Shape sensing of viscoelastic structures using the inverse finite element method: numerical and experimental validation

The inverse Finite Element Method (iFEM) is well established for shape sensing of elastic structures, but its performance under time-dependent viscoelastic deformation remains insufficiently assessed. This work presents, to the authors' knowledge, the first combined numerical and experimental assessment of iFEM under creep and recovery conditions within the small-deformation regime. The objective is to determine whether time-dependent displacement fields can be reconstructed directly from strain histories without introducing a viscoelastic constitutive law, material parameters, load histories, or internal variables into the inverse analysis. Two complementary case studies are considered. First, a viscoelastic abdominal-patch model is analysed under sustained pressure, with a calibrated Generalised Maxwell model used only in the forward finite element simulation to generate reference strain and displacement fields. Second, an SLA-manufactured NACA 0016 airfoil beam is experimentally tested under loading and unloading, using measured strain histories as iFEM input and LVDT measurements for validation. In the numerical case, the maximum error in central transverse displacement is 2.46%, while the field-based normalised RMSE remains below 2.26%. In the experimental case, the reconstructed tip displacement differs from the LVDT measurements by less than 5% for most of the test, with larger discrepancies during unloading. The results show that the kinematics-based iFEM formulation can reconstruct creep and recovery histories directly from measured strains, while the material time dependence is conveyed through the strain data rather than through a constitutive model within the inverse analysis.