This paper deals with layered plates and shells subjected to static loading. The kinematic assumptions are extended by a jump function in dependence of a damage parameter. Additionally, an intermediate layer is arranged at any position of the laminate. This allows numerical simulation of onset and growth of delaminations. The equations of the boundary value problem include besides the equilibrium in terms of stress resultants, the local equilibrium in terms of stresses, the geometric field equations, the constitutive equations, and a constraint which enforces the correct shape of a superposed displacement field through the thickness as well as boundary conditions. The weak form of the boundary value problem and the associated finite element formulation for quadrilaterals is derived. The developed shell element possesses the usual 5 or 6 degrees of freedom at the nodes. This is an essential feature since standard geometrical boundary conditions can be applied and the elements are applicable to shell intersection problems. With the developed model, residual load-carrying capacities of layered shells due to delamination failure are computed.
KEYWORDSdamage model, layered plates and shells, progressive delaminations, standard nodal degrees of freedom, thin intermediate layers
INTRODUCTIONDelamination, or interfacial cracking between layers, is one of the most common types of damage in laminated fibre-reinforced composite structures. The reason is the relative weak interlaminar strength. Delamination as result of impact or manufacturing defect can cause a significant reduction of the load-carrying capacity of a structure. In general, the fracture process in high performance composite laminates is quite complex, involving not only delamination but also occurrence of transverse matrix cracking or fibre fracture in the layers. Stress gradients that occur near geometric discontinuities such as ply drop-offs, stiffener terminations, bonded and bolted joints, and access holes promote delamination initiation, trigger intraply damage mechanisms, and may cause a significant loss of structural integrity. Thus, a reliable prediction of different failure modes is essential. The delamination failure mode is particularly important for the structural integrity of composite structures because it is difficult to detect during inspection.The simulation of delamination using the finite element method is performed by means of the virtual crack closure technique, eg, in the works of Rybicki and Kanninen 1 and Krueger, 2 or using cohesive finite elements, eg, in other works. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Another approach is to use continuum damage models within the layers, eg, in the works of Simon et al, [18][19][20] or to introduce thin intermediate layers along with a damage model or an inelastic material model with softening, eg, in the works 132 of Allix and Ladevèze, 21 Wagner et al, 22 and Groh et al. 23 In the works of Remmers et al, 24,25 the kinematics of solid-like shell elements is enhanced to allow for...
