Session: 13-19-02: Scientific Machine Learning (SciML) for Characterization, Modeling, and Design of Structures and Materials II

Paper Number: 173814

Design of 3d Heterogeneous Elastoplastic Tests and a Surrogate Error Function for Inverse Calibration of Constitutive Models 

Accurate calibration of yield loci in constitutive models is critical for predicting the behavior of metals under complex and multiaxial loading conditions. However, traditional material testing approaches are often time-consuming, costly, and sometimes insufficient to fully capture the rich, multiaxial strain paths required for calibrating advanced constitutive model parameters. To address these challenges, this study introduces an integrated computational and experimental framework that combines the design of novel three-dimensional (3D) heterogeneous elastoplastic specimens with the development of a machine learning–based surrogate error function, paving a new path for inverse calibration of constitutive models.

The first part of this work proposes a novel performance indicator that systematically evaluates heterogeneous mechanical tests by integrating two key metrics: load state diversity and measurement efficiency. Load state diversity quantifies the richness of strain-space coverage using convex hull analysis, while measurement efficiency assesses the spatial compactness of high-value plastic regions, ensuring compatibility with full-field Digital Image Correlation (DIC) techniques for experimental measurements. The indicator is also designed to account for material symmetry, tailoring its application to various forms of anisotropy encountered in metals and alloys. Using this metric, a 3D specimen geometry and experimental setup are optimized to produce highly diverse strain states within a single test, which is particularly desirable for inverse calibration of constitutive models and significantly reduces reliance on multiple traditional experiments.

The second component of this study develops a physics-informed, data-driven surrogate error function to mitigate bias and enhance the accuracy of inverse calibration in Finite Element Model Updating (FEMU) of the proposed 3D specimen. A shared-weight multi-layer perceptron (SW-MLP) architecture maps experimentally accessible strain-space features to corresponding weights, enabling the surrogate error function to accurately represent the underlying deviations between yield loci associated with experimental and simulation data. Extensive training and validation on synthetic datasets comprising over 3,200 finite element simulations with varied hardening laws and constitutive parameters demonstrate the effectiveness of the surrogate error function. Training across multiple plastic strain thresholds (PEEQ cut-offs) achieves more than a threefold improvement in the root mean square error (RMSE) between surrogate error function values and the true deviations between yield loci of different comparisons.

Finally, a novel mechanical test setup is constructed, and the optimized 3D specimen is fabricated and tested. Strain measurements obtained using a multi-view stereo-DIC system confirm the generation of rich, heterogeneous strain fields that facilitate high-fidelity inverse calibration of constitutive models. This integrated framework bridges advanced experimental test design and machine learning–based error metrics, providing a unified methodology for robust and accurate calibration of complex constitutive models.

Presenting Author: Fakhreddin Emami University of South Carolina

Presenting Author Biography: Fakhreddin (Dean) Emami is a Ph.D. candidate in Mechanical Engineering at the University of South Carolina. His research focuses on computational mechanics, finite element analysis, and machine learning for the design and optimization of advanced materials and mechanical systems.

Authors:

Fakhreddin Emami University of South Carolina
Sabih Ahmad Khan University of South Carolina
Andrew Gross University of South Carolina