This module makes possible to calculate the edge effect on the stresses and displacement fields, and more importantly, the effect on the interlaminar stresses in a symmetric elastic laminate (q₁,...,q_n)_S. In this way, the software may help to predict delamination.

The classical laminates theories are not able to evaluate the edge effects. DEILAM calculations are based on the plates model M4-5N (Multiparticular model for Multi-layered Material with 5 kinematic fields per layer for a multi-layered material with N layers). Because of its constitution, this model is richer and more accurate than the classical laminates models. The construction of model M4-5N and its validation may be found in [1,2] . A first version of DEILAM has been already published and validated in [3] ; this first version made possible to evaluate the effects of a free edge on the interfacial stresses. In MAC LAM, the DEILAM version is modified so as to being able to consider any boundary condition at the edges. As we have already said in [1,2,3] , the evaluated interfacial stresses for DEILAM converge quickly and there are no singularities.

For the users interested in the underlying theory behind DEILAM calculations, we recommend to read the papers [1,2,3] or the theoretical outline.
We consider the symmetrical laminate (q₁,...,q_n)_S. The laminate may be subjected to:

• an uniform axial strain e in the x-direction (see Figure 1)
• displacements or stresses independent of x at the edges y = 0 and y = b (see Figure 1). These edge conditions verify the symmetry with respect to plane z = 0. The lower and upper skins of the multi-layered material are stress free.
• a temperature variation DT
• a variation in the moisture rate DH

Figure 1. Symmetrical multi-layer and simplification of the problem.

Owing to symmetries, the problem is reduced to the resolution of the problem in the red section in Figure 1. The application of model M4-5N only gives equations in y. These equations are solved with the finite elements method and a meshing of the interval [0, b] . The results of DEILAM are stresses and generalized displacements of the model calculated on the nodes of the mesh.

The following table gives the DEILAM input/output data.

• First you have to define the multi-layered material
• then you have to choose the Calculation and report options
• afterwards the loads have to be defined
• then we carry out the calculations by clicking on the button <<Analyze>> of the main window (see Figure 2).

Figure 2. Launching the DEILAM calculations.

• Now the screen in Figure 3 appears. In order to select the fields you want to plot as a function of the position y along the width, you have to click on the button <<Plot>> of Figure 3. Then the window in Figure 4 appears. In this window you have to (see Figure 4)
  • First select the kinds of fields to be plotted
  • Choose the fields
  • Type in the numbers of layers or interfaces for which the fields will be plotted (the format is the same as the one used for printing the pages of a document, e.g. 1,3-7,9). When you deal with shear forces, moments or displacements in the layers, the numbers of layers may vary from 1 to n (the symmetrical multi-layered material (q₁,...,q_n)_S has a total of 2n layers). When dealing with interfacial stresses, owing to symmetries, the shear stresses on the interface n are zero (central interface). Thus, for shear stresses, the interface numbers may vary from 0 to n-1. On the contrary, for interlaminar normal stresses s_xx (also noted as n in the theory of model M4-5N) the layers numbers may vary from 0 to n because these stresses may be non zero in the central interface.
  • Click on the button <<Plot>> (see Figure 4).

Figure 3. Where to click to select the fields to be plotted?

Figure 4. How to select the fields you want to plot?

• Next you will see your selected plot. For changing its color or line type, click on the button <<Chart properties>> in the window <<DEILAM results>> (see Figure 5). For visualizing the values of the selected fields on each node, click on the button <<See values>>.

Figure 5. Colors, line types and nodal values.

• If you want to create a graphical report that you may print, click on the button <<Create a graphical report>> of Figure 6. This report will also contain the data selected in the Options menu in the main window of MAC LAM. Finally, if you want to save the results in a file (for plotting them with Excel or another software) click on the button <<Save values>> (see Figure 6).
  

Figure 6. Creating a graphical report and saving the values in a file.

Calculation and report options

Before you launch the calculations in DEILAM, you have to define the Calculation and report options by clicking on "Options" in the menu bar in the main window (see Figure 7).

Figure 7. Where to click in order to define the DEILAM Calculation and report options?

Now, you will see the window in Figure 8. There you have to select the Calculation and report options. Among the options you will find

• To take or not into account hygrothermal loads
• Calculation and visualization of all of the generalized fields or only the interfacial stresses (in this case calculations are faster)
• Calculation and visualization of all of the residual hygrothermal fields

Figure 8. Calculation and report options in DEILAM.

Important remarks

References

[1] CARREIRA RP, CARON JF, DIAZ DIAZ A. "Model of multi-layered materials for interface stresses estimation and validation by finite element calculations", Mechanics of Materials, 34, 217-230, 2002.

[2] DIAZ DIAZ A., CARON JF, CARREIRA RP. "Un modèle de stratifiés". Comptes Rendus de l'Académie des Sciences, 329, 873-879 (2001).

[3] DIAZ DIAZ A., CARON JF, CARREIRA RP, "Software application for evaluating interfacial stresses in inelastic symmetrical laminates with free edges", Journal of Composite Structures, 58, 195-208, 2002