ELASTIC COMPLIANCES AND STIFFNESSES OF THE FCC LENNARD-JONES SOLID

The isothermal elastic compliances, stiffnesses, and bulk moduli of a Lennard-Jones solid organized into an fcc crystal structure (256 atoms in 4(3) unit cells) have been calculated as a function of testing tem perature (expressed as the mean kinetic energy per atom). Tests conduc ted in pure shear were used to determine S44 and C44 = G100, where 100 refers to crystallographic directions. Tests imposing axial elongatio n with fixed lateral dimensions established C-11 and C-12. Axial defor mation with zero lateral pressure (a tension test) was used to determi ne S11, S12, E100 and nu100. This provided an independent set of resul ts for comparison with the dilatational stiffnesses C-11 and C-12. The bulk modulus K was obtained by independent triaxial tension testing. The stiffnesses, compliances, and moduli were determined by regression analysis and digital filtering applied to combinations of the stress- tensor and strain-tensor data stored at each iteration during the cons tant-rate deformation experiments. While the cubic fcc Lennard-Jones s olid expectedly obeys the Cauchy relations for central-force potential s, it is not isotropic, allowing nu to take on values other than 1/4 a s originally proposed by Poisson. The present calculations show nu100 = 0.347 for the fcc Lennard-Jones solid with a Young's modulus of E100 = 61.1epsilon/sigma3, an initial (as indicated by superscript 0) shea r modulus of G(100)0 = 57.2epsilon/sigma3, and an initial bulk modulus of K0 = 71.2epsilon/sigma3 at zero temperature. The moduli all decrea sed with increasing temperature. Reuss, Voigt, and Hashin and Shtrikma n [J. Mech. Phys. Solids 10, 335 (1962)] bounds on the isotropic elast ic properties of polycrystalline aggregates of Lennard-Jones material were also determined. Computed values of the moduli are in reasonable agreement with experimental results for solid argon and crystalline po lyethylene.