An interface-enriched formulation for immersing complex domains

It is not always desirable to generate a mesh that conforms to the boundaries, for instance in cases where the boundary has a very complex shape or in cases where the boundary evolves, such as during optimization or in fluid-structure interaction. The Interface-enriched Generalized Finite Element Method (IGFEM) and Discontinuity-enriched Finite Element Method (DE-FEM) were developed for solving problems with interfaces and the combinations of interfaces and cracks, respectively. This work extends both methods to immersed boundary problems, where the boundaries of the domain are completely decoupled from and immersed into a structured finite element mesh. In contrast to other immersed boundary methods, essential boundary conditions with our approach can be prescribed strongly. Most important, this is the first enriched method for which a smooth traction field can be recovered in parts of the boundary with essential boundary conditions. This capability was showcased in the cover of the journal.

Immersed analysis of popcorn solid
Trulli
The image shows the analysis of a complex object by immersing it in a simple structured tetrahedral mesh and the smooth traction field recovered (ours is the first enriched FEA that shows this is possible).

Related publications

  • S. J. van den Boom, J. Zhang, F. van Keulen, A. M. Aragón. "Cover Image." International Journal for Numerical Methods in Engineering 120.10 (2019), pp. i–i  
  • S. J. van den Boom, J. Zhang, F. van Keulen, and A. M. Aragón. "A stable interface-enriched formulation for immersed domains with strong enforcement of essential boundary conditions." International Journal for Numerical Methods in Engineering 120.10 (2019), pp. 1163–1183    
  • E. De Lazzari, S.J. van den Boom, J. Zhang, F. van Keulen, and A. M. Aragón. "A critical view on the use of NURBS to improve geometry representation in enriched finite element methods." International Journal for Numerical Methods in Engineering, (2021), In Press.