A stabilized single-sided nonlinear inverse finite element framework for large-deformation displacement field reconstruction

This study develops a single-sided nonlinear inverse finite element method (iFEM) for displacement-field reconstruction under large geometric deformations using single-sided strain measurements. Two solution schemes are established, namely the single-sided nonlinear Inc-iFEM and the single-sided nonlinear Itr-iFEM. To address the ill-posedness induced by the coupling of single-sided measurements and geometric nonlinearity, scale normalization is introduced into the incremental formulation, while scale normalization combined with linear reference regularization is incorporated into the iterative formulation to improve numerical stability and convergence reliability. The proposed methods are systematically assessed through four numerical cases using finite element method (FEM) solutions as reference, with displacement-field distributions, maximum displacement errors, and load–displacement responses taken as evaluation metrics. Both methods achieve effective displacement-field reconstruction and show good agreement with FEM results, whereas the single-sided nonlinear Itr-iFEM, although not uniformly more accurate than the incremental scheme in every individual case, generally exhibits superior convergence behavior, numerical stability, and displacement-field continuity. Experimental validation further confirms the effectiveness of the iterative scheme under practical measurement conditions. The proposed method is mainly applicable to plate-like structures dominated by transverse loading and bending, for which the adopted weak through-thickness symmetric assumption remains physically reasonable, and provides a feasible solution for single-sided large-deformation displacement-field reconstruction within this scope. • A single-sided nonlinear iFEM is developed for large-deformation reconstruction. • A stabilization strategy improves Itr-iFEM convergence, stability, and field continuity. • Both schemes agree well with FEM, and experiments validate Itr-iFEM in practice.