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]
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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). 

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:

1. A. Qinami, E.C. Bryant, W.C. Sun, M. Kaliske, Circumventing mesh bias via r-and h-adaptive refinement techniques for the variational eigenfracture model, International Journal of Fracture, doi:10.1007/s10704-019-00349-x, ​2019. 
2. E.C. Bryant, W.C. Sun, Mixed-mode phase field fracture for secondary cracks in isotropic and anisotropic brittle rocks with consistent kinematics, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2018.08.008, 2018. [PDF]
3. E.C. Bryant, W.C. Sun, micromorphic-regularized anisotropic Cam-clay-type model for capturing size-dependent anisotropy, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2019.05.003, 2019. 
4. S. Na, E.C. Bryant, W.C. Sun, A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2019.112572, 2019. [PDF]
5. E.C. Bryant, W.C. Sun, ​Phase field modeling of frictional slip with slip weakening/strengthening  under non-isothermal conditions, in preparation. 

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 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: 

1. C. Liu", W.C. Sun, ILS-MPM: an unbiased implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles, Computer Methods in Applied Mechanics and Engineering, accepted, 2020. [PDF]
2. C. Liu", W.C. Sun, Shift domain material point method for solids in the finite deformation range, special thematic issue for Meshfree and Particle Methods for Modeling Extreme Loadings, Computational Particle Mechanics, doi: 10.1007/s40571-019-00239-y, 2019. [PDF]

Congratulations, Chuanqi!