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原文摘要

Periodic architected materials may be represented by representative volume elements (RVEs) combining continuum, truss, beam, and shell constituents. Their mixed translational and rotational kinematics complicate a consistent scale transition to a macroscale Cauchy continuum. We establish a nonlinear first-order computational homogenization framework for such mixed-dimensional RVEs. An auxiliary finite-strain Cosserat continuum serves solely as a power-equivalent carrier of their virtual power and generalized boundary kinematics. Its uniform rotation is identified with the macroscopic polar rotation and its wryness vanishes, so the effective medium remains of Cauchy type. Under periodic translational and rotational constraints, the Hill-Mandel condition yields a common nodal-force virial for the effective first Piola-Kirchhoff stress, independent of element type. For lower-dimensional members on periodically identified cell boundaries, fractional ownership of internal virtual work is shown to be variationally equivalent to a topology-preserving reduction retaining one representative of each set of periodic element copies. Because this equivalence covers the complete element virtual work and consistent linearization, it applies to geometrically and materially nonlinear and path-dependent constituents without rescaling section properties, constitutive parameters, or internal variables. Numerical examples recover the analytical small-strain response and cubic symmetry of a mixed continuum-shell-beam cell, verify the reduction and discrete power balance, and demonstrate finite-rotation buckling of a hyperelastic Octet lattice and history-dependent yield-surface evolution of an elastoplastic sandwich cell. The open-source implementation abqhom couples the framework to Abaqus.