Abstract
SUMMARY: This paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary, multiple intra-elemental discontinuities in 2D solids. The augmented finite element method (A-FEM) employs four internal nodes to account for the crack displacements due to an intra-elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single bilinear element that employs standard external nodal DoFs only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piece-wise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A-FEM's high-fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous, and heterogeneous solids have been demonstrated through several challenging numerical examples. It is shown that the proposed A-FEM, empowered by the new elemental condensation procedure, is numerically very efficient, accurate, and robust.
Original language | English (US) |
---|---|
Pages (from-to) | 438-468 |
Number of pages | 31 |
Journal | International Journal for Numerical Methods in Engineering |
Volume | 99 |
Issue number | 6 |
DOIs | |
State | Published - Aug 10 2014 |
Keywords
- Composites
- Damage
- Finite element methods
- Fracture
- Stability
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
- Numerical Analysis