An efficient approach for multilayered beams and wide plates with imperfect interfaces and delaminations

In multilayered systems with interfacial imperfections, such as imperfect bonding of the layers or delaminations, or where the plies are separated by thin interlayers allowing relative motion, the displacement field is highly discontinuous in the thickness, with a characteristic zig-zag pattern and interfacial jumps. Stresses also have large variations, especially for highly deformable interlayers or fully debonded layers. These effects cannot be captured using classical, first- or higher-order single-layer theories. A mechanical model is formulated for the solution of multilayered beams/wide plates with an arbitrary number of imperfect interfaces/delaminations loaded dynamically. The formulation is in the framework of the discrete-layer approach and the interfaces are described through affine traction laws which relate interfacial tractions and relative displacements. Homogenization and variational techniques define novel equilibrium equations depending on only four generalized displacement functions. Comparison with 2D elasticity solutions shows that complex discontinuous fields in thick, highly-anisotropic plates with an arbitrary number of sliding-interfaces are accurately predicted. The approach extends the range of problems which can be solved analytically compared to discrete-layer models where the unknowns depend on the number of layers/interfaces. The affine traction laws describe arbitrary branches of piecewise linear functions approximating nonlinear traction laws to represent different interfacial mechanisms.