Modelling of Nonlinear, Viscoelastic Material Behaviour for Highly Deformed Polymers towards Accurate Virtual Design in Advanced Electronic Development

This paper presents an overview of the material models of Bergstrom-Boyce (BB) and Three-Network-Model (TN) both of which can describe nonlinear viscoelastic behaviour of thermoset materials (NLVE). To determine the needed model parameters, mechanical measurements with variable force-deformation-time regimes were performed at multiple temperatures on the example of encapsulation compounds consisting of different types of polyurethane. A digital representation of the experiment, based on finite-element-analysis, was created. Subsequently the FE-model was used to determine the required NLVE model parameters. The measurement setup for tensile and compression experiments and the test specimens are presented. Wide range deformation rates between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.01 ~\text{mm} / \min$</tex> to 10 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{mm} / \min$</tex> have been conducted to excite the specimens and their mechanical response. Additionally, the setup has been enhanced to measurements at elevated and subzero temperatures which is essential for a complete material behaviour representation. The material behaviour shown has been measured at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$20^{\circ} \mathrm{C}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$75^{\circ} \mathrm{C}$</tex>. In the second step, the model parameters have been determined and calibrated. This has been done with an inverse method by using the FEM response calculations of the digital experiment and optimize towards the comparison with the experimental data. The individual workflows have been sped up by a factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10 x$</tex> with the model reduction towards a 2D-model. Both selected model approaches could be fit with very good accuracy. The Three-Network model seems to be better suited for temperature dependent data in the future. Overall, the presented numerical optimization procedure has been proven to be efficient and reliable. The proposed NLVE models, data acquisition and coefficient fitting method will bring large strain viscoelastic material behaviour into electronic design support simulations with low effort. More accurate simulation results for polymer strains, will increase the overall acceptance of virtual prototyping.