Stress and displacements in lamellar composites. I

A lamellar composite is approximated by a stack of very long longitudinal strips, of rectangular cross section, of elastic material bonded to rigid strips on their upper and lower faces and extended in a direction perpendicular to these faces. The lateral faces of the strips are assumed stress-free. The stresses and displacements in the cross section are calculated using two-dimensional stress analysis giving solutions in Fourier series. The effective modulus of the material is calculated for a range of thickness/width ratios and compared wth literature values. The analysis has relevance for the deformation of lamellar composites in polymeric and other materials.