Mechanics informatics-driven topology optimization for test specimen design and single-test material characterization: A Gaussian random field approach

Characterizing materials through conventional testing protocols often requires multiple separate tests, making it resource-intensive and introducing inter-specimen variability. This work presents an informatics-enabled approach that frames material characterization as an information utilization problem rather than a standardized testing problem. Instead of adapting specimen design to multiple simple tests, we adapt tests to a single complex, informative specimen, optimally designed to maximize stress state entropy, a quantitative measure of mechanical information. The specimen design methodology employs Gaussian random fields with Karhunen-Loève expansion as the generative basis for topology optimization, where eigenvalue configurations are tuned via Bayesian optimization to maximize stress state entropy. Applied to orthotropic elasticity and anisotropic plasticity, the framework generates specimens approaching theoretical entropy limits that simultaneously activate all stress states required for accurate characterization within a single uniaxial tension test. To validate this framework, we introduce a physics-informed neural network approach using an Input Convex architecture for learning orthotropic elasticity directly from full-field data while preserving thermodynamic consistency. Comparative analysis demonstrates that parameter identification accuracy scales directly with specimen information content, with the most informative specimen design achieving order-of-magnitude improvement in identification accuracy over specimens with low information content. Additionally, a parametric study reveals that void fraction has a significant influence on the information content of the designed specimen. This work establishes a general framework for informatics-driven test specimen design, enabling efficient material characterization across diverse constitutive models.