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In this work, we first use MD data to train a deep neural network to create the "first draft" of the continuum surrogate model, then use well known physics constraints from continuum mechanics (e.g. material frame indifference, material symmetry, growth condition, rank-one convexity) to further fine-tune the neural network. The resultant framework is used to predict the finite strain elasticity of Nitroamine high explosive (HMX), an application that requires robustness and consistency on the forecast quality. Link to research article: https://onlinelibrary.wiley.com/doi/10.1002/nme.6992 Link to the cover: https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7087 
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Link to research article: onlinelibrary.wiley.com/doi/10.1002/nag.3408 Link to the cover: https://onlinelibrary.wiley.com/doi/epdf/10.1002/nag.3437  When predicting plastic responses of complex microstructures, we often propose mechanisms to explain the physics of the yielding, then propose mathematical expressions to recapture what we describe in words, then propose algorithms to generate the constitutive updates. However, what if the materials are so complex that we cannot easily find a single equation to express them precisely? What if our symbolic regression skill is not sufficient to recover the surface to which those data points belong? The yield function or damage criterion of a material is a common example where our abilities to compose equations precisely and accurately are often put to test. A yield function may take many different types of variables (stress invariants, strain, sometimes also other descriptors such as volume fraction). A simple solution we proposed is to not propose the yield surface as a function in the parametric space but directly regard it as a manifold. In this work (first author = Mian Xiao), Mian and I explore the use of geometric prior to generating the yielding manifold based on point cloud data obtained from direct numerical simulations or experiments. By modifying the geometric approach by Williams, et al. CVPR 2019 to incorporate plastic flow information to regularize the yield surface, we have successfully recovered a highly complex yield surface through the construction of a collection of coordinate charts and the atlas, a task that is difficult to complete via training a single neural network. Meanwhile, we also show that the availability of local patches also enables us to overcome the longstanding slow convergence issue commonly exhibited in classical non-smooth plasticity models and leads to a very robust reconstruction of yield surface even with noisy data. Preprint available via ResearchGate. [PDF] Link to open-access article: https://onlinelibrary.wiley.com/doi/full/10.1002/nag.3380 Link to the cover: https://onlinelibrary.wiley.com/doi/10.1002/nag.3429  This article (see [preprint]) presents a multi-phase-field poromechanics model that simulates the growth and thaw of ice lenses and the resultant frozen heave and thaw settlement in multi-constituent frozen soils. In this model, the growth of segregated ice inside the freezing-induced fracture is implicitly represented by the evolution of two phase fields that indicate the locations of segregated ice and the damaged zone, respectively. The evolution of two phase fields is induced by their own driving forces that capture the physical mechanisms of ice and crack growths respectively, while the phase field governing equations are coupled with the balance laws such that the coupling among heat transfer, solid deformation, fluid diffusion, crack growth, and phase transition can be observed numerically. Unlike phenomenological approaches that indirectly capture the freezing influence on the shear strength, the multi-phase-field model introduces an immersed approach where both the homogeneous freezing and the ice lens growth are distinctively captured by the freezing characteristic function and the driving force accordingly. Verification and validation examples are provided to demonstrate the capacities of the proposed models. Support provided by US Army Research Office and National Science Foundation is gratefully acknowledged. The first author of this paper, the 6th graduated PhD of our group, Dr. Hyoung Suk Suh (see picture below) has received the DongJu Lee '03 Memorial Award in recognition of "his superior achievement and in honor of the integrity, curiosity, and creativity exhibited as a student at SEAS of Columbia." Congratulations, Hyoung Suk! I am looking forward for more great news in the upcoming year! This paper (see the preprint available here) introduces a manifold embedding data-driven paradigm to solve small- and finite-strain elasticity problems without a conventional constitutive law.  Traditionally, data-driven paradigm often replace a constitutive law with a search that select an experimental data point that is " the closest" to the balance principle. However, how distance or length is measured remains ambiguous. Often time, an arbitrarily energy norm is chosen, but such a practice has shown to be affected which closest data point is getting selected. In particular, in a nonlinear manifold, the shortest distance between two points and the Euclidean distance can be quite different when they are far apart. Furthermore, the resultant model-free simulation could be sensitive to the chosen norm used to measure distance (see figure below).  We follows the classical data-driven paradigm by seeking the solution that obeys the balance of linear momentum and compatibility conditions while remaining consistent with the material data through minimizing a distance measure. Our key point of departure is the introduction of a global manifold embedding as a means to learn the geometrical trend of the constitutive data mathematically represented by a smooth manifold. Conventionally, an incremental nonlinear constitutive update is sought by solving a sequence of linearized equations that moves along the admissible range of the constitutive law until the solution is found. Instead of doing this, we propose to simply deform the phase space where the nonlinear constitutive law exists such that the resultant constitutive law in the deformed space appear to be linear. A pair of neural networks (see below) are trained to learn (1) how to deform this nonlinear constitutive manifold to make it flat (i.e. there is one normal vector everywhere in the deformed hyperplane), and (2) how to deform the hyperplane back into a smooth manifold. Consequently, the flatness of the deformed hyperplane then makes it very easy to measure the distance between a point and the hyperplane, while the inverse map allows us to convert the local search result back into a point in the nonlinear constitutive law.  By training an invertible neural network to embed the data of an underlying constitutive manifold onto a Euclidean space, we reformulate the local distance-minimization problem such that it replace the computationally intensive combinatorial search to identify the optimal data points closest to the conservation law with a cost-efficient projection step. Meanwhile, numerical experiments performed on path-independent elastic materials of different material symmetries suggest that the geometrical inductive bias learned by the neural network is helpful to ensure more consistent predictions when dealing with data sets of limited sizes or those with missing data (see examples below).   Our paper on capturing evolving anisotropy of freezing clayey soil has been accepted by IJNAMG4/26/2022 Authors: Qing Yin, Edward Andò, Gioacchino Viggiani, WaiChing Sun Abstract: This paper presents a combined experimental-modeling effort to interpret the coupled thermo-hydro-mechanical behaviors of the freezing soil, where an unconfined, fully saturated clay is frozen due to a temperature gradient. By leveraging the rich experimental data from the microCT images and the measurements taken during the freezing process, we examine not only how the growth of ice induces volumetric changes of the soil in the fully saturated specimen but also how the presence and propagation of the freezing fringe front may evolve the anisotropy of the effective media of the soil-ice mixture that cannot be otherwise captured phenomenologically in the isotropic saturation-dependent critical state models for plasticity. The resultant model is not only helpful for providing a qualitative description of how freezing affects the volumetric responses of the clayey material, but also provide a mean to generate more precise predictions for the heaving due to the freezing of the ground. [PDF]  Congratulations to Dr. Hyoung Suk Suh for successfully defending his PhD dissertation (see URL). We are very grateful to other committee members, Professor Ronaldo Borja, Professor George Deodatis, Professor Majid Manzari and Professor Haim Waisman for their suggestions and feedbacks, and the Army Research Office and National Science Foundation for providing the financial support for his PhD study.
Hyoung Suk joined my research group in 2018 from Yonsei University. He has published the following works during his tenure at Columbia. His PhD work focuses on the microporomechanics of geomaterials at extreme temperature with implications on how climate changes may affect the freeze-thaw action in frozen soil in Alaska. In addition to his research accomplishment, Hyoung Suk is also a beloved TA and had also been nominated as the candidate for the Presidential awards for outstanding teaching at Columbia twice. Dr. Suh, thank you for the 4 years of hard work and dedications! It is a privilege to serve as your PhD advisor and colleague! Published work:
After 2 years of delay due to pandemic, we are back to the roads now for conferences. Below are two talks, one on phase field modeling of ice lens, one on immersed phase field for fluid-driven fracture with Darcy-Stokes flow. Talk 1: Multi-phase-field approach for modeling ice lens growth and thaw in frozen soil Talk 2: An immersed phase field fracture model in fluid-infiltrating porous media with evolving Beavers-Joseph-Saffman condition  Congratulations to Dr. Kun Wang who has been selected from around 200 applicants by ExxonMobil! He will join Computational Physics Section at EMRE’s Corporate Strategic Research Laboratories as a computational physicist to develop computational methods aimed at solving large-scale physical problems pertaining to the energy industry, with focus in the areas of flow in porous media, multi-scale phenomena, PDE-constrained optimization and uncertainty quantification.
Kun has a distinguished career at both Columbia University and Los Alamos National Laboratory. His recent work published in Nature Communication and PNAS has been featured at Economist. During his time at Columbia, he has published 12 papers with the research group, as listed below. Published Work:
While there are many neural network constitutive laws published, there are relatively little work on focusing on the validation against the physical constraints to make the predictions admissible. In this work, we train the neural network with multiple steps where it first fits the data, then corrections are made through transfer learning to introduce additional physical constraints, such as material frame indifference, material symmetry, as well as checking the ellipticity, growth conditions, stability and uniqueness (through examining the acoustic tensor). Another interesting point is that we are using the gradient and the Hessian data to back calculate the underlying scalar elasticity functional. The neural network model is used to predict the responses of a monoclinic organic molecular crystal, beta-HMX inferred from MD simulations. Accuracy of the blind predictions are tested in the parametric space. Preprint manuscript available at [URL]. Ran Ma and I have our latest work on finite deformation/microrotation MPM for micropolar materials accepted by CMAME before the winter break. There is a great body of work which proves that material point method (MPM) is a great tool to simulate extremely large deformation (even for Lagrangian granular flow). The potential of MPM to handle simulations with large rotation (metal forming, torsional wave...etc) and large micro-rotation for micropolar materials (e.g. sand, meta-materials), is less explored. In this work, we introduce a numerical framework that includes the necessary ingredients, include the explicit time integrator, the Lie-group projections between grid and material points, and a micropolar frictional models for the contact mechanics. Consequentially, the model enables us to introduce a unified approach to simulate dynamic responses of both solid and fluids that exhibit size effects. To the best of our knowledge, this is the first research successfully enable the simulations of micropolar continuua in MPM in the geometrical nonlinear regime. Preprint available [URL] Conventionally, neural network constitutive laws for path-dependent elasto-plastic solids are trained via supervised learning performed on recurrent neural networks, with the time history of strain as input and the stress as input. However, training neural networks to replicate path-dependent constitutive responses requires significantly more data due to the path dependence. This demand on diversity and abundance of accurate data, as well as the lack of interpretability to guide the data generation process, could become major roadblocks for engineering applications. In this work, we attempt to simplify these training processes and improve the interpretability of the trained models by breaking down the training of material models into multiple supervised machine learning programs for elasticity, initial yielding and hardening laws that can be conducted sequentially. To predict pressure-sensitivity and rate dependence of the plastic responses, we reformulate the Hamliton-Jacobi equation such that the yield function is parametrized in a product space spanned by the principal stress, the accumulated plastic strain and time. To test the versatility of the neural network meta-modeling framework, we conduct multiple numerical experiments where neural networks are trained and validated against (1) data generated from known benchmark models (2) data obtained from physical experiments and (3) data inferred from homogenizing sub-scale direct numerical simulations of microstructures. The neural network model is also incorporated into an offline FFT-FEM model to improve the efficiency of the multiscale calculations. Preprint available here [URL] If the injected fluid is much hotter or colder than the host matrix of the porous media and the specific heat capacities of the solid and fluid constituents are sufficiently different, then the assumption that the two constituents will have the same temperature at the continuum scale may not be correct. In this work, we formulate a dual-heat-transfer theory (in analog to the dual-permeability poromehanics theory) to examine how these local temperature difference affect the fracture patterns and the path-dependent responses at the small time scale and under what condition the one temperature theory is sufficient. To address the issue of the time scale difference of the coupled heat transfer problem, we introduce an asynchronous time integrator for the operator-split algorithm to improve the efficiency of the solver. Preprint available here [URL].  I am excited that the thesis committee (Professor George Deodatis, Professor JS Chen, Professor Richard Regueiro, Professor Marco Giometto and myself) have approved our team member Nick Vlassis's PhD dissertation "Towards Trustworthy Geometric Deep Learning for Elastoplasticity". Nick will continue to collaborate with us on the DOE NNSA project "Center for Micromorphic Multiphysics Porous and Particulate Materials Simulations with Exascale Computing Workflows (MSC)" (by led University of Colorado Boulder) as a Postdoctoral Research Scientist .
Nick's work focuses on formulating geometric learning tasks to create meta-models that generate interpretable constitutive laws from MD, DNF, DEM and experimental data across different length scales, often with physical constraints that often involves higher-order derivatives (see list of publication below). During PhD study, Nick has been awarded the Mindlin Scholarship by the Fu Foundation School of Engineering and Applied Science and a few NSF travel fellowships to conferences. Congratulations for the well-deserved distinction, Nick! We are looking forward for your outstanding contribution to the DOE NNSA project! Publications:
In this work, we simulate the fragmentation process of particles by extending the domain partition MPM first introduced by Homel and Herbold 2017 to analyze how the thermal-coupling and surface-conductance affect the contact/fracture mechanics of granular materials. This framework enables us to circumvent the unrealistic crack patterns caused by using the homogenized stress of each particle as a criterion for fragmentation or straight split while capturing the strain-rate sensitivity of the fragmentation process simply through simulating crack branching. Abstract: We propose a material point method (MPM) to model the evolving multi-body contacts due to crack growth and fragmentation of thermo-elastic bodies. By representing particle interface with an implicit function, we adopt the gradient partition techniques introduced by Homel and Herbold 2017 to identify the separation between a pair of distinct material surfaces. This treatment allows us to replicate the frictional heating of the evolving interfaces and predict the energy dissipation more precisely in the fragmentation process. By storing the temperature at material points, the resultant MPM model captures the thermal advection-diffusion in a Lagrangian frame during the fragmentation, which in return affects the structural heating and dissipation across the frictional interfaces. The resultant model is capable of replicating the crack growth and fragmentation without requiring dynamic adaptation of data structures or insertion of interface elements. A staggered algorithm is adopted to integrate the displacement and temperature sequentially. Numerical experiments are employed to validate the diffusion between the thermal contact, the multi-body contact interactions and demonstrate how these thermo-mechanical processes affect the path-dependent behaviors of the multi-body systems. Preprint: Available via ResearchGate: [URL] Video Summary: https://youtu.be/pg535F6bqtQ Starting next month, the PI of Sun Group will join the editorial board of Acta Geotechnica:
https://www.springer.com/journal/11440/editors 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). 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!  |
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