Complas 2025

COMPLAS 2025

Computational Homogenization of Shell-based Cellular Materials towards Microphysics-informed Continuum

Liu, Lei (Chalmers University of Technology)
Liu, Fang (Chalmers University of Technology)
Zenkert, Dan (KTH Royal Institute of Technology)
Åkermo, Malin (KTH Royal Institute of Technology)
van Maris, Marc (Eindhoven University of Technology)
Hoefnagels, Johan (Eindhoven University of Technology)
Fagerström, Martin (Chalmers University of Technology)

In session: 1501A - Multi-scale and computational scale bridging I

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Cellular materials, e.g. irregular foams and regular lattice structures, are being widely utilized in engineering applications due to their appealing specific mechanical properties with respect to low density. Extensive studies reveal that the mechanical behavior of cellular materials largely depends on their relative density and cell shape anisotropy, which can evolve upon loading. To efficiently incorporate these mesostructural evolution processes in the modeling of cellular materials, especially those characterized by an interconnected network of thin shells, a novel computational homogenization framework is developed in this work. The macroscopic component follows a solid continuum description, with the effective relative density and cell shape anisotropy introduced as the internal variables. At the mesoscale, a representative volume element (RVE) resolving individual cells is modeled, with the cell walls described as Reissner-Mindlin shells in a finite rotation setting. Following the classical homogenization scheme, imposing the macroscopic deformation gradient yields the microscopic RVE boundary conditions, which are consistent with the shell kinematics. The effective relative density and cell shape anisotropy are defined from the deformed RVE model configuration. The effective stress conjugated to the deformation gradient is defined by applying the Hill-Mandel condition. For a given RVE, relating these effective quantities leads to an effective continuum model which captures the relevant mesostructural evolution processes. This microphysics-informed continuum model, which could not be envisioned a-priori, is fully identified from a set of RVE simulations, thus enabling the efficient modeling of cellular materials at the macroscale. The developed effective continuum model is validated against direct numerical simulations (DNS) of an array of Kelvin cell lattice structures. The model predictive capability is demonstrated on a large plate made from Divinycell foam H100.