1. 2019 workshop to celebrate Prof. J.S. Chen's 60th birthday

11:00am – 11:15am March 11th  Alameda Room, ​The Pleasanton Marriot Hotel, Pleasanton, CA

An Adaptive Meta-Modeling Game for Automated Generations of Elasto-Plasticity Models with Self-Guided Discovery

Abstract:  We introduce a meta-modeling game based on concepts from multi-graph theory to find the optimal way to generate data and write models for blind predictions of a physical process We consider an idealized situation in which the modeling process of history-dependent process can be represented by a sequence of decision making where modelers make choices to formulate a sequence of actions to generate models.  While previous work on data-driven modeling often focus on completely replacing hand-crafted theory with a data-driven paradigm, our goal is to seek the best option that represents the hierarchy of material responses, i.e. the knowledge represented by a directed graph. As such, we introduce a new concept where all the modeling options can be recast as a directed multi-graph and each instant/configuration of the model can be understood as a path that links the source of the directed graph (e.g. strain history) to the sink (e.g. stress). This treatment enables us to further conceptualize the hybrid modeling process as a selection of the optimal choices in a decision tree search via deep reinforcement learning.  In the case where availability of data is limited, the meta-modeling algorithm also explores the weakness links in the constitutive laws and explore the optimal set of experiments to yield the best forward predictions under a limited budget. ​

2. Stanford Department Seminar 

4:30pm to 5:30pm March 12th, Shriram 104, Stanford University

Phase field damage-plasticity framework for fluid-infiltrating materials with size-dependent anisotropy

Abstract: Rock salt and clay are the prime candidates considered for nuclear waste geological disposal. In both materials, the microstructural attributes, such as the crystalline slip system, micro-fabric and mineral contacts, may lead to distinctive anisotropic responses at different length scales. In this talk, we present a unified mathematical framework designed to capture the size-dependent anisotropy of these path-dependent hydro-mechanical responses of geological materials used for nuclear waste disposal. In the brittle regime, we introduce a phase field fracture model in which the difference in critical energy release rates for different kinematics modes is considered. A search algorithm is used to determine the kinematic mode and propagation direction of the crack. In the ductile regime, we introduce a non-coaxial anisotropic regularization of the anisotropic modified Cam-Clay (MCC) model proposed by Semnani et al. 2016 to generate size-dependent plastic flow that could be non-coaxial to the stress gradient of the yield function. The influence of the size-dependent anisotropy on the formation of the shear band and the macroscopic responses of the effective media are analyzed in 2D and 3D numerical examples. The coupling between the damage and plastic responses of anisotropic materials, the transition from the brittle to ductile regimes and corresponding the poromechanical configurational force mesh adaption strategy required to capture the sharp gradients of pore pressure and phase field are also highlighted.  

The Mineral, Metals & Materials Society has published the report on "Verification & Validation of Computational Models Associated with the Mechanics of Materials" in which Professor Sun was served as the chair of the Planning Team. The report can be downloaded at http://tinyurl.com/y3slf8nf. Another related workshop titled "Advanced Computation and Data in Materials and Manufacturing: Core Knowledge Gaps and Opportunities" in which Professor Sun also participated is also available at http://tinyurl.com/y2bhjg79. We are thankful to the participants for contributing to these invited workshops, the members of the organization committee for their time and efforts, and the Mechanics of Materials and Structure Program of National Science Foundation for providing the important support, and the colleagues from TMS for making these workshop a great success. 

Prof. Sun has won the NSF CAREER award for his project, “Deep-reinforcement-learning-enhanced computational failure mechanics across multiple scales.”

Abstract ID: 417225 
Abstract Title: A Modified Phase Field Model for Mixed-Mode Crack Propagation with Consistent Kinematic Modes 
Final Paper Number: H21P-0991 
Presentation Type: Poster 
Session Date and Time: Tuesday, 11 December 2018; 08:00 - 12:20 
Session Number and Title: H21P: Risk Assessment of Fluid-Driven Fracturing in Heterogeneous Geologic Media: Numerical, Experimental, and Field Observations Posters 
Location: Convention Center; Hall A-C (Poster Hall)

In this work, we introduce a single-player game in which we attempt to use the formation of directed graph to represent the thought process / decision process of writing a cohesive zone model. In this work, the AI uses deep reinforcement learning to form knowledge of mechanics represented by directed graph, this knowledge is then used to generate constitutive law. Unlike previous supervised learning method, the automatically discovered/generated/implemented cohesive zone model is robust, accuracy and interpretable by human. Full details can be from the article [URL]. The second one will be coming soon. 

My PhD student Kun Wang has successfully defended his PhD qualification exam. His PhD thesis proposal "From multi-scale modeling to meta-modeling of poromechanics problems" is examined by the committee consisted of Santiago and Roberta Calatrava Family Professor George Deodatis (CEEM), and Fu Foundation Professor Qiang Du, and myself. In the proposed meta-modeling approach, Kun proposes a new method in which one uses a directed multi-graph to represent mechanics knowledge and then uses AI to form a directed graph that leads to a constitutive law. Furthermore, the AI also learns to improve its skill to write constitutive laws through practicing. Unlike previous ML which often leads to blackbox predictions and demands large amount of data, the resultant model is interpretable by human, can be trained with the same amount of data as the hand-crafted counterpart and yet much faster than sub-scale simulations. 

We thank all the committee members for their insightful questions, comments and time.

Kun Wang joined the research group in 9/2014, first as master student, then advanced to PhD in 1/2015.  His thesis focuses on the multiscale modeling and meta-modeling of porous media across multiple length and temporal scales. He has published 7 papers (including 4 CMAME papers) of which he served as the first author to 6 of them.  His work is supported by ARO, AFOSR, DOE, NSF and Columbia Engineering Seed Grant. His achievement and contribution to our research group are exemplified in the published papers, which are listed below. His recent work on data-driven multiscale modeling of porous media has been awarded him a travel grant to present at the Santa Fe Meshless workshop and selected as one of the finalists in the WCCM poster competitions (along with two other group members SeonHong Na and Eric Bryant). The slides of the qualification exam can be found at the bottom of this post. 

Congratulations for advancing to the final chapter of your PhD study, Kun! 

​Published Work:

• K. Wang, W.C. Sun, A semi-implicit discrete-continuum coupling method for porous media based on the effective stress principle at finite strain, Computer Methods in Applied Mechanics and Engineering,  doi:10.1016/j.cma.2016.02.020, 2016. [DRAFT]
• K. Wang, W.C. Sun, Anisotropy of a tensorial Bishop's coefficient for wetted granular materials, Journal of Engineering Mechanics, doi:10.1061/(ASCE)EM.1943-7889.0001005, 2015. [DRAFT] [Bibtex]
• K. Wang, W.C. Sun, S. Salager, S. Na, G. Khaddour, Identifying material parameters for a micro-polar plasticity model via X-ray micro-CT images: lessons learned from the curve-fitting exercises, accepted, International Journal of Multiscale Computational Engineering, 2016. [DRAFT]
• K. Wang, W.C. Sun, A unified variational eigen-erosion framework for interacting fractures and compaction bands in brittle porous media, doi:10.1016/j.cma.2017.01.017, Computer Methods in Applied Mechanics and Engineering, 2017. [DRAFT]
• K. Wang, W.C. Sun,   A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning​, Computer Methods in Applied Mechanics and Engineering, 334(1):337-380, doi:10.1016/j.cma.2018.01.036, ​2018. 
• R. Gupta, S. Salager, K. Wang, W.C. Sun, Open-source support toward validating and falsifying discrete mechanics models using synthetic granular materials Part I: Experimental tests with particles manufactured by a 3D printer, Acta Geotechnica, doi:10.1007/s11440-018-0703-0, 2018. 
• K. Wang, W.C. Sun, updated Lagrangian LBM-DEM-FEM coupling model for dual-permeability porous media with embedded discontinuities, Computer Methods in Applied Mechanics and Engineering, 10.1016/j.cma.2018.09.034, 2018. 
• K. Wang, W.C. Sun, Meta-modeling game for deriving theoretical-consistent, micro-structural-based traction-separation laws via deep reinforcement learning, under review.

An updated Lagrangian LBM-DEM-FEM coupling model for  dual-permeability fissured porous media with embedded discontinuities 

Kun Wang & WaiChing Sun

Many engineering applications and geological processes involve embedded discontinuities in porous media across multiple length scales (e.g. rock joints, grain boundaries, deformation bands and faults). Understanding the multiscale path-dependent hydro-mechanical responses of these interfaces across length scales is of ultimate importance for applications such as CO2 sequestration, hydraulic fracture and earthquake rupture dynamics. While there exist mathematical frameworks such as extended finite element and assumed strain to replicate the kinematics of the interfaces, modeling the cyclic hydro-mechanical constitutive responses of the interfaces remains a difficult task. This paper presents a semi-data-driven multiscale approach that obtains both the traction-separation law and the aperture-porosity-permeability relation from micro-mechanical simulations performed on representative elementary volumes in the finite deformation range. To speed up the multiscale simulations, the incremental constitutive updates of the mechanical responses are obtained from discrete element simulations at the representative elementary volume whereas the hydraulic responses are generated from a neural network trained with data from lattice Boltzmann simulations. These responses are then linked to a macroscopic dual-permeability model. This approach allows one to bypass the need of deriving multi-physical phenomenological laws for complex loading paths. More importantly, it enables the capturing of the evolving anisotropy of the permeabilities of the macro- and micro-pores. A set of numerical experiments are used to demonstrate the robustness of the proposed model. [DRAFT]

PhD student Kun Wang and postdoc research scientist Dr. Chuanqi Liu have received travel grant to present their work at the upcoming Meshfree and Particle Methods: Application and Theory, to be held in Santa Fe, NM, September 10-12, 2018. Chuanqi will present his previous work conducted at Tsinghua University, while Kun will discuss his work on metal-modeling of complex materials in the poster session. The support will cover the registration and travel for both team members. We thank the organizers for providing the support to us.