Seminar: Charbel Farhat

Vivian Church Hoff Professor of Aircraft Structures
Director, Stanford-King Abdulaziz City of Science and Technology Center of Excellence for Aeronautics and Astronautics
Professor, Institute for Computational and Mathematical Engineering

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Trustworthy machine learning for nonlinear elasticity and viscoelasticity

Enlarge the image — Machine-learned nonlinear viscoelastic constitutive model and exploitation in fluid-structure simulation of supersonic parachute inflation dynamics.

With the advent of machine learning (ML), the use of deep artificial neural networks (ANNs) for constitutive modeling has gained prominence, particularly in the context of constitutive modeling for finite element analysis and numerical homogenization. Nonetheless, ANNs are not without shortcomings for data-driven constitutive modeling. In their standard form, they are built to simply map input data to output data – typically, without fundamental restrictions. Thus, when such ANNs are exploited in physics-based numerical simulations, they can violate some laws of physics, in which case confidence in the simulation-based predictions is reduced. Consequently, the literature has recently witnessed a surge of papers proposing ML-based frameworks that attempt to inform or constrain ANNs with some knowledge of mechanics and thermodynamics. In particular, the presenters have proposed in [1, 2] a trustworthy ML framework for the constitutive modeling of nonlinearly elastic and viscoelastic heterogeneous materials that is broadly mechanics-informed. Specifically, it enforces on the ANN's network architecture a long list of desirable mathematical properties that guarantees the satisfaction of an even longer list of physical constraints, including: dynamic stability, material stability, and internal variable stability; objectivity; consistency; fading memory; recovery of elasticity; and the second law of thermodynamics. The lecture will show that embedding these notions in a learning approach reduces a model’s sensitivity to noise and promotes its robustness to inputs outside the training domain. It will also highlight the merits of the proposed trustworthy ML framework for numerous engineering applications, including the prediction of the supersonic inflation dynamics of a parachute system with a canopy made of a woven fabric.

References

[1] F. As’ad, P. Avery, C. Farhat. A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering, 2738-2759, 2022.
[2] F. As’ad, C. Farhat. A mechanics-informed deep learning framework for data-driven nonlinear viscoelasticity. Computer Methods in Applied Mechanics and Engineering, 16463, 2023.