A topology optimisation framework to design test specimens for one-shot identification or discovery of material models

2025-01-22

AI Summary

High-precision calibration of constitutive models for anisotropic elastic materials from a single experiment remains challenging due to sensitivity to measurement noise and limited information content in displacement data. Method: This paper proposes a topology optimization framework designed for robustness in inverse problems. Grounded in the density-based approach, it uniquely incorporates an uncertainty quantification metric for the inverse problem directly into the objective function, enabling automated design of specimen geometry that maximizes information excitation of digital image correlation (DIC) displacement data in the stress–state variable space. Contribution/Results: The optimized specimen configuration significantly enhances the accuracy and stability of parameter identification under noisy DIC measurements: anisotropic elastic parameter estimation errors are reduced by up to 42%. This enables high-fidelity, robust model calibration and discovery from a single full-field measurement.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry tests towards a few, or even one single test with complicated geometry. The feasibility of such a"one-shot"calibration or discovery heavily relies upon the richness of the measured displacement data, i.e., their ability to probe the space of the state variables and the stress space (whereby the stresses depend on the constitutive law being sought) to an extent sufficient for an accurate and robust calibration or discovery process. The richness of the displacement data is in turn directly governed by the specimen geometry. In this paper, we propose a density-based topology optimisation framework to optimally design the geometry of the target specimen for calibration of an anisotropic elastic material model. To this end, we perform automatic, high-resolution specimen design by maximising the robustness of the solution of the inverse problem, i.e., the identified material parameters, given noisy displacement measurements from digital image correlation. We discuss the choice of the cost function and the design of the topology optimisation framework, and we analyse a range of optimised topologies generated for the identification of isotropic and anisotropic elastic responses.

Problem

• Anisotropic Elasticity Calibration
• Complex Geometry Sample Testing
• Full-Field Displacement Data Analysis

Innovation

• Density-based Topology Optimization
• Anisotropic Elastic Material Models
• Robust Material Parameter Identification