Formula omitted] plate element based on strain energy updating and spline interpolation, for analysis of impact damage in laminated composites

Abstract

A computational model for investigating the local extent and the through-the-thickness position of the damage induced by low velocity impacts on laminated composites is presented, which is based on a refined 3D zig-zag approach. It fulfills the interlaminar transverse shear and normal stress contact conditions at the layer interfaces, those on the transverse normal stress gradient and the boundary conditions at the upper and lower bounding faces, as required by the theory of elasticity. Its functional d.o.f. are the three components of the elastic displacement and the two shear rotations, like in widespread smeared laminate models. Several classical models are particularized from it and confronted together to assess whether a sophisticated structural model can have practical advantages for the study of impacts, since this is a still open question. In order to improve the structural modelling with an affordable computational effort, the contributions by present model are incorporated updating the strain energy of a C 0 parent eight-node plate element based on the First Order Shear Peformation Plate theory and through a post-processing procedure based on spline interpolation of the involved quantities. The impact load is computed by the Hertz's contact law, integrating the equilibrium equations by the Newmark's algorithm. The Galerkin's method is used to obtain these equations, instead of using the finite element discretization, because accurate results are obtained at lower costs. Fibers, matrix and delamination failures are predicted using two different strength-based criteria for each single mode. Since their predictions can differ not slightly, a comparison gives an estimation of the variation range and helps to choose the one appropriate for the failure mode. According to the ply-discount theory, the degradation of properties after failure is simulated reducing the elastic properties of the failed plies, in conformity with the failure mode occurred. Different models with a different representation of displacements and interlaminar stresses are shown to provide quite different results in terms of displacements, contact force and damage. The application to a laminated stiffened panel shows the discrete-layer effects to play an important role for the simulation of impacts, even when the laminates are not thick, since high-order dynamic effects are involved. Present structural model, the contact force simulation and the failure criteria chosen appear able to simulate the impact induced damage extent and position across the thickness with a satisfactory accuracy, as shown by the comparison with ultrasonic detections.