Computational homogenisation of periodic cellular materials: Application to structural modelling

• Relevance of homogenisation approaches for the modelling of cellular structures.
• Influence of the architecture on the anisotropy and shape of yield surfaces.
• Identification of homogeneous equivalent laws to decrease computational costs.
• Study of boundary layer and core size effects on the mechanical behaviour.

The present paper aims at investigating the homogenisation of cellular materials in view of the modelling of large but finite cellular structures. Indeed, computation costs associated with the complete modelling of such structures can be rapidly prohibitive if industrial applications are considered. The use of a homogeneous equivalent medium (HEM) for these cellular materials can be an efficient approach to address this issue, but it requires the calibration of relevant homogeneous equivalent laws (HELs). Here, the considered cellular materials are tube stackings. Various uni-axial and multi-axial loading cases have been simulated, through the finite element method, on representative volume elements of such periodic stackings. From these simulations, anisotropic compressible elasto-plastic constitutive equations have been identified for the HEL. The anisotropy of the yield surfaces is discussed depending on the pattern of the tube stacking (e.g. square or hexagonal). A validation of the identified laws is proposed by simulating uni-axial compression and simple shear tests on sandwich structures made of tube stackings for their cores. A systematic comparison, between the results obtained from the fully meshed structures and those obtained from the structures whose core has been replaced with its HEM, allows us to address the limitations of the HEM-based approach and the boundary layer effects observed on finite structures.