Finite Element Analysis Overview
We use finite element analysis (FEA) in Abaqus/Explicit to simulate the double diaphragm forming (DDF) process, from vacuum draw-in through to the deep draw. The aim is to predict where and how wrinkles form in woven fabric, so that defect-reduction strategies can be tested virtually before they are tried on the double diaphragm forming rig. The models mirror the mechanical tests, so numerical and experimental results can be compared directly.
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​The silicone diaphragms are modelled as hyperelastic shells using a six-term Ogden material model for 1mm thick General Purpose 40 Shore A hardness silicone rubber. The woven glass fabric is modelled with a mutually constrained truss-and-membrane approach, either with a simple hyperelastic membrane or with a user-defined material subroutine (VUMAT) that captures the fabric's non-linear shear behaviour. The punch, die and blank holders are rigid bodies, and contact friction values are taken largely from published characterisation work, with some assumptions. Models were built for both the no-tension and optimal pre-tension blank holders.
No-Tension Blank Holder Model
Optimal Pre-Tension Blank Holder Model
The optimal pre-tension blank holder provides 50% pre-strain to the diaphragms when the vacuum draw-in step is complete. The no-tension blank holder provides negligible pre-strain on the diaphragms. The 50% diaphragm pre-strain significantly reduces the formation of wrinkles during the deep draw. Both simulations here are using 1 ply of fabric in the model. There are 4 steps: gravity, vacuum draw-in, tooling, and forming.
What we've found so far
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Diaphragm behaviour is validated. The simulated strain in the optimal pre-tension blank holder at the end of the vacuum draw-in is about 50%, matching the design target, and about 2% for the no-tension holder, matching theory.
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Wrinkle location and frequency are predicted well. For single-ply and three-ply lay-ups, the models reproduce the number of wrinkles and where they form, and shear angle peaks where the wrinkles appear.
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Wrinkle height is the main gap. Heights are under-predicted for the no-tension holder, but the optimal pre-tension 1 ply model matched the experiment closely (about 0.8 mm vs 0.6 mm).
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Forming force is over-predicted. This is largely down to friction assumptions. Lowering the tool-diaphragm friction brought the 3 ply result to within 3% of the experiment.
Current limitations and next steps. Several simulations abort before reaching full depth because of excessive element distortion in the upper diaphragm at wrinkle sites. Ongoing work focuses on refining friction coefficients and the diaphragm and fabric models so multi-ply lay-ups can complete the full draw, and on understanding what makes the draw-in itself stable.
Diaphragm Model Vacuum Draw-in
As you can see in the images below, the diaphragms are drawn in by the 1 bar of pressure, and meet in the centre of the blank holder cavity when the vacuum draw-in is complete. The graph below shows both the circumferential and radial strains reach approximately 50% engineering strain when the diaphragms meet and flatten horizontally in the centre of the blank holder cavity, matching the experiments and theory.
Simulation vs Experiment
Wrinkles are quantified the same way for experiments and simulations, so the two can be compared directly. Deformed diaphragms were 3D scanned with a handheld scanner (experiments) or exported from Abaqus as a mesh (simulations), then opened in CloudCompare, an open-source point-cloud tool. The model is aligned so the punch is vertical and the diaphragm lies flat. A radial-distance scalar field from the punch centre is then used to isolate a thin 4 mm ring just outside the punch flange, where most wrinkles form. The out-of-plane height of the points on this ring is exported and plotted against angle around the ring in MATLAB. This gives the wrinkle height, number and position. Simulation data is smoothed with a median and a mean filter to remove numerical noise before comparison.
No-tension 3 ply comparison (a) numerical model, (b) experimental 3D scan
Optimal pre-tension 1 ply comparison (a) numerical model, (b) experimental 3D scan
Fabric Model
The VUMAT fabric model tracks the in-plane shear angle between the warp and weft yarns as the fabric is drawn. The videos below show the shear angle developing in two single-ply simulations, one with the no-tension blank holder and one with the optimal pre-tension blank holder. In both, the shear angle is largest along the four diagonals, and these are the same regions where the wrinkles form. The shear angle peaks at roughly 7–8° in magnitude, with opposite signs on the two diagonal pairs. This shows the model captures the trellis shearing of the fabric and can identify where wrinkles will form, even though it does not yet predict their height accurately.
Shear angle during deep draw, no-tension blank holder, 1 ply (VUMAT fabric model)
