Numerical predictions of effective shear modulus and size effect for periodic cellular materials

Based on the classical cylinder torsion model, a simple and efficient method is proposed in this paper to predict the effective shear modulus and the size effect of periodic cellular materials. As representative examples, square-hole and circle-hole unit cells are used to clarify the problem and computing. Analytical expressions are established to determine the geometrical parameters of the cell in terms of the cell size factor n. Following conclusions can be drawn out from numeral results. The effective shear moduli of the two types of unit cells decrease as the scale factor n increases; when n → ∞, i.e., the size of the unit cell is small enough with respect to the size of the whole structure, the effective shear modulus tends to be a constant value. The increase of the material volume fraction of the unit cell will result in an increase of the effective shear modulus of the cellular material. Meanwhile, the unit cell substructure concept is proposed to predict the effective shear modulus and the size effect of the periodic cellular material based on its characteristic of structural symmetry. This modeling can greatly increase the computing efficiency.