USACM Technical Thrust Areas

Committee: Novel Methods in Computational Engineering and Sciences

Chair: John Foster, University of Texas at Austin
Vice-Chair: Pania Newell, University of Utah
Members-at-Large: Michael Hillman, Karagozian and Case, Inc.
Steve WaiChing Sun, Columbia University

Upcoming Seminar

There are no current upcoming seminars.

Past Seminars

2025 USACM Novel Methods Spring Seminar

March 28, 2025

Title: Lattice Boltzmann for solid mechanics: elastostatics and elastodynamics

Speaker: Dr. Laura De Lorenzis

Abstract: The talk overviews recent research by the authors on the development of second-order consistent and stable lattice Boltzmann formulations to solve elastostatics and elastodynamics problems. The first proposed scheme solves the quasi-static equations of linear elasticity in two dimensions using a collision operator with multiple relaxation times. In contrast to previous works, our formulation solves for a single distribution function with a standard velocity set and avoids any recourse to finite difference approximations. As a result, all computational benefits of the lattice Boltzmann method can be used to full capacity. The second proposed scheme solves the equations of linear elastodynamics in two dimensions (the extension to three dimensions is currently also available but still unpublished). The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference to conventional lattice Boltzmann formulations is the usage of vector-valued populations, so that once again all computational benefits of the algorithm are preserved. Both schemes are systematically derived using the asymptotic expansion technique. Stability is assessed for elastostatics with von Neumann analysis, whereas in elastodynamics we exploit the notion of pre-stability structures to prove stability for an arbitrary combination of material parameters under a CFL-like condition. Boundary formulations for various cases are proposed . All theoretical derivations are numerically verified by convergence studies using manufactured solutions and long-term stability tests.

Bio: Dr. Laura De Lorenzis started her academic career in her home country Italy; in 2013 she became Professor of Applied Mechanics at the Technical University of Braunschweig in Germany, and since 2020 she is Professor of Computational Mechanics at ETH Zürich. She is the recipient of several prizes, including the RILEM L’Hermite Medal, the AIMETA Junior Prize, an ERC Starting Researcher Grant, the IIFC Young Investigator Award, the election to EUROMECH Fellow, the election to IACM Fellow, two best paper awards and two student teaching prizes. She has authored or co-authored about 150 papers on international journals on different topics of computational and applied mechanics. Since 2023 she is Editor of Computer Methods in Applied Mechanics and Engineering.

Title: Breaking Through: Harnessing Exascale Computing and Peridynamics for Complex Fracture Modeling

Speaker: Dr. Pablo Seleson

Abstract: Fracture presents one of the most critical challenges in engineering, directly impacting the safety, durability, and performance of structures and materials. Its complex nature makes accurate modeling a significant hurdle. Peridynamics is a powerful nonlocal reformulation of classical continuum mechanics, specifically designed to excel in simulating material failure and damage. Unlike traditional models, peridynamicsnaturally captures material discontinuities, such as cracks, without the need for spatial differentiability assumptions. However, the nonlocal nature ofperidynamics, while highly effective, also introduces a substantial increase in computational costs compared to classical methods. To address this challenge, coupling (nonlocal) peridynamics with (local) classical continuum mechanics has emerged as an intriguing solution, combining the strengths of both approaches. Yet, local-to-nonlocal coupling brings its own set of challenges, including artifacts and the need for adaptive modeling techniques. Fortunately, recent advancements in GPU acceleration and the rise of exascale computing have made possible the development of new computational tools, providing an exciting alternative to these methods. This presentation will offer an overview of peridynamics and introduceCabanaPD, a meshfree, GPU-enabled peridynamics code designed for large-scale fracture simulations. Built on the robust libraries Kokkos and Cabana, both developed through the U.S. Department of Energy's (DOE’s) Exascale Computing Project, CabanaPD is performance-portable, exascale-capable, and optimized to run on the DOE’s supercomputers. We will demonstrate the use of CabanaPD for fracture simulation in various engineering problems.

Bio: Dr. Pablo Seleson is a Research Scientist in the Computer Science and Mathematics Division at the Oak Ridge National Laboratory, where he began as an Alston S. Householder Fellow. Dr. Seleson received both his Bachelor’s degree in Physics and Philosophy and his Master’s degree in Physics from the Hebrew University of Jerusalem in 2002 and 2006, respectively. Dr. Seleson completed his Ph.D. in Computational Science at Florida State University in 2010 under the advisement of Prof. Max Gunzburger. Afterward, he joined the Institute for Computational Engineering and Sciences (ICES) at The University of Texas at Austin as an ICES Postdoctoral Fellow under the supervision of Prof. J. Tinsley Oden, where he also worked in close collaboration with the Computer Science Research Institute at Sandia National Laboratories. Dr. Seleson’s research primarily focuses on multiscale materials modeling and the mathematical and computational analysis of peridynamics and related nonlocal models with application to computational fracture modeling. Dr. Seleson serves as an Associate Editor of Applicable Analysis and editorial board member of the Journal of Peridynamics and Nonlocal Modeling. He is also a Member-at-Large of the Executive Committee of the U.S. Association for Computational Mechanics (USACM), past Chair of the USACM Technical Thrust Area (TTA) on Large Scale Structural Systems and Optimal Design, Vice-Chair of the USACM TTA on Mathematical Methods in Computational Engineering & Sciences, and Member of the Computational Mechanics Committee of the Engineering Mechanics Institute (EMI) of the American Society of Civil Engineers (ASCE).

2024 USACM Novel Methods Fall Seminar

October 18, 2024

Title: Nonlocal Attention Operator: Towards a Foundation Model for Material Responses

Speaker: Prof. Yue Yu, Lehigh University

Abstract: While foundation models have gained considerable attention in core AI fields such as natural language processing (NLP) and computer vision (CV), their application to learning complex responses of physical systems from experimental measurements remains underexplored. In physical systems, learning problems are often characterized as discovering operators that map between function spaces, using only a few samples of corresponding function pairs. For instance, in the automated discovery of heterogeneous material models, the foundation model must be capable of identifying the mapping between applied loading fields and the resulting displacement fields, while also inferring the underlying microstructure that governs this mapping. While the former task can be seen as a PDE forward problem, the later task frequently constitutes a severely ill-posed PDE inverse problem.

In this talk, we will consider the learning of heterogeneous material responses as an exemplar problem to explore the development of a foundation model for physical systems. Specifically, we show that the attention mechanism is mathematically equivalent to a double integral operator, enabling nonlocal interactions among spatial tokens through a data-dependent kernel that characterizes the inverse mapping from data to the hidden microstructure/parameter field of the underlying operator. Consequently, the attention mechanism captures global prior information from training data generated by multiple systems (i.e., specimens with different microstructures) and suggests an exploratory space in the form of a nonlinear kernel map. Based on this theoretical analysis, we introduce a novel neural operator architecture, the Nonlocal Attention Operator (NAO). By leveraging the attention mechanism, NAO can address ill-posedness and rank deficiency in inverse PDE problems by encoding regularization and enhancing generalizability. To demonstrate the applicability of NAO to material modeling problems, we apply it to the development of a foundation constitutive law across multiple materials, showcasing its generalizability to unseen data resolutions and system states. Furthermore, we investigate the potentials of NAO in microstructure discovery and multiscale crack propagation problems. Our work not only suggests a novel neural operator architecture for learning an interpretable foundation model of physical systems, but also offers a new perspective towards understanding the attention mechanism.

Title: Unlocking the Challenge of Simulating Corrosion Through a New Phase Field Revolution

Speaker: Emilio Martinez-Pañeda, University of Oxford

Abstract: Corrosion has long been considered too complex to be predicted with computer models. However, increasing computer power and new multi-physics, phase field-based corrosion models enable the development of electro-chemo-mechanical phase field models that explicitly resolve the meso-scale phenomena involved and can therefore deliver predictions based on physical parameters and with minimal assumptions. Phase field modelling has revolutionised the modelling of many interfacial problems, from solidification to fracture mechanics, and this paradigm can also be used to predict the evolution of the corrosion front (electrolyte-metal interface). Recent developments in this emerging field of phase field corrosion have shown that this new class of models can capture key phenomena such as film rupture and repassivation, the transition from activation- to diffusion-controlled corrosion, interactions with mechanical fields, microstructural and electrochemical effects, intergranular corrosion, material biodegradation, and the interplay with other environmentally-assisted damage phenomena such as hydrogen embrittlement. Examples of potential future directions will also be provided to showcase the potential of this new, exciting field.

2024 USACM Novel Methods Spring Seminar

April 19, 2024

Title: Multiscale optimization of (meta-)materials by computational mechanics vs. machine learning

Speaker: Professor, Dennis Kochmann, ETH Zurich

Abstract: The optimization of materials and architected materials across scales is a crucial challenge towards the design of novel materials systems with as-designed, extreme, or peculiar mechanical properties. Especially the advent of architected materials has led to the emergence of a large array of new computational methods, which include both (more traditional) computational methods and data-driven approaches based on machine learning. We will survey some of these recent approaches for the inverse design of (meta-)materials: from multiscale topology optimization of cellular solids and ray tracing in spatially graded metamaterials to the use of machine learning. We will show how the latter can efficiently solve the inverse homogenization problem (a classically ill-posed problem) through generative modeling of novel material architectures with as-designed properties – beyond what classical methods can achieve.

Biography: Dennis M. Kochmann received his education at Ruhr-University Bochum in Germany and at the University of Wisconsin-Madison. After postdoc positions at Wisconsin and Caltech, he became Assistant Professor of Aerospace at the California Institute of Technology in 2011, and Professor of Aerospace in 2016, a position he held through 2019. Since April 2017 he has been Professor of Mechanics and Materials at ETH Zürich, where he served as Head of the Institute of Mechanical Systems and as Deputy Head of Department. His research focuses on the link between microstructure and properties of natural and architected materials, which includes the development of theoretical, computational, and experimental methods to bridge across scales from nano to macro. His research has been recognized by, among others, IUTAM’s Bureau Prize in Solid Mechanics, GAMM’s Richard von Mises Prize, an NSF CAREER Award, ASME’s T.J.R. Hughes Young Investigator Award, an ERC Consolidator Grant, and IACM’s John Argyris Award. He is Associate Editor of Archive of Applied Mechanics and Applied Mechanics Reviews.

Title: Data driven modeling of mechanical systems

Speaker: Assistant Professor, Emma Lejeune, Boston University

Abstract: Over the past decade, there has been a growing interest in leveraging machine learning techniques to model complex mechanical systems. Compellingly, these techniques have become invaluable tools for applications ranging from topology optimization, to uncertainty quantification, to real-time prediction, to multi-scale modeling and beyond. Typically, researchers take either a “problem-centric” or “model-centric” approach to this work. Namely, they focus on either an overarching engineering challenge, or they focus on developing machine learning methods and model architectures. In this talk, we will present a “data-centric” approach to data driven modeling of mechanical systems. Specifically, we will discuss work where we focus on defining and curating datasets as our top priority. First, we will share our work in developing and disseminating benchmark datasets for engineering mechanics problems. Then, we will share our work in defining an open science based methodological foundation for data driven modeling of (bio)mechanical systems. In brief, we envision a methodological framework with three essential components: (1) open access datasets, (2) open source software to extract interpretable quantities of interest from these data, and (3) combined mechanistic and statistical models of (bio)mechanical behavior informed by these data. As an illustrative example, we will discuss our recent collaborative work in cardiac tissue engineering. Overall, the goal of this talk is to spark discussion and inspire future work on “data-centric” approaches to mechanical modeling.

Biography: Emma Lejeune is an Assistant Professor in the Mechanical Engineering Department at Boston University. She received her PhD from Stanford University in September 2018, and was a Peter O’Donnell, Jr. postdoctoral research fellow at the Oden Institute at the University of Texas at Austin until 2020 when she joined the faculty at BU. Current areas of research involve integrating data-driven and physics based computational models, and characterizing and predicting the mechanical behavior of heterogeneous materials and biological systems.