Apparent elastic and elastoplastic behavior of periodic composites

We investigate scale and boundary conditions effects on the elastic and elastoplastic behavior of periodic fiber-reinforced composites. Four boundary conditions, including displacement controlled, traction controlled, mixed (normal displacements and zero shear tractions specified on each boundary) and periodic boundary conditions, are considered. Influence of several factors - such as the window size, the mismatch between component phases' properties, and the types of boundary conditions - on the apparent mechanical response (elastic and elastoplastic) is studied. It is shown that the apparent properties obtained under our mixed and periodic conditions are the same within numerical accuracy, and they are bounded by those obtained using displacement and traction controlled boundary conditions. From our study of elastic case, it is found that the bounds are very sensitive to the mismatch of phase moduli: the higher the mismatch, the wider are the bounds. In the study of elastoplastic case, monotonically increasing proportional loading is applied to different sized windows under each of the above four boundary conditions. An explanation of response curves can be reached through the observation of shear bands, under these various boundary conditions.