Non-linear viscoelastic Material Models of Polymers for Electronics Simulation - Measurement, Modelling, Validation

This paper presents an overview and selection of material models that can describe nonlinear viscoelasticity (NLVE) of thermoset materials. To evaluate them, mechanical measurements with variable force-deformation-time regimes were performed on the example of encapsulation compounds consisting of different types of polyurethane. A digital twin of the experiment, based on Finite Element Analysis (FEA), was created, and used to determine the required NLVE model parameters. The parameter extraction has been done for the Bergstrom-Boyce-Model as well as the Three-Network-Model. First, the mechanical experiments were performed to establish a sufficient database for model calibration. The measurement setup for tensile and compression experiments and the test specimens are presented. Wide range deformation rates between 0.05 mm/min to 50 mm/min have been conducted to excite the specimens and their mechanical response. The investigated types of polyurethanes are characterized by significant NLVE behavior, which becomes visible in stress relaxations with different displacement excitations. In the second step, the model parameters 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 root-mean-square error of the comparison with the real measurement curves. The workflows for the optimization have been efficiently implemented in a python environment which controls the FEM model in Ansys. As a result, it could be shown that the simulation results with reduced mesh density and datapoints are sufficient with error deviation $\lt2$% and thus can be used speed up the model calibration by up to 900x. Both the BB- and the TN-model could be fitted to the experimental data well. In the future, the proposed NLVE models, data acquisition and parameterization method will bring large strain viscoelastic material behavior into electronic design support tools in a timely manner and with manageable expenses.