A simple design rule for variable thickness shell based architected materials with improved stiffness

Architected materials have emerged as a promising solution for achieving novel mechanical property combinations, offering high stiffness-to-weight ratios, specific strength, and superior energy absorption. The Hashin–Shtrikman upper bound establishes a theoretical limit on the maximum stiffness of 3D multiphase isotropic materials. To reach this bound, the strain energy density must be uniformly distributed throughout the material. A novel strategy is introduced to enhance the structural efficiency of shell-based architected materials by iteratively adjusting thickness to achieve uniform strain energy density. Each shell element’s thickness is modified based on its strain energy deviation to approach the Hashin–Shtrikman bound. Local variations enable precise control over structural behavior, improving mechanical performance. Unlike traditional optimization methods, this deterministic iterative approach avoids gradient-based calculations and stochastic variables. Instead, it uses finite element models and theoretical limits to guide strain energy distribution. Local deviations dictate thickness adjustments, driving stiffness toward the Hashin–Shtrikman bound. This method is applied to four common uniform-thickness hollow cellular materials under hydrostatic strain with periodic boundary conditions. In uniform-thickness lattices, strain energy density is highly non-uniform, but iterative thickness adjustments yield a nearly uniform distribution. Structural efficiency improved significantly, achieving more than a fivefold increase in just 16 iterations. Final designs undergo random perturbations in shell thickness to assess whether the structures reach a local maximum. A comprehensive analysis of thickness variations is conducted to examine localized material concentrations, particularly near lattice nodes. These trends are explored across different strut slenderness ratios and relative densities.