Assessment and correction of theories for multilayered plates with imperfect interfaces

The response of multilayered plates with imperfectly bonded interfaces and delaminations to quasi static and dynamic loadings is conveniently studied by assuming the displacements as two length-scales fields, given by global displacements, which are continuous in the thickness, and local perturbations or enrichments, which account for the multilayered structure and the jumps at the interfaces. The a priori imposition of interfacial continuity conditions then leads to a homogenized field defined by the global variables only. The number of displacement unknowns is independent of the number of layers and is equal to five or six, for sliding or mixed mode interfaces, respectively. Dynamic equilibrium equations are derived using variational principles. This effective idea, which was originally proposed in the zigzag theories for fully bonded plates, was first applied to plates with imperfect interfaces by Cheng et al. (J Appl Mech, 63:1019–1026, 1996), Schmidt and Librescu (Nova J Math Game Theory Algebra, 5:131–147, 1996), and Di Sciuva (AIAA J, 35(11):1753–1759, 1997). These pioneering models, as all subsequent models which extend the theories to various problems, suffer from a common omission in the treatment of the interfacial energy in the derivation of the equilibrium equations, which leads to solutions which are accurate only for fully bonded/debonded plates. In this paper a linear, first order model which resolves the inaccuracy and extends the theories to more general interfacial traction laws is presented along with the corrected formulations of the original models. The formulations are validated using exact 2D elasticity solutions for multilayered plates in cylindrical bending.