A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables​

SeonHong Na, Eric C Bryant, Waiching Sun
​
We introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multi-physical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp changes of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after re-meshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal value and direction are projected onto a smooth field interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator, in general, leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the re-meshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain. [PDF]

2019-07-29
#1971999 - A Cooperative Two-player Game for Data-driven Discovery of Elasto-plasticity Knowledge Represented in Directed Graph
02:00 - 02:20
Minisymposium#203 Data-driven Modeling Using Uncertainty Quantification, Machine Learning and Optimization
Authors Kun Wang ,WaiChing Sun * ,Qiang Du
LocationR oom # Lone Star Ballroom F - LVL 3
​We introduce a multi-agent meta-modeling game to generate data, knowledge, and models that make predictions on constitutive responses of elasto-plastic materials. We introduce a new concept from graph theory where a modeler agent is tasked with evaluating all the modeling options recast as a directed multigraph and find the optimal path that links the source of the directed graph (e.g. strain history) to the target (e.g. stress) measured by an objective function. Meanwhile, the data agent, which is tasked with generating data from real or virtual experiments (e.g. molecular dynamics, discrete element simulations), interacts with the modeling agent sequentially and uses reinforcement learning to design new experiments to optimize the prediction capacity. Consequently, this treatment enables us to emulate an idealized scientific collaboration as selections of the optimal choices in a decision tree search done automatically via deep reinforcement learning.

2019-07-31
#1971644 - Data-driven Validation of Bishop’s Effective Stress Principle through Deep Reinforcement Learning
02:20 - 02:40
Minisymposium#105 Computational Geomechanics, in honor of Prof. Mary F. Wheeler
Authors Yousef Heider * ,Kun Wang ,Hyoung Suk Suh ,WaiChing Sun
Location Room # Lone Star Ballroom C - LVL 3

In analogy to Terzaghi’s effective stress principle in fully-saturated porous media, Bishop’s effective stress principle presents a partition of the total stress in unsaturated porous media between suction and effective stress contributions. Although widely applied in Geomechanics, the validity and generality of Bishop’s principle across saturation regimes still a matter of debate, especially for path-dependent materials that exhibit hysteresis retention behaviors. The proposed meta-modeling automated learning approach makes use of data-based constitutive modeling, generated via reinforcement learning, to evaluate the validity and generality of Bishop’s effective stress principle for various types of blind predictions involving material failures, such as strain localization and brittle fracture. Synthetic micro-structural-based data of unsaturated granular materials (such as coordination number, fabric tensor, porosity, saturation, suction, and intrinsic permeability) are generated using the discrete element method DEM together with the pore-network approach, applied to a representative volume element (RVE). Data set generated from sub-scale simulations are used to automatically create, train, calibrate and validate plausible alternative stress partition theories represented by directed graphs until an optimal knowledge graph is formed. The blind prediction performance of the data-driven discovery will then be compared with predictions based on different variations of the effective stress principle for unsaturated porous media.

2019-07-31
#1971799 - A Micromorphic-regularized Cam-clay-type Model for Capturing Size-dependent Anisotropy in Geological materials
05:30 - 05:50
Minisymposium#105 Computational Geomechanics, in honor of Prof. Mary F. Wheeler
Authors Eric Bryant* ,WaiChing Sun
LocationRoom # Lone Star Ballroom C - LVL 3
We introduce a micromorphic-regularized anisotropic modified Cam-clay model which captures the size-dependent anisotropic elastoplastic responses for clay, mudstone, shales and sedimentary rock. To capture the distinctive anisotropic effect induced by the micro-structures of clay particle aggregate, clusters, peds, micro-fabric and mineral contact, we use a mapping the links the anisotropic stress state to a fictitious stress space to introduce anisotropy to the modified Cam-clay model at the material point scale. Meanwhile, the meso-scale aniostropy is captured via an anisotropic micromorphic regularization model such that the gradient-enhanced plastic flow may exhibit anisotropic responses via a diffusivity tensor. This diffusivity tensor enables the micromorphic regularized model to exhibit plastic flow non-co-axial to the stress gradient of the yield function without introducing non-associate flow rules and hence provide additional degree of freedom for modelers to capture the size-dependent ansiotropy of geological materials that exhibit different anisotropic responses across different length scales. Numerical examples are used to examine the volumetric locking and numerical stability issues that may occur at critical state where isochoric plastic flow dominates the deformation mode. In particular, we present evidence that the micromorphic regularization could also be a potential remedy to overcome the volumetric locking and the spurious checkerboard modes. The influence of the size-dependent anisotropy on the formation and propagation of shear band in the anisotropic material is demonstrated. In the future, we will explore coupling to a phase field fracture model, in order to predict the wide spectrum of brittle and ductile anisotropic responses.

Abstracts: 
We introduce a multi-agent meta-modeling game to generate data, knowledge, and models that make predictions on constitutive responses of elasto-plastic materials. We introduce a new concept from graph theory where a modeler agent is tasked with evaluating all the modeling options recast as a directed multigraph and find the optimal path that links the source of the directed graph (e.g. strain history) to the target (e.g. stress) measured by an objective function. Meanwhile, the data agent, which is tasked with generating data from real or virtual experiments (e.g. molecular dynamics, discrete element simulations), interacts with the modeling agent sequentially and uses reinforcement learning to design new experiments to optimize the prediction capacity. Consequently, this treatment enables us to emulate an idealized scientific collaboration as selections of the optimal choices in a decision tree search done automatically via deep reinforcement learning.  Preprint available at ResearchGate [URL]. 

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.