A global/local third-order Hermitian displacement field with damaged interfaces and transverse extensibility: analytical formulation

A third-order Hermitian zig-zag plate theory is presented as development of the classical cubic zig-zag displacement field. In addition to the capabilities of the previous model ((i) transverse shear flexibility, (ii) through-the-thickness continuity of the transverse shear stresses, (iii) traction-free condition on the two external surfaces of the laminate and (iv) possibility to study damaged interfaces), the Hermitian model offers some interesting improvements ((i) through-the-thickness linear varying transverse displacement, (ii) evaluation of the normal transverse deformability in general and of the corresponding normal stress in particular, (iii) traction equilibrium condition on the external surfaces and (iv) use of the displacements and transverse shear stresses of the external surfaces as degrees of freedom of the plate model). By means of the virtual work principle of the three-dimensional linear elasticity theory, the two-dimensional equations of motion and boundary conditions are obtained. Some numerical results are finally presented to show the particular nature of the through-the-thickness Hermitian shape functions and to test the model performances in evaluating the transverse normal stress.