Abstract:

We introduce a regularized anisotropic modified Cam-clay (MCC) model which captures the size-dependent anisotropic elastoplastic responses for clay, mudstone, shales, and sedimentary rock. By homogenizing the multiscale anisotropic effects induced by clay particle aggregate, clusters, peds, micro-fabric, and mineral contact across length scales, we introduce two distinctive anisotropic mechanisms for the MCC model at the material point and mesoscale levels. We first employ a mapping that links the anisotropic stress state to a fictitious isotropic principal stress-space to introduce anisotropy at the material point scale. Then, the mesoscale anisotropy is introduced via an anisotropic regularization mechanism. This anisotropic regularization mechanism is triggered by introducing gradient-dependence of the internal variables through a penalty method such that the resultant gradient-enhanced plastic flow may exhibit anisotropic responses 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. [PDF]

Abstract: 
We introduce a mathematical framework designed to enable a simple image-to-simulation workflow for solids of complex geometries in the geometrically nonlinear regime. While the material point method is used to circumvent  the mesh distortion issues commonly exhibited in Lagrangian meshes,
a shifted domain technique originated from [Main and Scovazzi, 2018a,b] is used to represent the boundary conditions implicitly via a level set or signed distance function. Consequently, this method completely bypasses the need to generate high-quality conformal mesh to represent complex geometries and therefore allows modelers to select the space of the interpolation function without the constraints due to the geometrical need. This important simplification enables us to simulate deformation of complex geometries inferred from voxel images. Verification examples on deformable body subjected to finite rotation have shown that the new shifted domain material point method is able to generate frame-indifferent results. Meanwhile, simulations using microCT images of a Hostun sand have demonstrated that this method is able to reproduce the quasi-brittle damage mechanisms of single grain without the excessively concentrated nodes commonly displayed in conformal meshes that represent 3D objects with local fine details. [PDF]

WaiChing "Steve" Sun, an assistant professor in the Department of Civil Engineering and Engineering Mechanics, is part of a team who recently won a highly competitive Department of Defense (DoD) MURI (Multidisciplinary University Research Initiative) grant to develop computational/data-driven/machine-learning-enhanced mathematical models for energetic materials with an integrated experimental and modeling efforts across university. The team is led by University of Missouri-Columbia, and includes researchers from University of Iowa, UIUC, Rensselaer Polytechnic Institute, Purdue University, and Columbia.  The five-year $7.5 million AFOSR (Air Force Office of Scientific Research) grant was awarded for the DoD’s “MURI Topic #24: Microstructurally-Aware Continuum Models for Energetic Materials;” the project is titled “Integrating Multiscale Modeling and Experiments to Develop a Meso-Informed Predictive Capability for Explosives Safety and Performance” (See press release from Department of Defense here). Since its inception in 1985, the tri-service (ARO, ONR, AFOSR) MURI program has been supporting teams whose members have diverse sets of expertise as well as creative and different approaches to tackling problems. It’s a program that remains a cornerstone of the DOD’s legacy of scientific impact. 

Sun's work focuses on the development of theoretical and computational models and the corresponding computer algorithms for porous media, with applications in geomechanics and computational mechanics, and mechanics for civil infrastructure. This is the first DoD MURI grant obtained by Sun and the seventh Department of Defense grant Sun's research group has obtained since 2014. His work is supported by multiple federal funding agencies, including two highly competitive Young Investigator Program Awards from Army Research Office (ARO) and Air Force Office of Scientific Research (AFOSR), an 800K grant from Department of Energy Nuclear University Program (DOE NEUP) on nuclear waste disposal, and recently an NSF CAREER award from the mechanics of materials and structures program of CMMI division in NSF. 

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.