A computational framework for homogenization and multiscale stability analyses of nonlinear periodic materials

This article presents a consistent computational framework for multiscale first-order finite strain homogenization and stability analyses of rate-independent solids with periodic microstructures. The formulation is built on priori discretized microstructure, algorithms computing the matrix representations homogenized stresses tangent moduli are consistently derived. results lose their validity at onset first bifurcation, which can be computed from analysis. instabilities include: (a) microscale structural instability calculated by Bloch wave analysis; (b) macroscale material rank-1 convexity checks moduli. Implementation details analysis provided, including selection vector space retrieval real-valued buckling mode complex-valued wave. Three methods detailed solving resulted constrained eigenvalue problem—two condensation null-space projection method. Both verified using numerical examples hyperelastic elastoplastic materials. Various phenomena demonstrated. Aligned theoretical results, show that microscopic long wavelength equivalently detected loss