Multilayer models for composite and sandwich structures

Multilayer structures often present a challenge for equivalent single layer theories which are based on single displacement approximation through the thickness. This chapter first discusses the need for a different approach and then discusses two types of discrete layer approaches: layerwise theories and zigzag theories. In layerwise theories, separate displacement fields are assumed in each layer and displacement continuity conditions are enforced at each interface. This results in a number of variables to be determined that increases with the number of plies and discontinuities in the transverse normal and shear stresses at the interfaces. Zigzag theories reduce the number of variables by enforcing continuity of the transverse stresses and by discribing the kinematics of the deformation in terms of both global and ply-level variables. This results in a fixed number of unknowns regardless of the number of layers in the laminate. Both layerwise and zigzag theories treat each layer the same which can be a problem when there is a sharp contrast between plies in terms of material properties and/or thicknesses. This is the case for sandwich structures and, as a result, many theories have been developed with different assumptions for the facings and the core. The last section presents a comprehensive view of existing theoriess for analyzing sandwich structures.