Topic: Exploring the low-data regime in hyperelasticity and elastoplasticity

Abstract: Machine learning techniques are gearing up to play a significant role in the field of computational solid mechanics and multiphysics, enabling the integration of experimental data and physical constraints towards data-driven constitutive laws, acceleration of computational techniques for multi-scale modeling, and new paradigms for the solution of forward and inverse problems, to name a few. This talk will cover recent advancements in the area of ML-enabled constitutive modeling I) A physics-informed data-driven constitutive modeling approach for isotropic and anisotropic hyperelastic materials is developed using tensor representation theorems. The trained surrogates (using laGPR and NNs) are able to respect physical principles such as material frame indifference, material symmetry, and the local balance of angular momentum. Overall, the presented approach is tested on synthetic data from isotropic and anisotropic constitutive laws and shows surprising accuracy even far beyond the limits of the training domain, indicating that the resulting surrogates can efficiently generalize as they incorporate knowledge about the underlying physics. Additionally, it is shown that the inherent material symmetries can be discovered directly from data. II) Finally, we proceed to tackle elastoplasticity in a modular framework. Employing convexity for the yield functions we recover texture-parametrized yield functions using input convex (IC)NNs and propose a hybrid model-data-driven framework to recover yield functions with tension compression asymmetries in the low data regime. Additionally, by employing thermodynamic requirements in an NN-based framework we learn hardening laws from limited experimental data.

Biography: Dr. Bouklas is an Assistant Professor at the Sibley School of Mechanical and Aerospace Engineering at Cornell University. Prior to that, he was a postdoctoral researcher at the Laboratory for Multiscale Materials Modeling at EPFL, Switzerland, and at the Oden Institute at the University of Texas at Austin. He received his Ph.D. from the Aerospace Engineering and Engineering Mechanics department at the University of Texas at Austin and obtained his Diploma in Mechanical Engineering from the Aristotle University of Thessaloniki, Greece. Dr. Bouklas' research focuses on the fields of theoretical and computational solid mechanics. Developing theoretical frameworks and advanced computational methods, he aims to improve the fundamental understanding of materials and structures and enhance the predictive capabilities in relevant engineering applications. He is interested in the study of soft materials, active materials, and biomaterials, fracture and instabilities, as well as multiscale modeling in coupled multi-physical systems. He is the recipient of the Young Investigator Program award from the Air Force Office of Scientific Research