A meso-scale site-bond model for elasticity: Theory and calibration

A meso-scale site-bond model is proposed to simulate the macroscopic elastic properties of isotropic materials. The microstructure of solids is represented by an assembly of truncated octahedral cells with sites at the cell centres and bonds linking the nearest neighboring sites. Based on the equivalence of strain energy stored in a unit cell to strain energy stored in a continuum of identical volume, the normal and shear stiffness coefficients of bonds are derived from the given macroscopic elastic constants: Young’s modulus and Poisson’s ratio. To validate the obtained spring constants, benchmark tests including uniaxial tension and plane strain are performed. The simulated macroscopic elastic constants are in excellent agreement with the theoretical values. As a result, the proposed site-bond model can be used to simulate the macroscopic elastic behaviour of solids with Poisson’s ratios in the range from -1 up to 1/2.