Finite-Size Accuracy and Engineering Applicability of Equivalent Continuum Models for BCC Lattice Structures

Abstract

Equivalent continuum models provide an efficient alternative to explicitly resolving the internal architecture of lattice structures, but their accuracy in finite components depends strongly on structural scale, boundary effects, constitutive behavior, and numerical discretization. This study quantitatively evaluates the finite-size accuracy and engineering applicability of a first-order equivalent continuum model for body-centered cubic (BCC) lattice structures. A periodic representative unit cell is first used to determine the effective elastic stiffness of a BCC lattice with a unit-cell size of 5 mm, a strut radius of 0.3 mm, and a relative density of 6.99%. The resulting stiffness matrix exhibits the expected cubic symmetry and pronounced directional anisotropy, while the maximum component-wise difference between the 0.050 and 0.025 mm RVE meshes is only 0.0584%. Explicit lattice structures and corresponding homogeneous continua containing N = 1–5 cells along each direction are then compared under lateral loading and quasi-static compression. The lateral displacement deviation decreases overall from 18.69% at N = 1 to 10.84% at N = 5. Under consistent linear-elastic compression, the reaction-force deviation decreases monotonically from 74.52% to 22.62%, confirming that substantial finite-size and boundary-related effects remain even after constitutive inconsistency is removed. Comparison with elastoplastic simulations further shows that plastic softening can partially mask the underlying lattice–continuum discrepancy. The explicit solid-element modeling strategy is independently verified against a published 7 × 7 × 7 BCC compression experiment, predicting an effective modulus of 0.565 GPa compared with the reported 0.54 GPa, a difference of approximately 4.6%. A dedicated macro-mesh study further demonstrates that the homogeneous model can be substantially coarsened while retaining accurate global response. These results provide practical guidance for selecting between explicit and equivalent-continuum representations according to structural scale, response quantity, constitutive regime, and required engineering accuracy.