ICME: The design of Fit-for-Purpose Materials

With the increased emphasis on reducing the cost and time to market of new materials, ICME (Integrated Computational Materials Engineering) has become a fast growing discipline within materials science and engineering. The vision of ICME is compelling in many respects, not only for the value added in reducing time to market for new products with advanced, tailored materials, but also for enhanced efficiency and performance of these materials. Although the challenges and barriers (both technical and cultural) are formidable, substantial cost, schedule, and technical benefits can result from broad development, implementation, and validation of ICME principles. ICME is an integrated approach to the design of products, and the materials that comprise them, by linking material and structural models at multiple time and length scales. NASA’s Transformational Tools and Technology (TTT) Project sponsored a study (performed by a team led by Pratt & Whitney) in 2016 to define the potential 25-year future state required for integrated multiscale modeling of materials and systems (e.g., load-bearing structures) to accelerate the pace and reduce the expense of innovation in future aerospace and aeronautical systems. This talk will briefly review ICME, the findings of the 2040 Vision study, and discuss NASA’s TTT 2040 implementation activities: with special emphasis on recent accomplishments.  The 2040 study,  NASA CR 2018- 219771, envisions the development of a cyber-physical-social ecosystem comprised of experimentally verified and validated computational models, tools, and techniques, along with the associated digital tapestry, that impacts the entire supply chain to enable cost-effective, rapid, and revolutionary design of fit-for-purpose materials, components, and systems by enabling the engineer to not only “design-with-the” material but also concurrently “design-the” material.

Bio:  Dr. Steven M. Arnold is currently the Technical Lead for Multiscale Modeling within the Materials and Structures Division at NASA Glenn Research Center with over 35 years of experience. He also is the Technical Lead for the Materials and Structures Discipline within the Transformative Tools and Technology (TTT) project. Dr. Arnold conducts research involving theoretical and experimental investigations of structural material behavior of advanced aircraft propulsion systems and spacecraft structures. He has over 500 technical publications, 116 of which are journal publications and is a co-author of two books on micromechanics of composites, i.e., “Micromechanics of Composite Materials: A Generalized Multiscale Analysis Approach” 2013 and “Practical Micromechanics of Composite Materials” 2021.  He received NASA’s Exceptional Service Medal in 2019, NASA’s Exceptional Technology Achievement Medal in 2014 and the NASA Glenn Abe Silverstein outstanding research award in 2004.  He also was awarded the ASC/DEStech Award in Composites for 2015.  He is, on the NAFEMS Americas Steering Committee; an ASM International Fellow (class of 2013), Chairs the Core and Emerging Technologies Council for ASM, and participates on the Materials Data Information & Data Analytic Technical Committee; a member of AIAA and Chairs the Materials Technical Committee and ICME working group, and participates on the Digital Engineering Integration Committee (DEIC) in both the digital twin and digital thread subcommittees; and co-founder and chairman of the Material Data Management Consortium (MDMC). 

Scientific Machine Learning in computational fluid dynamics and mechanics: methods and examples in industrial settings

Scientific machine learning (SciML) has shown great promise in the context of accelerating classical physics solvers and discovering new governing laws for complex physical systems. However, while the SciML activity in foundational research is growing exponentially, it lags in real-world utility, including the reliable and scalable integration into industrial pipelines. SciML algorithms need to advance in maturity and validation, which in the context of traditional and advanced industrial settings, requires operating in cyber-physical environments marked by large-scale, three-dimensional, streaming data that is confounded with noise, sparsity, irregularities and other complexities that are common with machines and sensors interacting with the real, physical world. 

In this talk, I will highlight some of the current challenges in applying SciML in industrial contexts. Special attention will be on the generation of fast and flexible surrogates for flow and heat exchange problems with emphasis on graph-based Neural Operators and, if time allows, Gaussian processes.

Open science approaches to data-driven modeling of mechanobiological systems

From the beating heart to tissue assembly and repair, it is well accepted that mechanics plays an important role in the behavior of biological systems. Mechanical forces are not only fundamentally important to biological materials (e.g., the mechanics of growth), but are also fundamental drivers of cellular behavior change. However, it is often difficult to determine mechanical state both in vitro and in vivo, and it is often difficult to determine how mechanical perturbations (e.g., changes to boundary conditions) will change the mechanical state throughout the domain. Over the past several decades, mathematical modeling has emerged as an important tool to bridge this gap. And, more recently, there has been a surge in interest towards using data-driven statistical techniques to create predictive models of biological system behavior. As experimental techniques and data-driven methods simultaneously advance, there is an unprecedented opportunity to gain biological insight. In this talk, we will describe our preliminary and ongoing work in data driven modeling of in vitro biological systems with applications focused on both cardiac tissue engineering and wound healing. In brief, we envision a methodological framework with three essential components: (1) open access datasets of time-lapse movies of cells and tissue, (2) open source software to extract interpretable quantities of interest from these time-lapse movies, and (3) combined mechanistic and statistical models of biological behavior informed by these data. We are presently working on creating these datasets, software, and models in partnership with experimental collaborators, and releasing them to the community under permissive licenses. Looking forward, we anticipate that these large open access curated datasets combined with open source tools to extract information from them will enable significant advances in our understanding of, and ability to control, living systems. Critically, these open source tools will directly enable the exploration of diverse modeling approaches applied to biological systems. Through this talk, we hope to foster further discussion and collaborations at the interface of mechanics, biology, and open science.

Dynamic energy balance, continuum damage and fracture in a peridynamic formulation

Peridynamic formulations provide a unique platform to leverage non-locality for studying the free fracture problem.

Here we discuss a nonlocal model for dynamic damage evolution consisting of two branches one elastic and the other inelastic. Evolution from the elastic to the inelastic branch depends on material strength and is mediated through the constitutive law relating force to strain. The energy for the model interpolates between elastic energy for small strains and surface energy for infinite strains.  For three dimensional problems with a flat crack, power balance delivers the crack tip velocity in terms of the rate of work done by the load and the change in both the kinetic energy and elastic potential energy of the specimen. Subsequent passage to the limit of vanishing non-locality in a pre-cracked plate subjected to mode I loading delivers a sharp fracture evolution that agrees with classic dynamic fracture mechanics.

Computational methods based on peridynamics and nonlocal operators

A dual-horizon peridynamics (DH-PD) formulation for dynamic fracture is presented. DH-PD naturally includes varying horizon sizes and resolves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Two-dimensional and three-dimensional dynamic fracture examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. The method is extended to model fracture in composites.

Based on dual-horizon peridynamics, the nonlocal operator method (NOM) is presented which is applicable to the solution of any partial differential equations (PDEs). The nonlocal operator can be regarded as the integral form “equivalent” to the differential form in the sense of a nonlocal interaction model for solving the unknown field. The variation of a nonlocal operator plays an equivalent role as the derivatives of the shape functions in the meshless methods or those of the finite element method, thus it avoids the calculation of shape functions and their derivatives. The nonlocal operator method can consistently applied with common procedures leading to the weak forms, i.e. the variational principle and the weighted residual method. Based on these, the residual and the tangent stiffness matrix can be obtained with ease. The nonlocal operator method is enhanced here also with an operator energy functional to satisfy the linear consistency of the field. Higher order nonlocal operators and higher order operator energy functional are also generalized. The nonlocal strong forms of different functionals can be obtained easily via the concept of support and dual-support. Several numerical examples of different types of PDEs are presented in the end to show the effectiveness of the NOM.

Climbing higher and digging deeper 

I will offer some reflections on the past 25 years of peridynamics research and thoughts about the future. We have seen steady growth in the level of research activity on peridynamics in many parts of the world. New applications are discovered regularly. Papers on peridynamics appear frequently in leading journals. There is a natural compatibility between peridynamics and full-field measurement techniques in experiments. There is growing interest and progress in the connection between peridynamics, machine learning, and data-driven model development.

Peridynamics plays a natural role in the modeling of important areas of technology such as the nanoscale design of materials and diffusive transport over a wide range of length scales. The concept of a bond force has a simple interpretation in terms of elementary concepts familiar to all engineers. This makes it an appealing way to model the fundamental processes in many kinds of systems, especially when the interaction between multiple physical fields is involved. The properties of the theory in modeling fracture are being explored in greater depth.

The essential importance of nonlocality in many aspects of the natural world is gaining increasing recognition in the modeling community. Applied mathematicians are exploring fundamental aspects of nonlocal modeling and providing better solvers. The issues underlying the implementation of boundary conditions in nonlocal equations are increasingly understood, offering the prospect of nonlocal models that provide the user experience that engineers are familiar with. The connections between local and nonlocal theories are being exploited both in coupling techniques and methods like the peridynamic differential operator.  

I will share some experiences and observations about the progress we have made in peridynamics, the challenges we face, and trends in the level of acceptance in the research and engineering communities.

Designing Preferential Breakage Patterns in Strengthened Glass Containers

with Konstantin Koreshkov, Jiahua Yan, Jamie T. Westbrook, William J. Furnas, Jamie L. Morley, Vijay Subramanian, David Wilcox

A concern for food and drug manufacturers is maintaining the sterility of package contents from failing during transport and storage until consumer use. While glass containers are superior to many alternative materials, they are not unbreakable and occasionally experience damage from handling and transport. Cracks that extend through the wall thickness may form, compromising the sterility of the contents but not leading to catastrophic failure of the package. Such cracks may result in recalls when detected by a health care professional or end consumer at the point of use and can be costly to the pharmaceutical or foodstuff manufacturer. Accordingly, a need exists for alternative designs for glass containers for use in storing pharmaceutical products.

This talk explores, through the use of Peridynamic simulations, a strengthened glass container for holding either pharmaceutical products or foodstuff in a hermetic and/or sterile state. The strengthened glass container undergoes a strengthening process that produces compression at the surface and tension within the container wall. Certain geometrical features are explored that result in residual stresses which favor desirable crack propagation behaviors. The crack propagation behavior of the strengthened glass container is controlled to ensure catastrophic failure of the container, thus rendering the product unusable, should sterility be compromised by a through-wall crack.

Bio: Ross Stewart graduated from Alfred University with degrees in Mechanical Engineering, focusing on Multiscale Modeling of Material Failure. He has been working at Corning Incorporated since 2013, currently a Development Associate, where he studies material damage and failure, ranging from the molecular level up to larger scales of fracture and fragmentation, using Peridynamic modeling methods.

Nonlocal theories and peridynamics: A perspective from thermo-mechanics of heterogeneous materials (from minute 48:17 to end)

With the development of heterogeneous materials, especially metamaterials, a consensus emerges that the macroscopic governing equations of heterogeneous materials should be nonlocal, even the constituents are governed by the conventional local theory. The relations between the involved nonlocal parameters and the physical properties of the constituents need to be established. We present a bottom-up dynamic homogenization framework for dynamics and transient heat conduction of heterogeneous materials. The macroscopic governing equations derived are shown to be spatiotemporal nonlocal, and all parameters in the macroscopic governing equations are analytically determined by material and geometrical parameters of the constituents. The macroscopic governing equations can correspond to the peridynamic formulation, and the peridynamic horizon can be related to the microscopic parameters. Some special characteristics of the peridynamic media are revealed by analytical solutions.

Biography

      Jianxiang Wang is currently Changjiang Scholar Professor of Mechanics in Department of Mechanics and Engineering Science of Peking University. He received his PhD from The University of Sydney in 1995. He joined Peking University in 1998, after doing post-doctoral research in Imperial College in 1996 and Aalborg University in 1997. Jianxiang Wang’s research interests cover mechanics of heterogeneous materials and nano-structured materials, surface effects in heterogeneous materials and nanomaterials, and the Eshelby formalism. Jianxiang Wang once served as secretary-general of the 23rd International Congress of Theoretical and Applied Mechanics (ICTAM2012) of the IUTAM, and member of Congress Committee of the IUTAM (2014-2022). 

Peridynamics in China: a brief history and recent progress (from start to minute 48:16)

The last decade has witnessed the introduction of peridynamics to China and its subsequent development into a fruitful field for both fundamental investigations and engineering applications. This presentation will outline milestones in this brief history and review major achievements made by Chinese scholars on peridynamic theories, models, algorithms and software, with a focus on topics such as static and dynamic failure analysis of materials and structures, penetration and explosion impact failure problems, multi-physics coupling problems, and geotechnical problems. Some applications will also be discussed in fields including aerospace engineering, mechanical equipment engineering, transportation engineering, civil engineering, and water conservancy and hydropower engineering. The presentation will conclude with an overview of emerging trends and future directions of peridynamics in China. 

Bio: Qing Zhang is a professor in the Department of Engineering Mechanics of Hohai University, China. He received his B.S. in Engineering Mechanics in 1984 and his M.S. in Solid Mechanics in 1987 from Hohai University (named East China University of Water Resources before 1985) and became an associated professor there in 1994. He received his Ph.D. in Hydraulic Structure Engineering from Hohai University in 2000 and was promoted to full professor in the same year. Prof. Zhang has published more than 260 academic papers and 9 books and received 12 governmental and international awards. He is on the editorial boards of 8 academic journals, and has also served as a vice president of Chinese Association of Computational Mechanics (2007-2020) and as chairman of Liaison Committee on Computational Mechanics of South China (2008-). He is an EC member of ICACM (2007-), a GC member of IACM (2012-) and a GC member of APACM (2019-).