Reliability of Hybrid Inverse Identification Based on Stereo-DIC Measurements to Assess HIPS Hyperelastic Parameters: Case of Isothermal Tensile Loads

Abstract

Thermo-mechanical behaviors of thin thermoplastic sheets under thermoforming conditions are generally studied in the frameworks of hyperelasticity and large deformations. The boundary conditions of the mechanical problem which represents the shaping operation are defined by the clamping configuration of the free edges of the sheet. By heating a flat thermoplastic sheet of totally or partially constrained edges during a thermoforming process, incontrollable changes of the initial boundary conditions manifest by buckling and warpage. Without consideration of the real process conditions, the mechanical problem risks to be ill posed. The current study focuses on representative unidirectional stretching tests under isothermal conditions conducted on high impact polystyrene (HIPS) specimens with free lateral edges. The aim is to identify the parameters of the Mooney-Rivlin hyperelastic model which is generally admitted in the case of the HIPS for temperatures above the glass transition. To measure the non-negligible out-of-plane deformations which manifest during the stretching operation, a hybrid numerical-experimental approach is introduced. This approach combines kinematic fields measured by the stereo digital image correlation (stereo-DIC) technique and a finite element model updating (FEMU) procedure. First, a dataset of displacement fields measured during stretching tests at controlled temperatures and strain rates is constructed. Second, sequential quadratic programming (SQP) based inverse identification procedure is implemented to minimize an objective function which combines the experimental and numerical displacement fields. A case of study is presented to test the limits of the hybrid numerical-experimental approach under incremental stretching levels. The optimization results indicate that the extent of the kinematic fields compared to the effective size of the tested specimen and the excessive stretching of the stereo-DIC speckle are the major limits to the applicability of the approach. The conducted study constitutes a preliminary step towards more accurate consideration of real boundary conditions to simulate thermoforming of thin thermoplastic sheets.