A Force‐Based Identification Scheme for Constitutive Parameters Regularized by Admissible Elemental Internal Forces

ABSTRACT We present a new regularized inverse formulation, built upon the paradigm of force‐based Finite Element Model Updating (FEMU‐F), for identifying constitutive parameters from full‐field displacements and integrated external forces. In force‐based methods such as FEMU‐F and Equilibrium Gap Method (EGM), the minimized loss function is defined in terms of FE force residuals after imposing measured displacements as Dirichlet constraints. Such force‐based loss functions are known to be sensitive to noisy displacements. To overcome this limitation, we propose a new robust force‐based loss function that operates directly on elemental internal forces without assembling them into nodal values. The key innovation is the introduction of admissible elemental internal forces (AEIFs) as additional unknown variables into the proposed inverse formulation with inherent regularization effects. By definition, AEIFs satisfy static equilibrium with external forces, independent of kinematics and constitutive relations. The proposed loss function measures the discrepancy between AEIFs and the elemental internal forces computed from the FE model. The static equilibrium of AEIFs imposes purely force‐based admissibility conditions, which build a systematic reduction procedure delivering a compact, independent representation of the AEIFs space. This enables an analytical solution for unknown AEIFs when minimizing the proposed loss function, while the constitutive parameters are identified numerically. Numerical examples show that the regularized formulation reduces sensitivity to noisy full‐field displacements and inaccurate Dirichlet boundary conditions and mitigates FEMU‐F's bias toward local information near measured forces. Owing to its force‐only formulation, the method is simpler to implement than stress‐based approaches such as Constitutive Equation Gap (CEG). It identifies heterogeneous elasticity more accurately than FEMU‐F using a single measured integrated force. The method is also shown to remain robust in identifying parameters of a nonlinear, path‐dependent constitutive law with strain localization, highlighting its suitability for such challenging materials where measured full‐field displacements are directly imposed as Dirichlet constraints.