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Abstract:
A finite-strain identification framework based on the Virtual Fields Method (VFM) is proposed for the characterization of hyperelastic polymer materials subjected to heterogeneous deformation. The approach exploits full-field displacement measurements obtained by digital image correlation during physical experiments and formulates the inverse problem through the principle of virtual work. To enhance parameter sensitivity and identifiability, a T-shaped specimen together with a dedicated experimental setup was specifically designed to generate pronounced nonuniform strain fields from the onset of loading. The constitutive response is described within a finite deformation setting using hyperelastic strain-energy density functions, and the unknown material parameters are determined by direct inversion of the weak form of the equilibrium equations. A dedicated integration strategy based on Voronoi tessellation of the measurement points is developed to ensure consistent evaluation of the virtual work integrals. The proposed framework is assessed using both experimental data and synthetic data generated by nonlinear finite element simulations. The results demonstrate accurate and robust recovery of hyperelastic parameters, highlighting the effectiveness of the combined experimental–numerical approach and specimen design with an enhanced VFM formulation for reliable material characterization at finite strains.

Keywords:
Identification of material constants, Digital image correlation, Finite element analysis, Optimization, Hyperelasticity