Technical Thrust Area

Nanotechnology and Lower Scale Phenomena

Chair: Jaroslaw Knap, U.S. Army Research Laboratory
Vice-Chair: Amartya Banerjee, University of California Los Angeles
Nikhil Chandra Admal, University of Illinois Urbana-Champaign
Susanta Ghosh, Michigan Technological University

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Upcoming Event

Webinar Series

September 27, 2023; 2pm CDT

Join via Zoom: (Meeting ID: 845 4127 4013
Passcode: 799065)

SpeakerKaushik Bhattacharya
Discussant: Miguel Bessa, Brown University

TitleData-driven constitutive relations: Multiscale modeling and experimental inference

The talk addresses the challenge of computing complex phenomena at the scale of applications.  In addition to the universal laws (balance of mass, momenta etc.), these phenomena require a constitutive (closure) relation that describes the behavior of the medium at the scale of applications.    Such behavior can be nonlinear, nonlocal, anisotropic, history dependent etc., and thus impossible to characterize to the desired level by the classical approach of postulating a parametrized relation and fitting the parameters to selected experiments.  The talk describes two broad approaches to using data-driven methods to overcome this challenge.  The first approach is multiscale modeling where one recognizes that the effective behavior at the scale of applications is determined by physics at multiple length and time scales: electronic, atomistic, domains, defects etc.  The data-driven constitutive relation is obtained as a neural approximation is trained using data generated by repeated solution of the small scale problem.  The second approach seeks to infer it from automated experiments that are not amenable to easy inversion.  The talk will describe these approaches, challenges they raise and strategies to overcome them.  The ideas will be illustrated with applications from materials science and geology.

Past Webinars

August 30, 2023

Speaker: Krishna Garikipati
Discussants: Harley T. Johnson, University of Illinois Urbana-Champaign and Shailendra P. Joshi, University of Houston

TitleA free energy-based framework for scale bridging in crystalline solids--with some use of machine learning methods

The free energy plays a fundamental role in theories of phase transformations and microstructural evolution in crystalline solids. It encodes the thermodynamic coupling between mechanics and chemistry within continuum descriptions of non-equilibrium materials phenomena. In mechano-chemically interacting materials systems, consideration of compositions, order parameters and strains results in a high-dimensional free energy density function. Since its origins lie in the electronic structure, a rigorous representation of the free energy presents a framework for scale bridging in solids. In this study we have been exploring such a framework, while developing practical machine learning methods to contend with high dimensionality and efficient sampling. We have developed integrable deep neural networks (IDNNs) that are trained to free energy derivative data generated by statistical mechanics simulations. The latter are based on cluster Hamiltonians, themselves trained on density functional theory calculations. The IDNNs can be analytically integrated to recover a free energy density function. We combine the IDNNs with active learning workflows for well-distributed sampling of the free energy derivative data in high-dimensional input spaces. This enables scale bridging between first-principles statistical mechanics and continuum phase field models. As prototypical material systems we focus on applications in Ni-Al alloys and in the battery cathode material: Li$_x$ CoO$_2$.

October 26, 2022

Speaker: Stefanie Reese, RWTH Aachen University
Discussant: Celia Reina, University of Pennsylvania

Title: Data-Driven Mechanics for Elastic and Inelastic Problems Including Uncertainty Quantification
(not recorded at presenter's request)

The data-driven computing paradigm for mechanical systems as proposed in [1] is further extended. Its main principle, to define the solution of boundary value problems explicitly in the material data has several advantages. While generally accepted physical principles such as conservation laws and thermodynamic constraints are enforced, any functional modelling of the material data is avoided. The open-ended process of modelling and calibration as the material data set grows is thus circumvented. Model uncertainties regarding the choice of functions, proper usage within its range of validity and loss of information are thus minimized. One main challenge is the extension to inelastic material behaviours, also included in the talk. The approach of a previous work [2] is extended by material-independent thermodynamic constraints, involving the Helmholtz free energy as first principal data, which may be obtained by increasingly accurate low-scale simulations. Further important aspects are the data search [3] as well as the uncertainty quantification [4]. The talk will be concluded by structural examples.

[1] Kirchdoerfer, T., & Ortiz, M. (2016). Data-driven computational mechanics. Computer Methods in Applied Mechanics and Engineering, 304, 81-101.
[2] Eggersmann, R., Kirchdoerfer, T., Reese, S., Stainier, L., & Ortiz, M. (2019). Model-free data-driven inelasticity. Computer Methods in Applied Mechanics and Engineering, 350, 81-99.
[3] Eggersmann, R., Stainier, L., Ortiz, M., & Reese, S. (2021). Efficient data structures for model-free data-driven computational mechanics. Computer Methods in Applied Mechanics and Engineering, 382, 113855.
[4] Prume, E., Reese, S., Ortiz, M. (2022). Model-free data-driven inference in computational mechanics,, arXiv:2207.06419 [cs.CE]

Join via Zoom:
(Meeting ID: 845 4127 4013/Passcode: 799065)

October 12, 2022

Speaker: Steve WaiChing Sun, Columbia University
Discussant: Amartya Banerjee, University of California, Los Angeles

TitleGeometric Learning for Discovering Complex Material Behaviors of Microstructures

Plasticity models often include a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. However, a surface can also be represented explicitly by a manifold of which the tangential space is Euclidean. In this work, we introduce the concept of yielding manifold. This yielding manifold is reconstructed by stitching local multi-resolution patches together. This treatment enables us to construct a highly complex and precise yield envelope by breaking it down into multiple coordinate charts. The global atlas is then built to enforce the consistency of the machine learning generated yield surface. In contrast to data from smooth manifolds, data collected from sensors and numerical simulations are often discrete. As such, we propose to use graph embedding to create latent space inferred from 3D microstructural data represented via weighted graphs. Vectors of this latent space are used as both geometrical descriptors and internal variables of which a decoder can be used to convert predictions in the latent space back as a weight graph. This approach establishes a direct connection between nonlinear dimensional reduced simulations with machine learning constitutive models. Potential applications of geometric reinforcement learning for inverse problems and the design of experiments in the limited data regime will also be discussed. 

August 31, 2022

Speaker: Michael Shields, Johns Hopkins University
Discussant: Anter El-Azab, Purdue University

TitleThe Intersection of Machine Learning & Uncertainty Quantification in Physics-Based Modeling for Materials Systems

Machine Learning (ML) and Uncertainty Quantification (UQ) have gained widespread popularity in the scientific community, to such an extent that ML/UQ seems to appear in some capacity in nearly all modern scientific investigations. This is particularly true in physics-based modeling where machine learning algorithms are being specially designed to adhere to physical principles, such as the popular physics-informed neural networks (PINNs). In this talk, we will discuss the relationship between these two important research areas in the context of physics-based modeling, with an emphasis on simulating materials systems. We will specifically discuss how the two areas complement one another to enhance modeling capability by making the critical distinction between UQ for ML and ML for UQ. In the former case, we will argue that modern ML methods require UQ as an integral component and show recent advances in the learning of uncertainty-aware Bayesian Neural Networks. In the latter case, we will argue that UQ can be viewed as an exercise in ML and will show how modern ML methods (from Hamiltonian Neural Networks to manifold learning) enable UQ in physical systems while, in many cases, remaining constrained by the underlying physics. Applications to materials modeling will be shown ranging from equation of state modeling for warm dense matter to hierarchical multi-scale models for structural mechanics.

July 27, 2022

Speaker: Michael Falk, Johns Hopkins University
Discussant: Anter El-Azab, Purdue University

TitleQuesting for Structural Predictors of Plastic and Failure Response in Glasses

For decades materials scientists, mechanicians and physicists have searched for structural predictors for plastic flow and failure in glasses and other amorphous materials. Due to the lack of any crystalline order in these materials, disorder rules the day on many scales. This makes quantifying the microstructures of amorphous materials difficult. Such quantification is necessary for building predictive theories that can guide materials design and the development of processing to improve mechanical properties. Here I will consider some particular case studies from my own work with collaborators: the use of machine learning to fit a constitutive model to molecular dynamics data, the use of computer modeling to quantify of the local yield surface in two- and three-dimensions, and an attempt to use an equation-free method to harvest simulation data for the quantification of plastic constitutive response in a 3D binary glass. Reflections on these efforts will be discussed in order to consider the prospects for harnessing machine learning for the development of physically interpretable structural characterization and materials response theories.

June 29, 2022

Speaker: Markus Hütter, Eindhoven University of Technology
: Joerg Rottler, University of British Columbia

Title: Molecular Approach to Plasticity in Polymer Glasses: A Journey

A major benefit of multiscale modeling is that it helps to shed light on constitutive assumptions in macroscopic approaches to mechanics [1]; the stress tensor and the rate of plastic deformation are of particular interest. Nonequilibrium statistical mechanics is a powerful technique in this field, and it has been applied to study the plastic deformation of solids [2,3]. In this presentation, the focus is on multiscale modeling of solids in the glassy state. Structural glasses are particularly interesting (and challenging) for two reasons: they can age in the course of time, and the microscopic carriers of plastic deformation have not been identified to date (in contrast to the well-known dislocations for crystalline materials). Molecular simulations will be used to study glassy materials, in particular polymers. The goal is to establish a fine level of description that is suitable for a subsequent coarse-graining step to the macroscopic continuum level.
When studying polymer glasses on a molecular level, the structural rearrangements related to physical ageing and plastic deformation are rare events, in comparison to the rapid and continuously ongoing molecular vibrations. For studying in an efficient manner these rare events while still keeping molecular detail, a procedure has been proposed that scans the space of molecular configurations specifically for local minima and transitions between them [4]. A key ingredient in this procedure is the calculation of the free energy under appropriate mechanical boundary conditions [5]. In this contribution, we present results of the rare-event sampling for atactic polystyrene - as a prototypical example - below its glass-transition temperature. In the absence of deformation, we obtain rate constants for the minimum-to-minimum transitions extended over 30 orders of magnitude, with well-defined peaks at the time scales corresponding to the subglass relaxations of polystyrene [6]. As deformation is imposed, we observe that the transition states go through an instability and eventually collapse abruptly onto one of the connected local minima; furthermore, we present results about the transition rates as a function of deformation [7]. It will be discussed how these observations will eventually relate to the rate of macroscopic plastic deformation.
Acknowledgment: Part of this work is support by the Dutch Polymer Institute (DPI), projects no. 745ft14 and 820.
[1] E. van der Giessen, et al., Modelling Simul. Mater. Sci. Eng. 28 (2020) 043001 (61pp).
[2] M. Hütter, T.A. Tervoort, Adv. Appl. Mech. 42 (2008) 253-317.
[3] M. Kooiman, M. Hütter, M.G.D. Geers, J. Mech. Phys. Solids 90 (2016) 77-90.
[4] G.C. Boulougouris, D.N. Theodorou, J. Chem. Phys., 127(8) (2007) 084903.
[5] G.G. Vogiatzis, et al., Comput. Phys. Commun., 249 (2020) 107008.
[6] G.G. Vogiatzis, L.C.A. van Breemen, M. Hütter, J. Phys. Chem. B, 125(26) (2021) 7273-7289.
[7] G.G. Vogiatzis, L.C.A. van Breemen, M. Hütter, J. Phys. Chem. B (submitted, 2022).

May 25, 2022

Speaker: Alejandro Strachan, Purdue University; 
Discussant: Arun Mannodi Kanakkithod, Purdue University

Title: Enhancing Physics-Based Modeling and Extracting Physical Insight from
Data Using Machine Learning 

The synergy between principles-based modeling and data science is playing an increasingly important role in materials science and engineering. In addition, there is significant interest in using machine learning (ML) tools to extract physical laws as well as symmetries and associated invariants from data. I will discuss recent progress in my group on machine learning applied to multiscale modeling and in the development of interpretable models that balance accuracy with parsimony.
ML for multiscale modeling. ML interatomic potentials have shown near quantum mechanical accuracy at a fraction of the cost, enabling large-scale atomistic simulations. We developed an iterative approach to address the challenge of generating training data and address the stochastic nature of NN training. I will demonstrate the approach with the development of neural network reactive force fields (NNRF) for energetic materials over a wide range of temperatures and pressures and the phase change material GeSbTe of interest in electronics. The next step of the multiscale ladder is coarse-graining atomistic simulations, and I will show how dimensionality reduction techniques like non-negative matrix factorization and autoencoders can extract physically interpretable collective variables from MD simulations. Specifically, we developed a reduced-order chemical kinetics model with three components and two reactions starting from a 280-dimensional space.
Making workflows and data FAIR. Finally, I will also describe recent developments in nanoHUB, an open cyberinfrastructure for cloud scientific computing, towards making simulation workflows and their data findable, accessible, interoperable, and reusable (FAIR). We introduce Sim2Ls (pronounced sim tools) and the Sim2L Python library that allow developers to create and share end-to-end computational workflows with well-defined and verified inputs and outputs. The Sim2L library makes Sim2Ls, their requirements, and their services discoverable, verifies inputs and outputs, and automatically stores results in a globally accessible simulation cache and results database.

1)Yoo P, Sakano M, Desai S, Islam MM, Liao P, Strachan A. Neural network reactive force field for C, H, N, and O systems. npj Computational Materials. 2021 Jan 22;7(1):1-0.
2)Sakano MN, Hamed A, Kober EM, Grilli N, Hamilton BW, Islam MM, Koslowski M, Strachan A. Unsupervised learning-based multiscale model of thermochemistry in 1, 3, 5-Trinitro-1, 3, 5-triazinane (RDX). The Journal of Physical Chemistry A. 2020 Oct 28;124(44):9141-55.
3)Hunt M, Clark S, Mejia D, Desai S, Strachan A. Sim2Ls: FAIR simulation workflows and data. Plos one. 2022 Mar 10;17(3):e0264492.

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