Surface-based stress tomography of architected metamaterials via physics-constrained generative learning

Area of Science:

• Materials Science
• Mechanical Engineering
• Computational Science

Background:

• Internal stress fields are critical for understanding metamaterial failure and performance.
• Current methods for stress evaluation, like volumetric imaging and finite element (FE) simulations, are time-consuming and impractical for non-destructive assessment.
• Bicontinuous spinodoid architectures exhibit complex mechanical behavior highly dependent on their geometry.

Purpose of the Study:

• To develop a generative framework for reconstructing 3D internal stress fields directly from surface observations.
• To enable rapid, non-destructive stress assessment and facilitate design optimization of architected metamaterials.
• To overcome the limitations of traditional volumetric analysis methods.

Main Methods:

• A physics- and topology-constrained generative framework utilizing surface-derived stress representations.
• Differentiable physics constraints to regularize equilibrium equations and boundary condition residuals.
• Topology-aware feature regularization to preserve bicontinuous load-transfer pathways.
• Integration with a genetic algorithm for stress-field-driven parameter optimization.

Main Results:

• Successful reconstruction of volumetric stress fields from surface data alone, demonstrating structural coherence and mechanical informativeness.
• Reliable localization of stress concentration regions in GRF-defined spinodoid designs, even in novel stiffness regimes.
• Demonstration of non-destructive stress inference using smartphone images, correlating reconstructed stress with experimentally observed fracture initiation.
• Experimentally validated improvements in multi-directional mechanical response through stress-field-driven design optimization.

Conclusions:

• The developed framework offers a surface-based approach for equilibrium-regularized internal stress field reconstruction.
• This method enables efficient, non-destructive stress analysis and design of metamaterials without volumetric measurements.
• The approach facilitates stress-field-driven design optimization, leading to enhanced material performance.