Corrugated beams mechanical behavior modeling by the homogenization method

The exact solutions of problems about bending of the corrugated beam are found and illustrated as an application to undulated yarns. The analysis of the solutions reveals the peculiarities of the projections of forces, moment and displacements on the axis equidistant to the tops of the crimp. These peculiarities permit to apply the asymptotic homogenization method to predict the mechanical properties of the corrugated beams. For this purpose the equilibrium equations and constitutive relations are derived in terms of projections. The effective elastic coefficients for bending and tension are obtained. The crimp profile providing the highest tensile stiffness of the beam is evaluated.