Two-node method for the effective elastic properties of periodic cellular truss materials and experiment verification via stereolithography

A two-node method is proposed in this paper to predict the effective elastic properties of periodic cellular truss materials based on the traditional representative volume element (RVE) method. Through the two-node method, the original unit cell with multiple boundary nodes is transformed into a new equivalent unit cell with only two boundary nodes, and the effective elastic properties of the original unit cell can be indirectly obtained by the new equivalent unit cell. The accuracy of the present method is theoretically and numerically validated by using the asymptotic homogenization (AH) method and experimentally validated by the quasi-static uniaxial compression tests of the 3D printed cellular structures. Both theoretical and numerical results show that the present two-node method is more accurate and easier to implement than the traditional RVE method and the AH method when the size of the unit cell is negligible relative to the size of the macrostructure. For periodic cellular truss materials with rod elements, the present method can provide results with the same accuracy as the AH method but with more efficiency. For periodic cellular materials with beam elements, the present method can provide more accurate lower bound of the effective elastic properties than the traditional RVE method. The uniaxial compression tests results show that the elastic modulus of the equivalent structure obtained by the two-node method is almost the same as its original structures and is in good agreement with the calculation results obtained by the AH method.