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Predict failure index, strength ratio, and failure envelope of 3D orthogonal woven plate

by Xin Liu

Problem Description

In this example, failure index, strength ratio, and failure envelope of a 3D orthogonal woven plate are predicted using MSG failure functions. For computing failure index and strength ratio, an external load can be defined. Since we are using MSG plate model, the load is in terms of plate stress resultants such as {N11, N22, 2N12, M11, M22, 2M12}. Therefore, the corresponding strength constants are also in terms of plate stress resultants. For the failure envelope analysis, a biaxial loading case is assumed with N11:N22 = 1:1.

Solution Procedure

* step 1 The SG of an 3D orthogonal woven plate is first created as shown in the figure below, which is created using the 3D weave function in texgen4sc with the default parameters.

* step 2 Once the SG is created, we need to perform homogenization analysis using mesoscale function just as in the previous example. Note that this example is using MSG plate model as shown in the figure below.
The results will pop up. Note that the results are plate stiffness/compliance matrix as shown here.

* step 3 Once the homogenization analysis is finished. We can perform the failure analysis by using the initial failure analysis as shown in the figure below. The load is assumed that N11=1 N/mm, N22=1 N/mm and other components are 0. The matrix failure criterion is Mises and the yarn failure criterion is Tsai-Wu.
The results are the failure index (first column) and strength ratio (second column) as shown below:

* step 4 Next, we want to perform a failure envelope analysis in terms of N11 and N22. The parameters are defined in the following:
The results are given as:

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