We study planar elastic responses of fiber-matrix composite materials and cellular materials. In the case of composites, the fibers are of circular cylinder shape, aligned in the axial direction, and arranged either periodically or randomly, with no overlap, in the transverse plane. We focus on the effects of scale of observation and boundary conditions on the overall elastic moduli of such composites. We conduct this analysis numerically at the mesoscale level by considering finite "windows of observation." We subject these regions to several different boundary conditions: displacement-controlled, traction-controlled, periodic, and mixed to evaluate the mesoscale moduli. We cover a range of stiffness ratios from composites with very soft inclusions (approximating holes) to those with very stiff inclusions (approaching rigid fibers). This investigation provides insight on the size of the Representative Volume Element for such composites. Extensions of these concepts to micropolar elasticity (prediction of couple stress moduli) are also briefly discussed.
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