysis and design of bistable and thermally reversible metamaterials inspired by shape-memory alloys

In this work, we study lattice structures that exhibit a bistable behavior, i. e., they can snap from one stable state to another, and are also completely reversible, capable of reverting back to its original state through a heat treatment. We design this behavior by constructing lattice structures using networks of nonlinear springs that display tension-compression asymmetry and have different thermal expansion coefficients. The mismatch in the thermal expansion coefficients induces residual stresses in the springs which results in the lattice structure exhibiting bistability at low temperatures and monostability at high temperatures. This behavior mimics the crystallographic phase transformations of shape memory alloys, but here artificially introduced in a structural lattice. By analyzing a representative unit cell, we quantify the effect that the stiffness and the thermal expansion coefficient of the springs have on the stability of the structural lattice. In addition, for simple 2D lattices, using the concept of universal unfoldings of singularity theory, we perform a perturbation analysis to identify the key variables of the structure where controlling defects is important, as they lead to drastic changes in the bifurcation behavior of the lattice. Finally, we verify numerically our analytical predictions in both 2D and 3D simulations using continuation techniques. The examples proposed confirm that the bistable and reversible features of the unit cell carry on to the macroscale, opening the route for the design of lattice structures for energy absorption applications that can hea} with a heat treatment.