l Enriched FEM for material interfaces | Aragón's research

An interface-enriched generalized finite element method for weak discontinuities

Enriched finite element methods (FEM) have gained traction in recent years due to the added versatility and flexibility in choosing the finite element discretization. In particular, enriched FEM can resolve discontinuities without loosing accuracy, which has given these methods an advantage over standard FEM for problems with complex and/or evolving discontinuities.

The Interface-Enriched Generalized Finite Element Method (IGFEM) was first introduced in 2012 to decouple the finite element mesh from weak discontinuities, such as those that arise at material interfaces. The method has been shown to be optimally convergent, and it is thus suitable for parametric studies given that virtually any number of realizations can be simulated with the same FE mesh.

Damage of microstructure
Damage in the matrix of a heterogeneous adhesive comopsed of spherical elastic inclusions. The spheres are completely decoupled from the discretization by means of IGFEM.

Related publications

  • S. J. van den Boom, F. van Keulen, and A. M. Aragón. "Fully decoupling geometry from discretization in the Bloch–Floquet finite element analysis of phononic crystals." Computer Methods in Applied Mechanics and Engineering 382 (2021), p. 113848.    
  • E. De Lazzari, S. J. van den Boom, J. Zhang, F. van Keulen, and A. M. Aragón. "A critical view on the use of Non-Uniform Rational B-Splines to improve geometry representation in enriched finite element methods." International Journal for Numerical Methods in Engineering (2021), pp. 1195-1216.    
  • A. M. Aragón, B. Liang, H. Ahmadian, and S. Soghrati. "On the stability and interpolating properties of the Hierarchical Interface-enriched Finite Element Method." Computer Methods in Applied Mechanics and Engineering 362 (2020), p. 112671    
  • 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    
  • A. Cuba-Ramos, and A. M. Aragón, S. Soghrati, P. H. Geubelle, and J.-F. Molinari. "A new formulation for imposing Dirichlet boundary conditions on non-matching meshes." International Journal for Numerical Methods in Engineering 103.6 (2015), pp. 430–444  
  • A. M. Aragón, S. Soghrati, and P. H. Geubelle. "Effect of in-plane deformation on the cohesive failure of heterogeneous adhesives." Journal of the Mechanics and Physics of Solids 61.7 (2013), pp. 1600–1611  
  • S. Soghrati, A. M. Aragón, C. Armando Duarte, and P. H. Geubelle. "An interface-enriched generalized FEM for problems with discontinuous gradient fields." International Journal for Numerical Methods in Engineering 89.8 (2012), pp. 991–1008