Using Mixed Discrete-Continuum Representations to Characterize the Dynamics of Large Many-Body Dynamics Problems

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The goal of this project is to understand how computer simulation can be used to predict the motion of large systems of bodies interacting with each other through friction and contact. Studying these so-called "many-body dynamics problems" has theoretical and practical relevance in several disciplines (physics, chemistry, astronomy, geomechanics), industries (pharmaceuticals, food processing, farming, manufacturing, construction, mining), and engineering applications (additive manufacturing, nanoparticle self-assembly, robotics, ground vehicle mobility). In terms of educational and outreach impact, initiatives undertaken as part of this project will (i) promote the discipline of Computational Science at middle and high-school levels via a "The Science Behind Video Gaming" short course and a residential summer program, respectively; (ii) update and expand curricula in two graduate courses on high performance computing and advanced computational dynamics; (iii) expand a biannual advanced computing forum that facilitates transfer of technology; and, (iv) provide training via a Master of Engineering distance learning program for practitioners who need to analyze, process, and solve problems using information generated by the growing use of data collection in engineering design and industrial operations.The research effort will focus on investigating techniques that facilitate a discrete-continuum dual representation in the simulation of many-body dynamics problems. The fundamental question answered is how should one handle parts of a many-body dynamics problem using a continuum formalism so that the new mixed discrete-continuum representation manages to preserve the dynamics of the original problem? Also, how should a continuum representation be fine-grained into a discrete one, and conversely, what techniques should be used to coarse-grain a discrete representation into a continuous one? Mechanical engineering expertise (dynamics of many-body systems, solid mechanics, plasticity), applied math techniques (meshless methods for solving partial differential equations, optimization methods), and computer science components (machine learning, software engineering) will combine in a coordinated effort to solve the stated problem. In this context, the goal of this project is to (a) establish a systematic methodology for producing rheologies that, when embedded in a continuum mechanics model, produce a solution that is close to that of a large discrete many-body dynamics problem; and (b) use this methodology to understand whether there are rheologies that have a universal attribute; i.e., that are applicable to all, or a large spectrum of, many-body dynamics problems. In this context, a rheology is regarded as a methodology that ties at microscale the dynamics/flow of a continuum to the forces acting on it. The research plan is built around the idea of augmenting physical insights with a machine learning process that uses large amounts of data generated by fully-resolved, many-body dynamics solutions to produce rheology candidates.