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]

In recognition of his groundbreaking research illuminating the mechanics and physics of porous geomaterials like rocks, soil, concrete and salt, Professor Steve WaiChing Sun has earned the prestigious John Argyris Award for Young Scientists. This award is given by the International Association for Computational Mechanics (IACM).
Bridging mathematical science, theoretical mechanics, and industrial applications, Sun’s interests focus on computational poromechanics and geomechanics for a variety of applications, ranging from carbon dioxide storage to disposal of nuclear waste. In addition to the John Argyris award, Sun has received several prominent international awards in theoretical and computational mechanics, including the Zienkiewicz Numerical Methods in Engineering Prize from Institution of Civil Engineers (UK), the ASCE Engineering Mechanics Institute Leonardo de Vinci Award (USA), Dresden Fellowship (Germany), as well as the young investigator awards from funding agencies, including the US National Science Foundation CAREER Award, the US Air Force Young Investigator Program Award, and the US Army Young Investigator Program Award.
Highlighting distinguished scholarship and outstanding accomplishments, the biennial John Argyris Award for Young Scientists celebrates influential researchers 40 and under. Sun, an assistant professor of civil engineering and engineering mechanics since 2014, will be the first Columbia faculty member and the first Chinese American to receive this honor. He will receive the award at the opening ceremony for the joint organization of the 14th IACM World Congress in Computational Mechanics and the 8th European Congress on Computational Methods in Applied Science and Engineering this summer in Paris. [URL]

My colleagues and I have obtained the approval from the board of governors of ASCE EMI to establish a new committee in the ASCE Engineering Mechanics Institute for applying machine learning to AI. The first meeting for this new committee will occur during the ASCE EMI conference at Columbia University this coming May. ​See [URL]

Abstract:

This paper examines the frame-invariance  (and the lack thereof) exhibited in simulated anisotropic elasto-plastic responses generated from supervised machine learning of classical multi-layer and informed-graph-based neural networks, and proposes different remedies to fix this drawback. The inherent  hierarchical relations among physical quantities and state variables in an elasto-plasticity model are first represented as directed graphs,  where three variations of the graph are tested. While feed-forward neural networks are used to train path-independent constitutive relations (e.g., elasticity), recurrent neural networks are used to replicate responses that depends on the deformation history, i.e. or path dependent. In dealing with the objectivity deficiency, we use the spectral form to represent tensors and, subsequently, three metrics, the Euclidean distance between the Euler Angles, the distance from the identity matrix, and geodesic on the unit sphere in Lie algebra, can be employed to constitute objective functions for the supervised machine learning. In this, the aim is to minimize the measured distance between the true and the predicted 3D rotation entities. Following this, we conduct numerical experiments on how these metrics, which are theoretically equivalent, may lead to differences in the efficiency of the supervised machine learning as well as the accuracy and robustness of the resultant models. Neural network models trained with tensors represented in component form for a given Cartesian coordinate system are used as a benchmark. Our numerical tests show that, even given the same amount of information and data, the quality of the anisotropic elasto-plasticity model is highly sensitive to the way tensors are represented and measured. The results reveal that using a loss function based on geodesic on the unit sphere in Lie algebra together with an informed directed graph yield significantly more accurate rotation prediction than the other tested approaches. [PDF]

We are a part of the multi-university team who has been awarded a 2 million grant for leveraging interpretable  augmented intelligence for multiscale discovery. 

Award Abstract #1940203

Collaborative Research: I-AIM: Interpretable Augmented Intelligence for Multiscale Material Discovery

NSF Org:Office of Advanced Cyberinfrastructure (OAC)

ABSTRACT

The ability to model, predict, and improve the mechanical performance of engineering materials such as polymers, composites, and alloys can have a significant impact on manufacturing, with important economic and societal benefits. As advanced computational algorithms and data science approaches become available, they can be harnessed to disrupt the current approaches to materials modeling, and allow for the design and discovery of new high-strength, high-performance materials for manufacturing. Bringing together multidisciplinary teams of researchers can maximize the impact of these new tools and techniques. This Harnessing the Data Revolution Institutes for Data-Intensive Research in Science and Engineering (HDR-I-DIRSE) award supports the conceptualization of an Institute to develop novel data science methods, address fundamental scientific questions of Materials Engineering and Manufacturing, and build such multidisciplinary teams. The project will apply novel data science methods to advance the analysis of large sets of structural data of composite materials and alloys from the atomic scale to correlate with and predict mechanical properties. The methods are based on machine learning techniques and uncertainty quantification, and will help uncover underlying structural features in the materials that determine the properties and performance. The methods and results will help accelerate the development of ultra-high strength and lightweight carbon-based composites for aerospace applications, and multi-element superalloys for more durable engine parts, by navigating in the large possible design space and providing faster predictions than experiments and traditional simulation methods. The project will also lead to new methods and computational algorithms that will become publicly available. The investigators will train graduate and undergraduate students from various disciplines with a focus on engaging women and minorities in STEM fields, develop short courses that integrate novel Materials Science and Engineering applications and Data Science methods, and foster vertical integration of interdisciplinary research from undergraduate students to senior scientists.

This project aims at building an effective and interpretable learning framework for materials data across scales to solve a major challenge in current data-driven materials design. The combined Materials Science and Data Science approaches will synergistically contribute to the development and use of interpretable and physics-informed data science methodologies to gain new understanding of mechanical properties of polymer composites and alloys, with the potential to be expanded into different property sets and different systems. The PIs will utilize available data efficiently through combination with physical rules and prior knowledge, to develop an interpretable augmented intelligent system to learn principles behind the association of input structures with material properties with uncertainty quantification. The interconnected tasks involve the (1) collection and curation of large amounts of computational and experimental data for polymer/carbon nanotube composites and alloys from open data sources and targeted calculations and experiments, (2) the development of geometric and topological methods incorporating physical principles to generate a better, more sensitive low-dimensional representation of the multidimensional data and characterize the parameter space related to mechanical properties, (3) the development of a Bayesian deep reinforcement learning framework to generate interpretable knowledge graphs that depict the relational knowledge among physical quantities with uncertainty quantification, and (4) the prediction of mechanical properties to reveal design principles to improve materials performance, evaluate and validate the methods, and develop software for dissemination.

This project is part of the National Science Foundation's Harnessing the Data Revolution (HDR) Big Idea activity and is co-funded by the Division of Civil, Mechanical and Manufacturing Innovation.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. 

More information can be found in the official announcement from NSF [URL].  

A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables​

SeonHong Na, Eric C Bryant, Waiching Sun
​
We introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multi-physical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp changes of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after re-meshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal value and direction are projected onto a smooth field interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator, in general, leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the re-meshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain. [PDF]