Effect of a curved fiber on the overall material stiffness

•The effect of fiber curvature on the overall material stiffness is studied.•The stiffness contribution tensor (N-tensor) formalism is used for the analysis.•N-tensors of individual fibers are calculated numerically and estimated analytically.•Proposed approximation procedure gives good predictions for all N-tensor components.•Replacement relations are tested for the considered fiber geometries. The effect of fiber curvature on the overall material stiffness of fiber-reinforced composites is discussed using the formalism of stiffness contribution tensor for the special case of a continuous sinusoidal fiber. Stiffness contribution tensors of individual sinusoidal fibers with different crimp ratios are presented for the first time. The tensors are calculated numerically using Finite Element Analysis and analytically by representing fibers as equivalent sets of ellipsoids following the procedure available in the literature for approximation of effective composite stiffness. It is demonstrated that the existing procedure results in large approximation errors in several components of the stiffness contribution tensors of the considered fibers. A modification to the procedure is proposed to improve the accuracy of the predictions. Replacement relations that interrelate stiffness contribution tensors of inhomogeneities having the same shape but different material properties are tested for the studied fiber geometries.