This article introduces a unified mathematical framework to replicate both desiccation-induced and hydraulic fracturing in low-permeable unsaturated porous materials observed in experiments. The unsaturated porous medium is considered as a three-phase solid-liquid-gas effective medium of which each constituent occupies a fraction of the representative elementary volume. As such, an energy-minimization-based phase-field model (PFM) is formulated along with the Biot's poroelasticity theory to replicate the sub-critical crack growth in the brittle regime.

Unlike hydraulic fracturing where the excess pore liquid pressure plays an important role at the onset and propagation of cracks, desiccation cracks are mainly driven by deformation induced by water retention. Therefore, the wettability of the solid skeleton may affect the evolution of the capillary pressure (suction) and change the path-dependent responses of the porous media. This air-water-solid interaction may either hinder or enhance the cracking occurrence. This difference of capillary effect on crack growth during wetting and drying is replicated by introducing retention-sensitive degradation mechanisms in our phase field fracture approach. To replicate the hydraulic behaviors of the pore space inside the host matrix and that of the cracks, the path-dependent changes of the intrinsic permeability due to crack growth and porosity changes are introduced to model the flow conduit in open and closed cracks. Numerical examples of drying-induced and hydraulic fracturing demonstrate the capability of the proposed model to capture different fracture patterns, which qualitatively agrees with the fracture mechanisms of related experiments documented in the literature. [PDF]

The ability to model, predict, and improve the mechanical performance of engineering materials such as polymers, composites, and alloys can have a significant impact on manufacturing, with important economic and societal benefits. As advanced computational algorithms and data science approaches become available, they can be harnessed to disrupt the current approaches to materials modeling, and allow for the design and discovery of new high-strength, high-performance materials for manufacturing. Bringing together multidisciplinary teams of researchers can maximize the impact of these new tools and techniques. This Harnessing the Data Revolution Institutes for Data-Intensive Research in Science and Engineering (HDR-I-DIRSE) award supports the conceptualization of an Institute to develop novel data science methods, address fundamental scientific questions of Materials Engineering and Manufacturing, and build such multidisciplinary teams. The project will apply novel data science methods to advance the analysis of large sets of structural data of composite materials and alloys from the atomic scale to correlate with and predict mechanical properties. The methods are based on machine learning techniques and uncertainty quantification, and will help uncover underlying structural features in the materials that determine the properties and performance. The methods and results will help accelerate the development of ultra-high strength and lightweight carbon-based composites for aerospace applications, and multi-element superalloys for more durable engine parts, by navigating in the large possible design space and providing faster predictions than experiments and traditional simulation methods. The project will also lead to new methods and computational algorithms that will become publicly available. The investigators will train graduate and undergraduate students from various disciplines with a focus on engaging women and minorities in STEM fields, develop short courses that integrate novel Materials Science and Engineering applications and Data Science methods, and foster vertical integration of interdisciplinary research from undergraduate students to senior scientists.

This project aims at building an effective and interpretable learning framework for materials data across scales to solve a major challenge in current data-driven materials design. The combined Materials Science and Data Science approaches will synergistically contribute to the development and use of interpretable and physics-informed data science methodologies to gain new understanding of mechanical properties of polymer composites and alloys, with the potential to be expanded into different property sets and different systems. The PIs will utilize available data efficiently through combination with physical rules and prior knowledge, to develop an interpretable augmented intelligent system to learn principles behind the association of input structures with material properties with uncertainty quantification. The interconnected tasks involve the (1) collection and curation of large amounts of computational and experimental data for polymer/carbon nanotube composites and alloys from open data sources and targeted calculations and experiments, (2) the development of geometric and topological methods incorporating physical principles to generate a better, more sensitive low-dimensional representation of the multidimensional data and characterize the parameter space related to mechanical properties, (3) the development of a Bayesian deep reinforcement learning framework to generate interpretable knowledge graphs that depict the relational knowledge among physical quantities with uncertainty quantification, and (4) the prediction of mechanical properties to reveal design principles to improve materials performance, evaluate and validate the methods, and develop software for dissemination.

This project is part of the National Science Foundation's Harnessing the Data Revolution (HDR) Big Idea activity and is co-funded by the Division of Civil, Mechanical and Manufacturing Innovation.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

More information can be found in the official announcement from NSF [URL].

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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]

#1971999 -

02:00 - 02:20

Minisymposium#203 Data-driven Modeling Using Uncertainty Quantification, Machine Learning and Optimization

Authors Kun Wang ,

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 -

02:20 - 02:40

Minisymposium#105 Computational Geomechanics, in honor of Prof. Mary F. Wheeler

Authors

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 -

05:30 - 05:50

Minisymposium#105 Computational Geomechanics, in honor of Prof. Mary F. Wheeler

Authors

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.]]>

**1. A multiscale FE-FFT approach for modeling crack initiation and propagation in polycrystalline rock salt. **Poster** **presentation by postdoc research scientist Dr. Ran Ma.

Rock salt formations are widely considered as potential sites for underground repositories for nuclear wastes due to the low permeability and high thermal conductivity. Nevertheless, the nearly impermeable rock salt may exhibit material failures, such as strain localization and fractures such that leakage may occur within the excavation distributed zone. Crack initiation and propagation within these regions are difficult to predict using conventional damage-plasticity model, due to the anisotropic nature originated from the microstructures of the polycrystal salt. While the phase field fracture model may be effective to reproduce complex fracture patterns at small scales, the length scale material parameter nevertheless limits the mesh size and hence not suitable for field-scale simulations. In this work, we provide an FE-FFT multiscale method for polycrystal rock salt. In the microscale, a fast Fourier transform (FFT) based method is employed to explicitly model the interaction between microcrack and grain boundary, while the microscale quantities are homogenized to investigate the macroscale damage distribution within bulk rock salt. By introducing modification on the Hill-Mandel lemma for the phase field energy-conjugate pair, we introduce upscaling procedure such that the anisotropic responses can be captured. Numerical examples on polycrystal are used to demonstrate the accuracy, robustness, and efficiency of the proposed scheme.

**2. A cooperative game for automated learning of elastoplasticity knowledge graphs and models with AI-guided experimentation**. Oral presentation by the PI (WaiChing Sun). MS25, Room: 142 Keck (72) Thursday 20th 10:30 am-10:45 am

We introduce a multi-agent meta-modeling game to generate data, knowledge, and models that make predictions on constitutive responses of elasto-plastic materials. Based on concepts from directed multigraph theory, we introduce deep reinforcement learning to train two artificial intelligence agents tasked with generating models and data respectively. In this cooperative game, the modeling agent explores all the possible ways to interpret and represent the cause-and-effect relationships among physical attributes and finds an optimal subgraph. This subgraph is the resultant information flow that optimizes an objective function designed to make the most plausible blind prediction for history-dependent materials. We focus on an idealized situation in which the modeling process of path-dependent materials can be represented by a sequence of choice-making decisions where choices (e.g. yield surfaces, flow rules for plastic deformation, strain hardening laws) are made to formulate a sequence of actions to generate constitutive laws. 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 target (e.g. stress). 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.

**3. An adaptive ensemble phase field predictions for localized failures in geological materials**. Oral presentation by the PI of Sun group. MS25, Room: 142 Keck (72) Thursday 20th 10:45 am-11:00 am

This work presents an adaptive phase field method to employ ensemble predictions for history-dependent materials. We consider a case in which the material responses of a domain can be captured by a weighted sum of constitutive responses from surrogate models, each associated with one phase field and is specialized in one type of predictions (e.g. contractive shear band, mixed-mode fracture). A deep recurrent network is used to generate the driving force that governs the weight function in the space-time continuum. Consequently, the high-fidelity sub-scale modeling is only used to generate incremental constitutive updates in the regions where all surrogate models fail to make good blind predictions and hence become necessary. Meanwhile, the region of less importance is first identified, then assign to a fast surrogate model to enhance efficiency. In the transiting zone where new model is activated, we propose methods to transfer variables that represent loading history among different models. The surrogate models can be automatically generated from our previously developed meta-modeling procedure using experimental data according to different objective functions. As an example, we apply this idea to formulate this multi-model framework to predict two common classes of material failures, brittle fracture and strain localization. A multi-fold cross-validation exercise is conducted to examine the speed, robustness and accuracy of the multi-model predictions.

**4. A micromorphic-regularized anisotropic Cam-clay-type model for capturing size-dependent anisotropy**. Oral presentation by PhD student Eric Bryant, MS25, Room: 142 Keck (72) Thursday 20th 10:30 am-10:45 am

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 freedoms for modelers to capture the size-dependent ansiotropy of geomaterials that exhibits different anisotropic responses across different length scales. Numerical examples are used to examine the volumetric locking and numerical stability issues that may occur at the 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.

**5. Shift domain material point method: an image-to-simulation workflow for solids of complex geometries undergoing large deformation. **Oral presentation by postdoc research scientist Chuanqi Liu, MS25, Room: 142 Keck (72) Thursday 20th 11:30 am-11:45 am

We introduce a mathematical framework designed to enable a simple image-to-simulation workflow for solids of complex geometries undergoing large deformation in the geometrically nonlinear regime. In particular, we adopt the integration scheme of the material point method to resolve the convergent issues for Lagrangian meshes due to mesh distortion, while using a shifted domain technique originated from Main and Scovazzi 2018 to represent the boundary condition 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-indifference 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.

**6. Adaptive mesh-refinement for poromechanics Problems of high-order continua: a configurational force approach**, Oral presentation given by Professor SeonHong Na (PhD graduate and former research scientist of the group, now assistant professor at McMaster University), Room 142 Keck (72), Friday 21st, 2 pm-2:15 pm.

Mechanical and hydraulic behaviors of many geological materials, such as clay, limestone, and sedimentary rock are inherently anisotropy and size-dependent. This size-dependence can be exploited to formulate high-order models that circumvents the pathological mesh dependence in the softening regimes. However, the onset of deformation band and other forms of strain localization may still lead to sharp displacement and pore pressure gradients that must be resolved properly to maintain accuracy. To resolve this issue, we derive a new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow. This configurational force takes account of the energy flux due to the gradient terms and hence is a suitable remeshing criterion for higher-order continua. In addition, a Lie algebra internal variable mapping is used such that the history-dependent behaviors for the new configuration can be captured in the new equilibrate state. Our numerical results indicate that the proposed method enables one to resolve sharp gradient without an initial fine mesh. This salient feature is important for simulating hydro-mechanical coupling behaviors in the post-bifurcation regimes.

**7. Bootstrapping critical state plasticity models for predicting cyclic undrained responses of granular Materials with a hierarchical knowledge polytree**. Oral presentation by Nikolaos Vlassis, Wednesday 19th, 11:45 am-12:00 pm.

Predicting cyclic responses of undrained granular materials is a notoriously difficult task. Despite the significant progress made in constitutive modeling, the most advanced elasto-plastic material models typically only yield qualitatively matching predictions on the stress path and pore pressure time history. In this work, we attempt an alternative approach in which multiple material models, each with different strengths and weaknesses are collectively used to make ensemble predictions with an adaptive weighting function. This weighting function is inferred from a hierarchical knowledge graph generated by unsupervised learning. In particular, a set of experimental data is decomposed into multiple subsets via data clustering applied multiple times across scales. These clustered data are then used to train specific models with desirable traits tailored to each cluster. Predictions are then made by weight-averaging these highly specialized models in which the weight evolves to maximize an objective function that estimates the accuracy of the predictions. This divide-and-conquer approach enables complex behaviors to be replicated by simpler predictions propagating through a hierarchy of knowledge mathematically represented by a directed graph. K-fold validation exercises are used to compare this big data approach with the established constitutive laws to analyze the robustness, accuracy, and efficiency of the proposed method.

]]>

Rock salt formations are widely considered as potential sites for underground repositories for nuclear wastes due to the low permeability and high thermal conductivity. Nevertheless, the nearly impermeable rock salt may exhibit material failures, such as strain localization and fractures such that leakage may occur within the excavation distributed zone. Crack initiation and propagation within these regions are difficult to predict using conventional damage-plasticity model, due to the anisotropic nature originated from the microstructures of the polycrystal salt. While the phase field fracture model may be effective to reproduce complex fracture patterns at small scales, the length scale material parameter nevertheless limits the mesh size and hence not suitable for field-scale simulations. In this work, we provide an FE-FFT multiscale method for polycrystal rock salt. In the microscale, a fast Fourier transform (FFT) based method is employed to explicitly model the interaction between microcrack and grain boundary, while the microscale quantities are homogenized to investigate the macroscale damage distribution within bulk rock salt. By introducing modification on the Hill-Mandel lemma for the phase field energy-conjugate pair, we introduce upscaling procedure such that the anisotropic responses can be captured. Numerical examples on polycrystal are used to demonstrate the accuracy, robustness, and efficiency of the proposed scheme.

We introduce a multi-agent meta-modeling game to generate data, knowledge, and models that make predictions on constitutive responses of elasto-plastic materials. Based on concepts from directed multigraph theory, we introduce deep reinforcement learning to train two artificial intelligence agents tasked with generating models and data respectively. In this cooperative game, the modeling agent explores all the possible ways to interpret and represent the cause-and-effect relationships among physical attributes and finds an optimal subgraph. This subgraph is the resultant information flow that optimizes an objective function designed to make the most plausible blind prediction for history-dependent materials. We focus on an idealized situation in which the modeling process of path-dependent materials can be represented by a sequence of choice-making decisions where choices (e.g. yield surfaces, flow rules for plastic deformation, strain hardening laws) are made to formulate a sequence of actions to generate constitutive laws. 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 target (e.g. stress). 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.

This work presents an adaptive phase field method to employ ensemble predictions for history-dependent materials. We consider a case in which the material responses of a domain can be captured by a weighted sum of constitutive responses from surrogate models, each associated with one phase field and is specialized in one type of predictions (e.g. contractive shear band, mixed-mode fracture). A deep recurrent network is used to generate the driving force that governs the weight function in the space-time continuum. Consequently, the high-fidelity sub-scale modeling is only used to generate incremental constitutive updates in the regions where all surrogate models fail to make good blind predictions and hence become necessary. Meanwhile, the region of less importance is first identified, then assign to a fast surrogate model to enhance efficiency. In the transiting zone where new model is activated, we propose methods to transfer variables that represent loading history among different models. The surrogate models can be automatically generated from our previously developed meta-modeling procedure using experimental data according to different objective functions. As an example, we apply this idea to formulate this multi-model framework to predict two common classes of material failures, brittle fracture and strain localization. A multi-fold cross-validation exercise is conducted to examine the speed, robustness and accuracy of the multi-model predictions.

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 freedoms for modelers to capture the size-dependent ansiotropy of geomaterials that exhibits different anisotropic responses across different length scales. Numerical examples are used to examine the volumetric locking and numerical stability issues that may occur at the 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.

We introduce a mathematical framework designed to enable a simple image-to-simulation workflow for solids of complex geometries undergoing large deformation in the geometrically nonlinear regime. In particular, we adopt the integration scheme of the material point method to resolve the convergent issues for Lagrangian meshes due to mesh distortion, while using a shifted domain technique originated from Main and Scovazzi 2018 to represent the boundary condition 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-indifference 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.

Mechanical and hydraulic behaviors of many geological materials, such as clay, limestone, and sedimentary rock are inherently anisotropy and size-dependent. This size-dependence can be exploited to formulate high-order models that circumvents the pathological mesh dependence in the softening regimes. However, the onset of deformation band and other forms of strain localization may still lead to sharp displacement and pore pressure gradients that must be resolved properly to maintain accuracy. To resolve this issue, we derive a new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow. This configurational force takes account of the energy flux due to the gradient terms and hence is a suitable remeshing criterion for higher-order continua. In addition, a Lie algebra internal variable mapping is used such that the history-dependent behaviors for the new configuration can be captured in the new equilibrate state. Our numerical results indicate that the proposed method enables one to resolve sharp gradient without an initial fine mesh. This salient feature is important for simulating hydro-mechanical coupling behaviors in the post-bifurcation regimes.

Predicting cyclic responses of undrained granular materials is a notoriously difficult task. Despite the significant progress made in constitutive modeling, the most advanced elasto-plastic material models typically only yield qualitatively matching predictions on the stress path and pore pressure time history. In this work, we attempt an alternative approach in which multiple material models, each with different strengths and weaknesses are collectively used to make ensemble predictions with an adaptive weighting function. This weighting function is inferred from a hierarchical knowledge graph generated by unsupervised learning. In particular, a set of experimental data is decomposed into multiple subsets via data clustering applied multiple times across scales. These clustered data are then used to train specific models with desirable traits tailored to each cluster. Predictions are then made by weight-averaging these highly specialized models in which the weight evolves to maximize an objective function that estimates the accuracy of the predictions. This divide-and-conquer approach enables complex behaviors to be replicated by simpler predictions propagating through a hierarchy of knowledge mathematically represented by a directed graph. K-fold validation exercises are used to compare this big data approach with the established constitutive laws to analyze the robustness, accuracy, and efficiency of the proposed method.

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].

Below is the list of published work Kun finished during his PhD study with our group. Congratulations, Kun! Well deserved!

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, An updated Lagrangian LBM-DEM-FEM coupling model for dual-permeability porous media with embedded discontinuities,*Computer Methods in Applied Mechanics and Engineering*, 344:276-305, doi:10.1016/j.cma.2018.09.034, 2019. [PDF][Bibtex]**K. Wang**, W.C. Sun, Meta-modeling game for deriving theory-consistent, micro-structure-based traction-separation laws via deep reinforcement learning,*Computer Methods in Applied Mechanics and Engineering,*accepted, 346:216-241, doi:10.1016/j.cma.2018.11.026, 2019. [PDF][Bibtex]**K. Wang**, W.C. Sun, Q. Du, A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation, submitted to*Computational Mechanics, special issue on data-driven modeling and simulation: theory, methods and applications,*2019.

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] ]]>