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

Based on the classical cylinder torsion model, a simpleand efficient method is proposed in this paper to predict the effectiveshear modulus and the size effect of periodic cellular materials. Asrepresentative examples, square-hole and circle-hole unit cells are used toclarify the problem and computing. Analytical expressions are established todetermine the geometrical parameters of the cell in terms of the cell sizefactor n. Following conclusions can be drawn out from numeral results. Theeffective shear moduli of the two types of unit cells decrease as the scalefactor n increases; when n \to \infty , i.e., the size of the unit cell issmall enough with respect to the size of the whole structure, the effectiveshear modulus tends to be a constant value. The increase of the materialvolume fraction of the unit cell will result in an increase of the effectiveshear modulus of the cellular material. Meanwhile, the unit cellsubstructure concept is proposed to predict the effective shear modulus andthe size effect of the periodic cellular material based on itscharacteristic of structural symmetry. This modeling can greatly increasethe computing efficiency.