[PDE & Applications seminar] Alejandro Aragon: Enriched Finite Element Analysis and Design of Metamaterials and Structures

28 September 2023 16:00 till 17:00 - Location: Van Katwijkzaal 08.150 | Add to my calendar

"Enriched finite element analysis (e-FEA) has an edge over standard FEA for problems that require complex meshing or those that involve moving boundaries. An e-FEA widely known is the eXtended/Generalized Finite Element Method (XFEM/GFEM). However, this methodology is no without issues, which include the lack of stability (arbitrarily large condition number of the stiffness matrix) when boundaries get arbitrarily close to standard mesh nodes, a non-trivial implementation of non-homogeneous essential boundary conditions, and a challenging computer implementation. These issues stem from the fact that enrichments are associated to standard mesh nodes. To circumvent these issues, while retaining the mesh-geometry decoupling property of XFEM/GFEM, a new family of interface- and discontinuity-enriched finite element methods has been proposed [1]. In these techniques, enrichments are placed directly along discontinuities, thereby solving the aforementioned issues of XFEM/GFEM.
This presentation will delve into e-FEA based on discontinuity-enriched FEMs. We will give an overview on the analysis capabilities of these methods for a wide set of problems, including the modeling of interfaces, fracture, immersed boundary problems, the coupling of non-conforming meshes and contact. We will also discuss recent developments in topology optimization, for which these e-FEA techniques are combined with a level set description of geometry. Problems investigated include compliance minimization [2], tailoring of fracture resistance in brittle solids [3], and in designing band gaps in phononic crystals [4].

References
[1] A.M. Aragón and A. Simone, The Discontinuity-Enriched Finite Element Method, International Journal for Numerical Methods in Engineering, 112(11), 1589-1613, 2017.
[2] S.J. van den Boom, J. Zhang, F. van Keulen, and A.M. Aragón, An interface-enriched generalized finite element method for level set-based topology optimization, Structural and Multidisciplinary Optimization, 63 (1), 1-20, 2021.
[3] J. Zhang, F. van Keulen, and A.M. Aragón, On tailoring fracture resistance of brittle structures: A level set interface-enriched topology optimization approach, Computer Methods in Applied Mechanics and Engineering 388, p. 114189, 2022.
[4] S.J.van den Boom, R. Abedi, F. van Keulen, A.M. Aragón, A level set-based interface-enriched topology optimization for the design of phononic crystals with smooth boundaries, Computer Methods in Applied Mechanics and Engineering 408, p. 115888, 2023."