Computational homogenization of regular cellular material according to classical elasticity

• A two-scale computational homogenization method is presented.
• Relationship between the micromechanical and continuum model is essential.
• Representative Volume Element (RVE) suffices for a regular structure.
• A set of kinematic and kinetic conditions needs to be satisfied.
• Effective elastic parameters do not depend on the RVE type used.

A two-scale computational homogenization method for deriving the effective elastic parameters of regular cell material is presented. In the present application, particle model is used as the micromechanical model and classical linear elasticity as the continuum model. The method is designed to render the same effective elastic parameters irrespective of the Representative Volume Element (RVE) used for a cell structure. This requires simultaneous fulfillment of the kinematic and kinetic conditions of computational homogenization derived in the study. Also, the relationship between the quantities of the micromechanical and continuum model needs to be invertible on a RVE. Effective elastic parameter expressions for eight planar cellular materials obtained with a typical cell as the RVE are compared to their counterparts in literature. As an application example, a new closed-form compliance expression covering e.g. the square, regular hexagon, rhombus, over-expanded hexagon, and re-entrant hexagon cell structures of literature is presented.