### Tech Briefs Modeling Delamination Conditions

A common type of damage in composite structures is delamination. Modeling delamination conditions is very important in finite element simulations since delamination can cause a significant reduction of the stiffness and strength of a composite structure which may ultimately lead to loss of structural integrity.

In ADINA v. 8.9, cohesive elements are available for such simulations. The cohesive elements are composed of top and bottom surfaces with initially zero thickness. They connect two solid elements as shown in Figure 1. (a) 4-node 2D cohesive element (b) 8-node 3D cohesive element

Figure 1  4-node and 8-node cohesive elements

A cohesive element uses a bilinear constitutive law that relates the traction, , to the relative displacement, , in the element local coordinates as shown in Figure 2. Initially linear elastic behavior followed by the initiation and evolution of damage is assumed. After the initiation of damage, the cohesive element can still transfer load in its softening envelope. Unloading subsequent to damage initiation is always assumed to occur linearly toward the origin as shown in Figure 2. Reloading subsequent to unloading also occurs along the same linear path until the softening envelope is reached. Once the softening envelope is reached, further reloading follows this envelope as indicated by the arrow in Figure 2. Figure 2  Constitutive law under pure mode delamination

For pure mode I, II or III loading, after the interfacial normal or shear tractions reach their respective tensile or shear strengths, the stiffnesses are gradually reduced to zero. Of course, mixed mode conditions can occur.

Figure 3 shows the analysis of a mixed mode bending (MMB) test which is usually used for the characterization of Mode I and Mode II delamination interaction. The schematic MMB test specimen is shown in Figure 3(a). The results from the ADINA simulation are in good agreement with the analytical solutions. However, large differences exist for the portion with large deflections. This is because the analytical solution does not take into account the geometrical nonlinearity while the numerical simulation does. (a) Schematic of MMB test (b) Movie showing the delamination process (c) Comparison of numerical and analytical results

Figure 3  Mixed mode delamination analysis

Figure 4 illustrates the analysis of a mixed mode multidelamination in a layered composite specimen (see Figure 4(a)). The model is based on the work described in the reference. As shown in Figure 4(b), the numerical result gives a good response prediction compared to the experimental data, except in the final stage where many cohesive elements lose strength in a very short time. The movie at the top shows the multidelamination process. (a) Schematic of multidelamination analysis (b) Comparison of numerical result and experimental data

Figure 4  Mixed mode delamination analysis

Considering composite structural analyses, the cohesive elements represent a powerful modeling tool in ADINA for simulation of delamination conditions.

Reference

• Alfano, G., and Crisfield, M. A. , "Finite Element Interface Models for the Delamination Analysis of Laminated Composites: Mechanical and Computational Issues," International Journal for Numerical Methods in Engineering, 50:1701-1736, 2001

Keywords:
Composite structures, damage, fracture, delamination, cohesive element, finite element method