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!  


​Reference: 

1. N. Vlassis, W.C. Sun, Sobolev training of thermodynamic-informed neural network for interpretable elasto-plasticity models with level set hardening, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2021.113695, 2021. [Video][preprint]
2. N. Vlassis, R. Ma", W.C. Sun, Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity, Computer Methods in Applied Mechanics and Engineering, doi:10.1016/j.cma.2020.113299, 2020. [PDF]
3. X. Sun, B. Bahmani, N. Vlassis, W.C. Sun, Y. Xu, Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty quantification, under review. 

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). 

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.