Abstract:

This paper examines the frame-invariance  (and the lack thereof) exhibited in simulated anisotropic elasto-plastic responses generated from supervised machine learning of classical multi-layer and informed-graph-based neural networks, and proposes different remedies to fix this drawback. The inherent  hierarchical relations among physical quantities and state variables in an elasto-plasticity model are first represented as directed graphs,  where three variations of the graph are tested. While feed-forward neural networks are used to train path-independent constitutive relations (e.g., elasticity), recurrent neural networks are used to replicate responses that depends on the deformation history, i.e. or path dependent. In dealing with the objectivity deficiency, we use the spectral form to represent tensors and, subsequently, three metrics, the Euclidean distance between the Euler Angles, the distance from the identity matrix, and geodesic on the unit sphere in Lie algebra, can be employed to constitute objective functions for the supervised machine learning. In this, the aim is to minimize the measured distance between the true and the predicted 3D rotation entities. Following this, we conduct numerical experiments on how these metrics, which are theoretically equivalent, may lead to differences in the efficiency of the supervised machine learning as well as the accuracy and robustness of the resultant models. Neural network models trained with tensors represented in component form for a given Cartesian coordinate system are used as a benchmark. Our numerical tests show that, even given the same amount of information and data, the quality of the anisotropic elasto-plasticity model is highly sensitive to the way tensors are represented and measured. The results reveal that using a loss function based on geodesic on the unit sphere in Lie algebra together with an informed directed graph yield significantly more accurate rotation prediction than the other tested approaches. [PDF]

We are a part of the multi-university team who has been awarded a 2 million grant for leveraging interpretable  augmented intelligence for multiscale discovery. 

Award Abstract #1940203

Collaborative Research: I-AIM: Interpretable Augmented Intelligence for Multiscale Material Discovery

NSF Org:Office of Advanced Cyberinfrastructure (OAC)

ABSTRACT

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].  

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].