Hot pressing simulation of thermoplastic foams


Within the scope of aerospace research project SOPHIA (Smart Processes and Optimised Designs for High Production Cadences), the behavior and skin formation of open-cell thermoplastic foams in a hot pressing process have been investigated. Skin formation is obtained by thermoplastic deformation of the foam to form a dense skin within the near-surface structure. Final skin and total thicknesses of the foam should be predicted by process simulation in order to subsequently be able to determine the mechanical properties of the finished sandwich structure with analytical calculations.

Material characterization

Varying loads as well as heating and cooling in the hot pressing process make it necessary to be able to describe the compaction stresses of the thermoplastic foam as a function of both, strain and temperature. Available material models for foams in commercial FE software tools can reproduce the complex compaction behavior, but do not allow a temperature-dependent description of the elastic and plastic deformation. The aim in this project is to develop a material model that can describe the temperature-dependent deformation of the foam surface layer and the compaction of the foam core. For this purpose, several thermoplastic foam materials were used, and their behavior was analyzed using isothermal compaction tests. Materials such as the polymer (polyetherimide PEI and polyethersulfone PESU) with different foam densities (40, 50 and 110 kg/m³)were investigated and compared depending on the compaction speed (1 and 10 mm/min) and temperature (23 to 245°C). The determined stress-strain curves were then reproduced via simulations in order to obtain calibrated material parameters for the hot pressing simulation.


For an accurate simulation of the hot pressing process, not only the material model is of great importance, but also the choice of the modelling method. Due to the foam's skin formation during the process, strong local deformations occur, which have to be accommodated by the modelling method. Therefore, a comparison of different modelling methods using solid, shell and SPH methods (Smooth Particle Hydrodynamics) in LS-DYNA® was conducted. Modelling with shell elements proved to be the most appropriate (see Figure 1).

To set up the simulation in LS-DYNA®, hexahedral solid elements are first generated in a desired component or specimen geometry. Shell elements are then created from the surfaces of the solid elements resulting in six elements forming a hollow, cube-shaped cellular mesh structure. The thickness of the shell elements is chosen depending on the material density, so that the mass of the FE model corresponds to the real foam mass. Since the FE model‘s resolution is not on a microscopic level, the thickness of the shell elements does not correspond to the wall thickness of the foam pores, but differs by several orders of magnitude depending on the discretisation.

The material parameters are calibrated for each measured temperature from isothermal compaction tests in a fitting process using the LS-OPT® optimisation software. In this process, relevant parameters such as compressive modulus and yield stress are passed on to LS-OPT and optimized with a polynomial metamodel in such a way that the mean squared error between the simulated and experimental stress-strain curve is minimized. 

The real foam behavior is ultimately described by the combination of the discretisation and the calibrated material parameters. In non-isothermal simulations, the compaction behavior of thermoplastic foams in the hot pressing process can be calculated with the calibrated FE model. (Figure 2).


A shell element based modelling approach has proven to be an appropriate method to simulate the hot compaction behavior of thermoplastic foams, especially with respect to the large amount of plastic deformation that occurs. By using a temperature-dependent material model, it is possible to simulate the non-isothermal hot pressing process. With the findings from simulations, the mechanical properties of the sandwich structure produced during the hot pressing process can ultimately be predicted.

The project "SOPHIA - Smart Processes and Optimized Designs for High Manufacturing Cadences" is funded by the Federal Ministry for Economic Affairs and Energy (BMWi), based on a decision of the German Bundestag (under the Aeronautics Research Program V-3, funding reference 20X1715D).

Further informationen:

Dipl.-Ing. Stefano Cassola
Scientific Staff Process Simulation
Leibniz-Institut für Verbundwerkstoffe GmbH
Erwin-Schrödinger-Straße 58
67663 Kaiserslautern
Phone: +49 631 2017-268

Figure 1: Comparison of the modelling method for a circular foam specimen in isothermal compaction tests with shell, solid and SPH elements including results at 210°C, 217°C, 225°C and 235°

Figure 2: Foam model in the non-isothermal hot pressing process with depicted temperature distribution.

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