Deep learning for interpreting elastic modulus and hardness from complex fractures

Abstract

Indentation is a widely used measurement for determining the elastic modulus, based on tip penetration into a sample versus load, and is also employed to estimate hardness. This study proposes a new approach for estimating elastic modulus and hardness from the complex fractures of shale, a heterogeneous medium. A deep learning model was developed, fine-tuned through trial and error, and applied with the adaptive momentum solver to analyze 24,738 nanoindentation images—3,534 original and 21,204 augmented. The nanoindentations were obtained under loads ranging from 100 mN to 1,095 mN, yielding elastic modulus values from 14.0 GPa to 127.1 GPa and hardness values from 0.13 GPa to 5.60 GPa. The proposed method achieved mean squared errors (MSEs) of 3.7e-3 for normalized elastic modulus and 2.1e-3 for normalized hardness in independent measurements. These findings are significant, demonstrating that complex fracture patterns encode quantitative information about the elastic properties of the solid medium.