A shear-lag model for laminated beams with extreme modulus mismatch between layers

Multilayer laminated beams, comprised of alternating stiff and soft layers, are widely used in flexible electronics and photonics. These structures exhibit complex mechanical behaviors that deviate from the Euler-Bernoulli beam theory under conditions of extreme inter-layer modulus mismatch. Extending beyond prior studies on trilayer beams, we present an analytical framework for laminated beams with arbitrary number of layers subjected to various bending conditions, and validate our theory with finite element analysis. We define an equivalent flexural rigidity, exploring its dependence on position and deformation, and systematically examine the impact of the number of layers, applied deformation, layer properties, and the layer aspect ratio.