Lattice structures as thermoelastic strain gradient metamaterials: Evidence from full-field simulations and applications to functionally step-wise-graded beams

The present work investigates the mechanical and thermomechanical bending response of beam structures possessing a triangular lattice microarchitecture. The validity of generalized continuum models, in general, and the associated dimensionally reduced models for functionally step-wise-graded microarchitectural beams, in particular, is approved by full-field finite element simulations. Most importantly, the necessity of the temperature gradient in the Helmholtz free energy is substantiated. The corresponding strong and weak forms for the associated Bernoulli–Euler and Timoshenko models of functionally graded beams are derived. The effective classical thermoelastic properties of a metamaterial with a triangular lattice microarchitecture are defined by means of computational homogenization. The additional length scale parameter involved in the generalized beam models, and associated to the particular triangular microarchitecture, is calibrated by fitting the mechanical bending responses of a series of lattice beams to the analytical solutions of the corresponding theoretical models. Strongly size-dependent mechanical and size-independent thermal bending responses are observed for both thin and thick beams with triangular lattice microarchitectures. Finally, different lattice beams with varying microarchitectures are introduced and shown to behave as generalized functionally step-wise-graded beams with respect to the higher-order elastic modulus, i.e., the length scale parameter varying in the direction of the beam axis.