SCALE EFFECTS IN MEDIA WITH PERIODIC AND NEARLY PERIODIC MICROSTRUCTURES, PART II - FAILURE MECHANISMS

Using the nonlinearly elastic planar lattice model presented in Part I , the influence of scale (i.e., the size of the representative volume, relative to the size of the unit cell) on the onset of failure in per iodic and nearly periodic media is investigated. For this study, the c oncept of a microfailure surface is introduced-this surface being defi ned as the locus of first instability points found along radial load p aths through macroscopic strain space. The influence of specimen size and microstructural imperfections (both geometric and constitutive) on these failure surfaces is investigated. The microfailure surface dete rmined for the infinite model with perfectly periodic microstructure, is found to be a lower bound for the failure surfaces of perfectly per iodic, finite models, and an upper bound for the failure surfaces of f inite models with microstructural imperfections. The concept of a macr ofailure surface is also introduced-this surface being defined as the locus of points corresponding to the loss of ellipticity in the macros copic (homogenized) moduli of the model. The macrofailure surface is e asier to construct than the microfailure surface, because it only requ ires calculation of the macroscopic properties for the unit cell, at e ach loading state along the principal equilibrium path. The relation b etween these two failure surfaces is explored in detail, with attentio n focused on their regions of coincidence, which are of particular int erest due to the possible development of macroscopically localized fai lure modes.