Theoretical And Numerical Study On Delamination Of Laminated Composites Based On Nonlocal Theory

It has been widely accepted that fiber reinforced polymer composites offer advantages of high specific stiffness, high specific strength, designability and versatility. More and more fiber reinforced polymer composites are applied in the field of astronautics and aeronautics. The consumption of laminated composites is one of the largest. The single layers stack laminate by different angle and there is weak shear strength in interlaminate. Consequently, delamination is one of the important problems. The stiffness and strength of the damage laminate will decrease, which affects the mechanical property of laminated composites. As a result, it is necessary to conduct in-depth research.In order to investigate the delamination of laminated composites, the general theoretical model describing the delamination process is established based on cohesive law. The mechanical property after delamination is predicted using the damage constitutive model and the onset and propagation for delamination is judged by quadratic criterion and B-K criterion. The delamination process is simulated by setting interface element corresponding to cohesive model at potential location of delamination. The simulated and experimental results are well coincided. However, the simulated result is related to the size of mesh.The delamination belongs to the problem of strain softening. The solution of governing equations is ill-posed from the analytic standpoint and the simulated result is dependent on mesh size when the strain softening is analyzed based on classical continuum damage mechanics.Aiming at the problem of ill-posedness, the nonlocal damage constitutive model, which is based on the regularization method of gradient enhanced nonlocal theory, is established by introducing gradient coefficient (or characteristic length) to remedy the classic damage constitutive equation. The strain softening of one-dimensional structure is analyzed based on the nonlocal damage constitutive model. The problem of ill-posedness is solved and the steady localization width is obtained.In the interest of overcoming the mesh-dependence of simulating strain softening, the nonlocal damage finite element model (FEM) is derived according to the weighted residual method and with the aid of divergence theorem and boundary condition. Aiming at the Laplacian of the field function, the C1 continuous Hermitian shape function is used for interpolation of the field function. The C0 and C1 hybrid element is established and the degrees are displacement, nonlocal equivalent strain and nonlocal equivalent strain gradient. Redevelopment is conducted to solve equations in terms of nonstandard degrees of freedom. The strain softening of two-dimensional structure is simulated based on the nonlocal damage FEM. The simulated result shows that the mesh-dependence is overcome and the result is verified by experiment.For the sake of overcoming the mesh-dependence of simulating delamination based on the cohesive model, the definition of nonlocal equivalent interface displacement is introduced. The nonlocal cohesive model is established by combining the cohesive model with the nonlocal damage model. The analytic solution is difficult to obtain because of the Laplacian of the nonlocal equivalent interface displacement in the model. Consequently, the nonlocal cohesive FEM is derived through virtual work principle and Newton's Third Law. The nonlocal interface element is established based on the interface element and the hybrid element. The delamination process is simulated by setting the nonlocal interface element which is evaluated by the formula of element size at potential location of delamination. The result shows that reduces the mesh-dependence, saves time and assures the accuracy and the correctness.In this paper, the study of theory and numerical simulation on delamination of laminated composites based on nonlocal theory, expands the application of nonlocal theory and reveals the mechanics of the onset and propagation for delamination. The study provides theoretical basis for structure design of laminated composites.