Inverse characterization of a material model using an ensemble-based four-dimensional variational method

[Display omitted] •A new data-assimilation-based method for material model characterization is proposed.•The data assimilation approach incorporates experimental and numerical uncertainties.•An ensemble-based four-dimensional variational method is used for characterization.•Sensitivity analysis for gradient-based optimization is easy and efficient.•Strain hardening parameters are inversely estimated from a uniaxial tensile test. The identification accuracy of material model parameters is essential for accurately predicting the deformation behavior of metallic materials (e.g., metal forming) using a finite element (FE) simulation. Numerous researchers have studied inverse material model characterization, where parameters are determined by minimizing a cost function that quantifies the difference between experimental data and mechanical test simulation results. However, sensitivity analysis in the optimization process hinders the extensibility of inverse methods due to issues like computational cost and complex numerical implementation. In this study, we developed a novel inverse methodology for material model characterization that improves extensibility by applying an ensemble-based four-dimensional variational method (En4DVar), which has the potential to address the challenges associated with conventional FE-based inverse material model characterization. The developed method was verified through numerical experiments in which En4DVar was applied to an elastoplastic FE simulation of the deformation of an aluminum alloy during a uniaxial tensile test, including diffuse necking. We investigated the estimation accuracy of the strain-hardening parameters in Swift’s hardening law and evaluated the simulation results under various conditions through numerical experiments. We focused on the effect of time and location to incorporate synthetic experimental data into the simulation to examine the quantities of synthetic experimental data required for parameter estimation. The results of the numerical experiments showed that En4DVar is a powerful approach for estimating the parameters and characterizing the deformation behavior of a material. Moreover, it was shown that accurate estimation results can be obtained even using synthetic experimental data with a relatively low temporal resolution or a small field of view. The proposed method's ease of extensibility using En4DVar expands the range of problems solvable in the field of material model characterization.