A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

TL;DR

This paper addresses the calibration of finite-strain elastoplastic constitutive models from full-field data by comparing FEMU and VFM. It advances the field by introducing numerically-exact gradient computations for both methods using forward and adjoint sensitivities and automatic differentiation, enabling a fair, computationally efficient comparison. Across six synthetic experiments, FEMU delivered higher accuracy, especially under model-form errors and noise, but at substantially higher computational cost, while VFM was significantly faster and more sensitive to data quality unless preprocessed. The findings guide practitioners in selecting the calibration approach based on desired accuracy, data quality, and available computational resources, and demonstrate the viability of exact-gradient VFM in PDE-constrained contexts.

Abstract

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. The two primary approaches in the experimental mechanics' community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we rigorously compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, both methods are tested on a finite strain elastoplasticity model. We conduct a series of test cases to assess both methods' robustness under practical challenges.

Figures (15)

• Figure 1: A prototypical characterization experiment. The test sample sits in machine grips (dark gray) and is pulled to failure. Only the light gray part of the visible region is modeled. Digital image correlation provides full-field displacement data over the entirety of this region, and a load cell measures axial load.
• Figure 2: BCs for the modeled geometry in Figure \ref{['fig:schematic_full_specimen_with_grips']}. The symbols $\Gamma_{g_i}$, $\Gamma^{\text{tf}}_{h_i}$, and $\Gamma^{\text{L}}_{h_i}$ denote portions of the boundary over which displacement, traction-free, and non-zero traction values are prescribed. Notably, FEMU and VFM necessitate different BCs, as $h_2(\boldsymbol{x})$ is generally unknown, but in VFM its integral is set equal to the measured axial load $\tilde{F}$. The values for the displacement BCs come directly from the measured field $\tilde{\boldsymbol{u}}$.
• Figure 3: Schematic representation of the asymmetrically notched plate, including its geometry, mesh, and boundary conditions. Additionally, to replicate the effect of the rigid mechanical grips holding the specimen, the horizontal movement at the top edge of the specimen is constrained. All dimensions are in mm.
• Figure 4: VFM finite difference gradient checks for the plate with asymmetric notches.
• Figure 5: A comparison of computation times for different inverse methods in calibrating material parameters demonstrates that VFM outperforms FEMU in computational efficiency for both identifying plasticity parameters alone and identifying elastic-plastic parameters.