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!
PhD student Eric Bryant successfully defended his PhD thesis and will join T-3 at Los Alamos National Laboratory
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.
Part I of our paper series on geometric learning and Sobolev training for computational mechanics has been accepted by CMAME
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]
Congratulations again to my Ph.D. student Jarett Poliner for winning the NDSEG Fellowship!
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 Dr. Chuanqi Liu has received an offer to join the Chinese Academy of Sciences as an associate professor.
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:
Our paper on modeling polycrystal salt with precipitation creep, fracture and healing has also been accepted by CMAME today
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.
Our paper on imposing the physical length scale of micro-polar phase field model for cohesive fracture has been accepted by CMAME
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]
Our paper on ILS-MPM modeling of granular assemblies with frictional contact mechanics is accepted by CMAME.
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]
News about Computational Poromechanics lab at Columbia University.