PhD student Nick Vlassis​ passed the qualification exam. Nick's work focuses on incorporating geometric learning for computational plasticity problems with special emphasis on applications related to polycrystalline and energetic materials. In the proposal presentation, Nick presented the work of two of his recent papers published in CMAME (see list below). Nick also recently received the WCCM Fellowship to attend the conference at Paris but the meeting has been converted into virtual format due to the pandemic (see video below). Congratulations for this accomplishment, Nick!
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Link for the seminar: https://lnkd.in/ePAJrUY Predicting the hysteresis retention behaviors of wetted porous media with a hand-crafted model can be a difficult task, especially for deformable porous media undergoing multiple wetting and drying cycles. In this, work, we introduce a model-free reinforcement learning algorithm that functions as an AI agent to design a recurrent neural network that predicts the water recurrent of a porous medium. As such, the AI agent may conduct numerous trial-and-errors to fine-tune the hyperparameters and design the neural network that yields the optimal performance. Preprint available at [URL]. In this work, our goal is to create a generic meta-model that generates constitutive laws for any rate-independent elastoplastic solid with non-vanishing yield surface. Instead of introducing complex neural network to facilicate the machine learning, we break down the process of writing constitutive laws into multiple parts (elasticity, yield surface evolution and plastic flow) each associated with a supervised learning problem designed for generating functionals with properties. This meta-model enable us to (1) more effectively explore the parametric space (i.e. knowing which experiments will improve the model performance), (2) discover previously unknown hardening/softening mechanisms (e.g. any deformation and translation of the yield surface in the principal stress space and the extension to general stress space), and (3) enforce/examine thermodynamic constraints (e.g. Drucker's Postulate) #machinelearning4mechanics #materialmodels. Preprint available [here]. An immersed phase field fracture model for microporomechanics with Darcy–Stokes flow Physics of Fluids 33, 016603 (2021); https://doi.org/10.1063/5.0035602 Hyoung Suk Suh (서형석) and WaiChing Sun (孫維正) ABSTRACT This paper presents an immersed phase field model designed to predict the fracture-induced flow due to brittle fracture in vuggy porous media. Due to the multiscale nature of pores in the vuggy porous material, crack growth may connect previously isolated pores, which leads to flow conduits. This mechanism has important implications for many applications such as disposal of carbon dioxide and radioactive materials and hydraulic fracture and mining. To understand the detailed microporomechanics that causes the fracture-induced flow, we introduce a new phase field fracture framework where the phase field is not only used as an indicator function for damage of the solid skeleton but also used as an indicator of the pore space. By coupling the Stokes equation that governs the fluid transport in the voids, cavities, and cracks and Darcy’s flow in the deformable porous media, our proposed model enables us to capture the fluid–solid interaction of the pore fluid and solid constituents during crack growth. Numerical experiments are conducted to analyze how the presence of cavities affects the accuracy of predictions based on the homogenized effective medium during crack growth.  For some polycrystalline materials such as austenitic stainless steel, magnesium, TATB, and HMX, twinning is a crucial deformation mechanism when the dislocation slip alone is not enough to accommodate the applied strain. To predict this coupling effect between crystal plasticity and deformation twinning, we introduce a mathematical model and the corresponding monolithic and operator splitting solver that couples the crystal plasticity material model with a phase field twining model such that the twinning nucleation and propagation can be captured via an implicit function. While a phase-field order parameter is introduced to quantify the twinning induced shear strain and corresponding crystal reorientation, the evolution of the order parameter is driven by the resolved shear stress on the twinning system. To avoid introducing an additional set of slip systems for dislocation slip within the twinning region, we introduce a Lie algebra averaging technique to determine the Schmid tensor throughout the twinning transformation. Three different numerical schemes are proposed to solve the coupled problem, including a monolithic scheme, an alternating minimization scheme, and an operator splitting scheme. Three numerical examples are utilized to demonstrate the capability of the proposed model, as well as the accuracy and computational cost of the solvers. [preprint] There are many journal articles dedicated to constitutive models that show good matches on selected data. However, how useful are these models if we don't report or know their weakness? Our recently accepted CMAME paper uses deep reinforcement learning and game theory to explore this important question. By conceptualizing the efforts to validating and falsifying the model as a competing activities, we introduce AI agents to compete against each others to explore each others' weakness and through competition improving the resultant model and finding the Nash equilibrium that represents the limits of the state-of-the-art of each model, hand-crafted or AI-generated. The interesting aspect is that this competition can be applied to any material laws and data set. Please consider submit data/model to us and we can validate and falsify the model for you. More information can be found in the preprint [PDF]. The lectures for the entire 3-day workshop can be found at the official website of ALERT. alertgeomaterials.eu/2020/10/videos-of-the-doctoral-school-2020/ Special thanks to the organizers, Professors Wei Wu and Manuel Pastor, and the colleagues who attend the talks. PhD student Hyoung Suk Suh passed the qualification exam. His work is on modeling the thawing and freezing of frozen porous media. In the proposal talk, Hyoung Suk introduces the mathematical framework requires to simulate the freezing and thawing of porous media at the pore scale (see the rehearsal Youtube Video below). Since joining the research group in Fall 2018, Hyoung Suk has published two journal articles and one conference paper.
H.S. Suh, D. O'Conner, W.C. Sun, A phase field model for cohesive fracture in micropolar continua, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2020.113181, 2020. H.S. Suh, W.C. Sun, An open source FEniCS implementation of a phase field fracture model for micropolar continua, International Journal of Multiscale Computational Engineering, doi:10.1615/IntJMultCompEng.2020033422, 2019. [open source code] H.S. Suh, W.C. Sun, An immersed phase field fracture model in fluid-infiltrating porous media with evolving Beavers-Joseph-Saffman condition, 2nd International Conference on Energy Geotechnics, La Jolla, California, USA, 2021. Congratulations, Hyoung Suk!  I am excited to announce that our PhD student Eric Bryant has successfully defended his dissertation "Capturing Evolving Size-Dependent Anisotropy from Brittle Fracture to Plasticity for Geological Materials" and will join Los Alamos National Laboratory as postdoc research associate. His primary appointment will be with the fluid dynamics and solid mechanics group of the Theoretical Division (T-3). During his tenure in the Sun research group, Eric has been awarded the Presidential Fellowship and the Guggenheim Fellowship. His PhD work focuses on modeling the size effect of evolving anisotropy of fracture and plastic deformation. Traditionally, one may introduce scaling law to incorporate how shear and tensile strengths depend on the size of the specimen. In his work, the main focus is also to investigate how does the rotation among the principal directions of the elastic strain, tensorial internal variables and stress tensor evolves across length scales and during the deformation process. He is the authors of 4 journal articles and one manuscript very close to completion. Among them, three of them published in Computer Methods in Applied Mechanics and Engineering, and one in International Journal of Fracture as listed below. Congratulations, Eric! Published work:
Author: Nikolas Vlassis, WaiChing Sun Abstract: We present a machine learning approach that integrates geometric deep learning and Sobolev training to generate a family of finite strain anisotropic hyperelastic models that predict the homogenized responses of polycrystals previously unseen during the training. While hand-crafted hyperelasticity models often incorporate homogenized measures of microstructural attributes, such as the porosity or the averaged orientation of constitutes, these measures may not adequately reflect the topological structures of the attributes. We fill this knowledge gap by introducing the concept of the weighted graph as a new high-dimensional descriptor that represents topological information, such as the connectivity of anisotropic grains in an assemble. By leveraging a graph convolutional deep neural network in a hybrid machine learning architecture previously used in Frankel et al. 2019, the artificial intelligence extracts low-dimensional features from the weighted graphs and subsequently learns the influence of these low-dimensional features on the resultant stored elastic energy functionals. To ensure smoothness and prevent unintentionally generating a non-convex stored energy functional, we adopt the Sobolev training method for neural networks such that a stress measure is obtained implicitly by taking directional derivatives of the trained energy functional. Results from numerical experiments suggest that Sobolev training is capable of generating a hyperelastic energy functional that predicts both the elastic energy and stress measures more accurately than the classical training that minimizes L2 norm. Verification exercises against unseen benchmark FFT simulations and phase-field fracture simulations using the geometric learning generated elastic energy functional are conducted to demonstrate the quality of the predictions. [manuscript]
Presenter: Dr. Steve WaiChing Sun, Columbia University Title: Some applications of graph theory in data-driven multi-scale mechanics Video: Watch a recording of the seminar Abstract: In this talk, we will share our experience in using undirected and directed graphs to solve computational solid mechanics problems with a variety of deep neural networks. In the first half of the talk, we will focus on the usage of undirected weighted graphs that represent the microstructures. We will demonstrate 1) how to effectively represent microstructures such as polycrystals, granular assemblies and composites as node-weighted graphs, a network of nodes with assigned attributes connected by edges, 2) how to create low-dimensional topological descriptors via graph convolution neural network that exhibits spatial and rotational invariance properties and 3) how these topological descriptors can be used to enhance the accuracy and robustness of the forward predictions and generalize the surrogate constitutive models generated via semi-supervised learning. In the second half of the talk, we will examine the application of directed multi-graphs that represent causality/relational knowledge of material laws. By idealizing the process of modeling constitutive laws as a multi-player game, we will examine 4) how the process of writing, validating and falsifying a constitutive law can be formulated as a Markov decision process, and 5) how a model-free deep reinforcement learning paradigm can introduce artificial intelligence (AI) modelers and experimentalists that learn to create hand-crafted-like constitutive models through competitions and repeated trial and errors. Examples will be provide to illustrate how these self-interacting, self-improving AI agents discover new hidden hierarchical structures of mechanics knowledge, spot the weakness of existing models and create new approaches to incorporate non-Euclidean data traditionally excluded in constitutive laws to make predictions more accurate and robust.  Our postdoctoral research scientist Chuanqi Liu has just received an offer from the Institute of Mechanics in the Chinese Academy of Sciences (CAS). He is selected by the 100 talent program (pioneering project) of CAS and is offered the position as an associate professor. During his tenure with us, Chuanqi has been a productive member of our team and has published the following peer-reviewed articles:
Congratulations, Chuanqi! We present a new thermal-mechanical-chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt. This paper is Part II of our work on modeling polycrystal salt for nuclear waste disposal. Reference
While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the material is non-polar and yet a length scale parameter must be introduced to enable the sharp cracks represented by a regularized implicit function. However, many materials with internal microstructures that contain surface tension, micro-cracks, micro-fracture, inclusion, cavity or those of particulate nature often exhibit size-dependent behaviors in both the path-independent and path-dependent regimes. This paper is intended to introduce a unified treatment that captures the size effect of the materials in both elastic and damaged states. By introducing a cohesive micropolar phase field fracture theory, along with the computational model and validation exercises, we explore the interacting size-dependent elastic deformation and fracture mechanisms exhibits in materials of complex microstructures. To achieve this goal, we introduce the distinctive degradation functions of the force-stress-strain and couple-stress-micro-rotation energy-conjugated pairs for a given regularization profile such that the macroscopic size-dependent responses of the micropolar continua is insensitive to the length scale parameter of the regularized interface. Then, we apply the variational principle to derive governing equations from the micropolar stored energy and dissipative functionals. Numerical examples are introduced to demonstrate the proper way to identify material parameters and the capacity of the new formulation to simulate complex crack patterns in the quasi-static regime. [manuscript] One key drawback of classical discrete/distinct/granular element methods for particulate mechanics is that they cannot generate any kinetic and kinematics information at the sub-grain scales. Nevertheless, many dissipative mechanisms of granular materials are actually originated from path-dependent behaviors at the sub-grain scales where wear, damage, fracture and fragmentation occurs. This simplification therefore may lead to a departure of force chain topology and therefore make the resultant simulations inaccurate. Recovery of these sub-scale information while capturing the geometry and form of each individual grains is inherently a difficult task. In this work, our postdoc Dr. Chuanqi Liu introduces an implicit material point method designed to bypass meshing of bodies by employing level set functions to represent boundaries at structured grids. This implicit function representation provides an elegant means to link an unbiased intermediate reference surface with the true boundaries by closest point projection as shown Leichner et al. 2019. We then enforce the contact constraints by a penalty method where the Coulomb friction law is implemented as an elastoplastic constitutive model such that a return mapping algorithm can be used to provide constitutive updates for both the stick and slip states. To evolve the geometry of the contacts properly, the Hamilton-Jacobi equation is solved incrementally such that the level set and material points are both updated according to the deformation field. To improve the accuracy and regularity of the numerical integration of the material point method, a moving least square method is used to project numerical values of the material points back to the standard locations for Gaussian-Legendre quadrature. Several benchmarks are used to verify the proposed model. Comparisons with discrete element simulations are made to analyze the importance of stress fields on predicting the macroscopic responses of granular assemblies. [manuscript]  In recognition of his groundbreaking research illuminating the mechanics and physics of porous geomaterials like rocks, soil, concrete and salt, Professor Steve WaiChing Sun has earned the prestigious John Argyris Award for Young Scientists. This award is given by the International Association for Computational Mechanics (IACM).
Bridging mathematical science, theoretical mechanics, and industrial applications, Sun’s interests focus on computational poromechanics and geomechanics for a variety of applications, ranging from carbon dioxide storage to disposal of nuclear waste. In addition to the John Argyris award, Sun has received several prominent international awards in theoretical and computational mechanics, including the Zienkiewicz Numerical Methods in Engineering Prize from Institution of Civil Engineers (UK), the ASCE Engineering Mechanics Institute Leonardo de Vinci Award (USA), Dresden Fellowship (Germany), as well as the young investigator awards from funding agencies, including the US National Science Foundation CAREER Award, the US Air Force Young Investigator Program Award, and the US Army Young Investigator Program Award. Highlighting distinguished scholarship and outstanding accomplishments, the biennial John Argyris Award for Young Scientists celebrates influential researchers 40 and under. Sun, an assistant professor of civil engineering and engineering mechanics since 2014, will be the first Columbia faculty member and the first Chinese American to receive this honor. He will receive the award at the opening ceremony for the joint organization of the 14th IACM World Congress in Computational Mechanics and the 8th European Congress on Computational Methods in Applied Science and Engineering this summer in Paris. [URL] My colleagues and I have obtained the approval from the board of governors of ASCE EMI to establish a new committee in the ASCE Engineering Mechanics Institute for applying machine learning to AI. The first meeting for this new committee will occur during the ASCE EMI conference at Columbia University this coming May. See [URL]
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] Abstract: This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a pre-conditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks. [PDF] A phase field framework for capillary-induced fracture in unsaturated porous media: drying-induced vs. hydraulic cracking Abstract: 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] 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] |
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