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Author: Xiao Sun, Bahador Bahmani, Nikolaos N. Vlassis, WaiChing Sun, Yanxun Xu Abstract: This paper presents a computational framework that generates ensemble predictive mechanics models with uncertainty quantification (UQ). We first develop a causal discovery algorithm to infer causal relations among time-history data measured during each representative volume element (RVE) simulation through a directed acyclic graph (DAG). With multiple plausible sets of causal relationships estimated from multiple RVE simulations, the predictions are propagated in the derived causal graph while using a deep neural network equipped with dropout layers as a Bayesian approximation for uncertainty quantification. We select two representative numerical examples (traction-separation laws for frictional interfaces, elastoplasticity models for granular assembles) to examine the accuracy and robustness of the proposed causal discovery method for the common material law predictions in civil engineering applications. The preprint is available at [URL]. The key ideas are to explore if causal discovery algorithm can deduce the plausible causal relations and whether the discovered causal relations match with our current state-of-the-art knowledge discovered by human. One interesting aspect I found quite interesting is that, while incorporating the causal relation into the deep learning constitutive laws might improve the interpretability, it does not always improve the accuracy (for instance, when prediction the properties of the immediate vertices is harder than that of the leaves of the causal graph).
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Abstract: Cyclotetramethylene-Tetranitramine (HMX) is a secondary explosive used in military and civilian applications. Its plastic deformation is of importance in the initiation of the decomposition reaction, but the details of plasticity are not yet fully understood. It has been recently shown that both the elastic constants and the critical resolved shear stress for plastic deformation are pressure sensitive. Since initiation takes place during shock loading, the pressure sensitivity of plasticity is highly relevant. In this work, we examine the pressure-sensitivity of the dynamic mechanical behavior of HMX. To this end, we use an elastic-plastic continuum constitutive model of single crystal HMX in which the anisotropic elastic constants and direction-dependent yield stress are rendered pressure-sensitive. The pressure sensitivity is calibrated based on input from molecular models. We observe that accounting for pressure sensitivity changes significantly the profile of the elastic-plastic wave and the wave propagation speed upon impact. The accumulated dissipation profile and the total dissipation also exhibit profound differences between the simulations that take account of the pressure-dependence of the plastic deformation and the pressure independent counterpart. Preprint: [PDF] 1. An immersed phase field model for fracture-induced Darcy-Stokes flow (presented by PhD student Hyoung Suk Suh). Invited paper published in Physics of Fluid [URL] 2. An accelerated model-free poroelasticity solver with multifidelity multiphysics data (presented by PhD student Bahador Bahmani). Paper accepted by CMAME [URL] 3. AI-generated interpretable plasticity theory (presented by PhD student Nick Vlassis). Paper accepted by CMAME [URL] 4. Crystal plasticity with precipitation creeping, crack growth and healing in rock salt (presented by associate research scientist Dr. Ran Ma). Paper accepted in CMAME [URL] 5. Domain Partitioning MPM for thermomechanical contact mechanics with fragmentation (presented by PhD student Mian Xiao). Paper under review. 6. ILS-MPM: an implicit level-set-based material point method for contact mechanics (presented by former postdoctoral research scientist, now associate professor of Chinese Academy of Sciences, Prof. Chuanqi Liu). Paper accepted in CMAME [URL] 7. Digital rock physics via FFT Solver (presented by PhD student Zeyu Xiong). 8. Numerical Investigation on freezing and thawing of saturated soil (presented by postdoc research scientist Dr. Qing Yin). Title: A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics dataata Abstract: We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer & Ortiz 2016, we introduce one model-free and two hybrid model-based/data-driven formulations capable of simulating the coupled diffusion-deformation of fluid-infiltrating porous media with different amounts of available data. To improve the efficiency of the model-free data search, we introduce a distance-minimized algorithm accelerated by a k-dimensional tree search. To handle the different fidelities of the solid elasticity and fluid hydraulic constitutive responses, we introduce a hybridized model in which either the solid and the fluid solver can switch from a model-based to a model-free approach depending on the availability and the properties of the data. Numerical experiments are designed to verify the implementation and compare the performance of the proposed model to other alternatives. Preprint Link: [URL] Short Video Introduction:  PhD student Hyoung Suk Suh has been selected as a top 10 finalist for the 2021 Presidential Awards for Outstanding Teaching by a Graduate Student Instructor. Hyoung Suk was a teaching assistant for the soil mechanics course for the last spring semester, and was selected among nearly 500 candidates from across the University. Congratulations, Hyoung Suk for this important distinction!  
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]
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