A discontinuity-enriched finite element method for weak and strong discontinuities

The finite element method is the procedure of choice for obtaining approximate solutions to boundary value problems in solid mechanics. However, problems with material interfaces (weak discontinuities) or cracks (strong discontinuities) are difficult to handle because, in order not to loose accuracy, the finite element discretizations have to be fitted to such interfaces. In practice, the creation of a matching FE mesh is a time consuming process that requires the use of powerful and robust mesh generators. Motivated by this, enriched finite element methods have gained a lot of attention in recent years because they made possible the decoupling of the FE mesh from the discontinuities, without losing accuracy.

The Discontinuity-Enriched Finite Element Method (DE-FEM) was introduced in 2017 as a new procedure for analyzing problems with both weak and strong discontinuities with a unified formulation. The technique is briefly showcased in the figure below, where both the crack and the material interface between trabecular and cortical bone are decoupled from the FE mesh used.

Bone fracture
Trulli
Analysis of cracked femur with a matching mesh to the external boundary but decoupled from the material interface and the crack

Related publications

  • 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.    
  • J. Zhang, S. J. van den Boom, F. van Keulen, and A. M. Aragón. "A stable discontinuity-enriched finite element method for 3-D problems containing weak and strong discontinuities." Computer Methods in Applied Mechanics and Engineering 355 (2019), pp. 1097–1123    
  • A. M. Aragón and A. Simone. "The Discontinuity-Enriched Finite Element Method." International Journal for Numerical Methods in Engineering 112.11 (2017), pp. 1589–1613