Isogeometric Shells with Emphasis on Modeling of Architected Structures

Yuri Bazilevs

Brown University, USA

While IGA has significantly impacted much of computational mechanics, one area that has benefited the most from IGA research is computational methods for shell structures. Because geometrically complex, smooth surfaces are naturally represented in CAD systems, much of that technology could be directly employed in the discretization of existing shell theories, with increased accuracy and robustness in general-purpose nonlinear applications relative to traditional FEA representations. In addition, the increased smoothness of CAD surface representation (by means of B-Splines and their rational and unstructured variants) enabled the formulation, and use in general-purpose nonlinear applications, of thin shell theories previously unattainable in traditional FEA. Many more developments followed, making shells some of the most mature of IGA technologies today and a prime candidate for implementation in commercial FEA codes. This presentation will focus on key recent developments in IGA for thin shell structures and show a novel application of IGA to the modeling of architected materials and structures.

In recent years, architected materials and structures have gained significant popularity due to their ability to reach enhanced performance for use in multifunctional and multidisciplinary applications. Among numerous options investigated, architected structures based on Triply Periodic Minimal Surfaces (TPMS) have gained increasing attention because they exhibit exceptional properties in multiple disciplines simultaneously. However, because of the complexities involved in the geometry representation and mechanical response of these structures, physics-based modeling for this problem class engenders a set of challenges. In this paper we address some of these challenges by developing a first-of-its-kind IGA-based geometry modeling and simulation framework for architected materials and structures. We focus on sheet TPMS-based structures, for which we first develop an IGA-suitable geometry modeling pipeline and then evaluate their mechanical performance in crushing simulations.

Biography: Yuri Bazilevs is the E. Paul Sorensen Professor in the School of Engineering at Brown University. His research interests are in computational science and engineering, with emphasis on the modeling and simulation in solids and structures, fluids, and their coupling in HPC environments. For his research contributions Yuri received many awards and honors, including the 2018 Walter E. Huber Research Prize from the ASCE, the 2020 Gustus L. Larson Award from the ASME, and the Computational Mechanics Award from the International Association for Computational Mechanics (IACM). He is included in the lists of Highly Cited Researchers, both in the Engineering (2015-2018) and Computer Science (2014-2019) categories. Yuri recently completed his service as the President of the US Association for Computational Mechanics (USACM) and as the Chairman of the Applied Mechanics Division of the ASME. He currently serves on the US National Committee for Theoretical and Applied Mechanics (USNC/TAM).