Effective mechanical response of biomimetic staggered composites: Closed-form estimates via a micromechanical variational formulation

Bio-inspired composite materials with staggered microstructures exhibit superior mechanical properties compared to traditional composites, paving the way for the development of advanced functional materials. The existing analytical models mainly address the macroscale constitutive response along the staggering direction using plane strain or plane stress assumptions. Consequently, a significant gap remains in the characterization of the equivalent material response in triaxial loading scenarios. This study presents a micromechanical variational formulation to derive an analytical and comprehensive characterization of the anisotropic homogenized behavior of biomimetic staggered composites. The microscale equilibrium problem, tailored to a suitable representative volume element, is tackled by applying stationary conditions to the total potential energy functional, evaluated over a class of quasi-compatible strain fields that capture the dominant microscale kinematics. A linearization technique leads to closed-form expressions that fully characterize the macroscale stiffness tensor of the material. Through a parametric case study, the obtained analytical results are compared with finite element simulations and theoretical solutions and bounds. The results confirm the validity of the proposed formulation, demonstrating the consistency and accuracy of the obtained analytical estimates.