What do Teeth have to do with Super Plastic Forming Process Simulation?

This guest contribution on Innovation Intelligence is written by Renganathan Sekar, M.Sc., researcher at MFRC, the developers of the intelligent metal forming simulation software AFDEX which is available through the Altair Partner Alliance.

Trying to define yourself is like trying to bite your own teeth” – Alan Watts

Inspired literally by the quote, I was trying to bite my teeth at the office. My colleagues were worried about my peculiar behavior and sure, it produced a chuckle amongst them. In fact, the quote was right. Neither could I define myself nor bite my teeth. But the good thing is, I ended up with an idea for writing this article.

Why not use AFDEX [1] for simulating something relevant to my teeth? An hour of searching online landed me on the superplastic forming process of an upper and lower denture.

Super plastic forming is a constant-volume deformation process which usually involves heating a compatible material in the furnace and then blow forming it into the die shape by application of pressure through an inert gas like Argon. The differential pressure applied by the gas provides the stretching force for the material to get deformed. This novel process was initially used by the aerospace industry as it could produce lightweight, structurally sound and geometrically complex parts. Over the past decade, the process has also found its way into the mainstream automotive industry. With the availability of biocompatible alloys and sufficient solver capabilities, it is no surprise that people are using this process in medical applications as well.

It seems people have already tried simulating partial dentures, Ridge Augmentation Membranes (RAM) and implant support structures [2], [3], [4] making my task easier. This might be due to the wide applicability and the pressing need for a precise single-step manufacturing process.

Figure 1. Upper denture, lower denture and assembled model (From left to right) [5]

With an idea and some basic information at my disposal, I searched through open source CAD hubs and luckily found convincing stl files required for the process simulation. The upper and lower dies were designed based on these geometries in such a way that an enclosed space is created where the gas pressure could be applied. The teeth shown in Figure 1 have been excluded from the analysis model for both upper and lower dentures.

Figure 2. Process setup – Lower denture (left) and Pressure versus time graph (right)

As the upper denture model is very similar, it is not presented here. It can be observed from the pressure versus time graph that the cycles closely match with each other and the upper denture requires a higher value of pressure. This is mainly due to the higher depth of penetration for the workpiece to realize full die contact as shown in Figure 3. When the sheet gradually encounters the die, the pressure required to maintain the desired strain rate increases because of the friction.

Figure 3. Die contact – Upper denture

The upper and lower dentures were discretized into 23755 tetrahedral MINI-elements. The maximum pressure value for the upper denture was 11.3 MPa with a corresponding forming time of 7452 s and 8.7 MPa with a forming time of 4833 s for the lower denture. From the perspective of numerical uncertainties, the penetration of the workpiece into the die and vice versa is one of the main factors not favoring the use of solid elements for sheet metal forming applications [6]. This negative phenomenon can be avoided or checked in a simulation by looking at the volume loss. The average volume loss for the simulation models was less than 0.2 %.

Figure 4. Lower denture – Final deformed shape

Figure 4 depicts the final deformed shape of the lower denture. Unlike the high computational time experienced when using the solid hexahedral elements [1] for a nearly equivalent model of the upper denture (21 hours), MINI-elements realized full die contact in approximately 3 hours. The ability to obtain quick and accurate results cannot be overemphasized for medical applications as the dimensions are different in every case and simulation results play a pivotal role in an optimized process.

The simulation results seem to be satisfactory in terms of computational time showing that MINI-elements provide quicker solutions compared to hexahedral elements. But if the maximum forming pressure is compared, MINI-elements seem to be on the higher side. This forming process is hugely dependent on the controlling the strain rate through the application of pressure. And, as the part geometry becomes more complicated, the pressure versus time cycle needs to be very carefully optimized. The simulation can also be optimized for different target strain rates and its effect on the forming time could be investigated in detail.

All these factors as such make the simulation of super plastic forming process complicated demanding a high amount of skill and creativity from the simulation engineer. Ending on a philosophical note, they say “Everything comes from within”. So, it’s time to dig deep within yourself, unleash the creative beast in you and apply it to your simulation.


  1. http://msjoun.gnu.ac.kr/pub/paper/2009/2009-ISMAI-04-AFDEX.pdf
  2. J. Bonet, R.D. Wood, R. Said, R.V. Curtis, “Numerical simulation of the superplastic forming of dental and medical prostheses” Biomechan Model Mechanobiol, vol. 1, pp. 177–196, Jul. 2002.
  3. D. Garriga-Majo, R.J. Paterson, R.V. Curtis, R. Said, R.D. Wood, J. Bonet, “Optimization of the superplastic forming of a dental implant for bone augmentation using finite element simulations” Dental Materials, vol. 20, pp. 409–418, Jul. 2003.
  4. J. Bonet, A. Gil, R.D. Wood, R. Said, R.V. Curtis, “Simulating superplastic forming” Comput. Methods Appl. Mech, Engg, vol. 195, pp. 6580–6603, Mar. 2005.
  5. Digital Removable Partial Dentures Models, LabMagic 3D CAD, 2015 https://grabcad.com/library/digital-removable-partial-dentures-models-1
  6. W. Chung, B. Kim, S W Lee, H. Ryu. M S Joun, “Finite element simulation of plate or sheet metal forming processes using tetrahedral MINI-elements”, Journal of Mechanical Science and Technology, vol. 28, pp. 237-243, 2014
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