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Thermodynamics-based Data-driven Computing for Inelastic Materials Modeling

J. S. Chen
Department of Structural Engineering
Department of Mechanical & Aerospace Engineering
University of Californian, San Diego, USA

Abstract

Characterization and modeling of complex materials by phenomenological models remains challenging due to difficulties in formulating mathematical expressions and internal state variables (ISVs) governing path-dependent behaviors. Data-driven machine learning models, such as deep neural networks and recurrent neural networks (RNNs), have become viable alternatives. However, pure black-box data-driven models mapping inputs to outputs without considering the underlying physics suffer from unstable and inaccurate generalization performance. This study proposes a machine-learned physics-informed data-driven constitutive modeling approach for path-dependent materials based on the measurable material states. The proposed data-driven constitutive model is designed with the consideration of universal thermodynamics principles, where the ISVs essential to the material path-dependency are inferred automatically from the hidden state of RNNs. For materials subjected to fracturing or strain localization, a neural network enriched Galerkin solution for weak and strong discontinuities and for adaptive refinement without re-meshing is introduced. These unique combinations of machine learning techniques and advanced computational methods have expanded the horizon of computational mechanics and scientific computing beyond what the conventional computational methods can offer. Applications to plasticity, localization, fracture, thermal fatigue, and digital twins will be presented to demonstrate the effectiveness of these new developments for computational mechanics.

Prof. Jiun-Shyan Chen (陳俊賢教授)

E-mail: jsc137@ucsd.edu 
William Prager Chair Professor, Distinguished Professor
Department of Structural Engineering, UC San Diego
Department of Mechanical and Aerospace Engineering, UC San Diego
Founding Director, Center for Extreme Events Research.

Prof. Jiun-Shyan Chen.jpg

Short-Bio

J. S. Chen is the William Prager Chair Professor and Distinguished Professor of Structural Engineering Department, Mechanical & Aerospace Engineering Department, and the Founding Director of Center for Extreme Events Research at UC San Diego. Before joining UCSD in 2013, he was the Chancellor’s Professor of UCLA Civil & Environmental Engineering Department, Mechanical & Aerospace Engineering Department, and Mathematics Department, where he served as the Department Chair of Civil & Environmental Engineering during 2007-2012. J. S. Chen’s research is in computational mechanics and multiscale materials modeling with specialization in the development of meshfree methods. He is the Past President of US Association for Computational Mechanics (USACM) and the Past President of ASCE Engineering Mechanics Institute (EMI). He has received numerous awards, including the Computational Mechanics Award from International Association for Computational Mechanics (IACM), the Grand Prize from Japan Society for Computational Engineering and Science (JSCES), the Ted Belytschko Applied Mechanics Award from ASME Applied Mechanics Division, the Belytschko Medal from U.S. Association for Computational Mechanics (USACM), the Computational Mechanics Award from Japan Association for Computational Mechanics (JACM), the ICACM Award from International Chinese Association for Computational Mechanics (ICACM), among others. He is the Fellow of USACM, IACM, ASME, EMI, SES, ICACM, and ICCEES. He received BS (Civil Engineering) from National Central University, Taiwan, and MS and PhD (Theoretical & Applied Mechanics) from Northwestern University.

Computing Saint-Venant Flexure-Torsion and Warping in Three Dimensions

Prof. Hong-Ki Hong (洪宏基教授)

Abstract

     A prismatic rod of arbitray cross section shape --- solid sections, open or closed thin-walled sections, even multi-cell sections --- is studied. For this rod the Saint-Venant flexure-torsion theory is unified with the theory of warping moment and warping torsion, allowing the stress function and warping function to vary along the axial direction and establishing formulae between warping moment and axial stresses. A case study of H shape illustrates the variation of warping moment (i.e. the so-called bimoment), axial stresses, warping torsion, and warping displacements for various support conditions. 
     The centroid for axial force and the shear center for transverse forces are investigated both for thin-walled sections and for solid sections. The computation excuted for the rod made of elastic material is further extended to elastoplastic material accounted for not only yield conditions but also plastic flow and hardening rules.

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Keywords : Saint-Venant flexure-torsion, warping torsion, warping moment, shear center, yield condition, plastic flow and hardening rule.
 

E-mail: hkhong@ntu.edu.tw

Hong-Ki Hong was an Engineer in Pescadores Islands, Taipei, Baltimore, and Richland. He was Convener of Civil Engineering Program, National Science Council of Taiwan; Director of the Office of Advisors of Science and Technology, Ministry of Transportation and Communications of Taiwan; Vice President for General Affairs, National Taiwan University (NTU). His current title: Professor Emeritus,, Department of Civil Engineering, NTU; Lifetime Distinguished Professor, NTU.

Prof. Hong-Ki Hong.jpg

Field: 

  1. civil engineering+structural mechanics (elasticity+plasticity leading to earthquake resistant analysis+design and constitutive experiments); 

  2. vibration control (structural dynamics, acoustics, sound and vibration, random vibration, viscoelasticity, active and passive control); 

  3. scientific computing (based on boudary elements, Lie groups and Clifford analysis).

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