List of Journal Publications
2022
3.
Liu, Dy, Boom, Sj, Simone, A., Aragon, Am
An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact Journal Article
In: COMPUTATIONAL MECHANICS, vol. 70, no. 3, pp. 477–499, 2022.
Abstract | BibTeX | Tags: Contact, Enriched FEM, IGFEM, Lagrange multipliers, Multiple-point constraints, Non-conforming meshes | Links:
@article{Liu2022,
title = {An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact},
author = {Dy Liu and Sj Boom and A. Simone and Am Aragon},
doi = {10.1007/s00466-022-02159-w},
year = {2022},
date = {2022-01-01},
journal = {COMPUTATIONAL MECHANICS},
volume = {70},
number = {3},
pages = {477–499},
publisher = {SPRINGER},
abstract = {We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multi-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. We show that the node-to-node enrichment ensures continuity of the displacement field-without locking-in mesh coupling problems, and that tractions are transferred accurately at contact interfaces without the need for stabilization. We also show the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.},
keywords = {Contact, Enriched FEM, IGFEM, Lagrange multipliers, Multiple-point constraints, Non-conforming meshes},
pubstate = {published},
tppubtype = {article}
}
We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multi-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. We show that the node-to-node enrichment ensures continuity of the displacement field-without locking-in mesh coupling problems, and that tractions are transferred accurately at contact interfaces without the need for stabilization. We also show the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.
2020
2.
Aragon, A. M., Simone, A.
Discussion on “A linear complete extended finite element method for dynamic fracture simulation with non-nodal enrichments” [Finite Elem. Anal. Des. 152 (2018)] by I. Asareh, T.-Y. Kim, and J.-H. Song Journal Article
In: FINITE ELEMENTS IN ANALYSIS AND DESIGN, vol. 168, 2020.
Abstract | BibTeX | Tags: DE-FEM, IGFEM, NXFEM, strong discontinuities, Weak discontinuities, XFEM | Links:
@article{Aragon2020,
title = {Discussion on “A linear complete extended finite element method for dynamic fracture simulation with non-nodal enrichments” [Finite Elem. Anal. Des. 152 (2018)] by I. Asareh, T.-Y. Kim, and J.-H. Song},
author = {A. M. Aragon and A. Simone},
doi = {10.1016/j.finel.2019.103340},
year = {2020},
date = {2020-01-01},
journal = {FINITE ELEMENTS IN ANALYSIS AND DESIGN},
volume = {168},
publisher = {Elsevier B.V.},
abstract = {The subject paper purportedly proposes a novel enriched finite element method for modeling problems with strong discontinuities such as those encountered in fracture mechanics. The purpose of this document is to demonstrate that the method in the subject paper (Non-nodal eXtended Finite Element Method, NXFEM) is conceptually identical to the Discontinuity-Enriched Finite Element Method (DE-FEM) [Int. J. Numer. Meth. Eng. 2017; 112:1589–1613] proposed by Aragón and Simone.},
keywords = {DE-FEM, IGFEM, NXFEM, strong discontinuities, Weak discontinuities, XFEM},
pubstate = {published},
tppubtype = {article}
}
The subject paper purportedly proposes a novel enriched finite element method for modeling problems with strong discontinuities such as those encountered in fracture mechanics. The purpose of this document is to demonstrate that the method in the subject paper (Non-nodal eXtended Finite Element Method, NXFEM) is conceptually identical to the Discontinuity-Enriched Finite Element Method (DE-FEM) [Int. J. Numer. Meth. Eng. 2017; 112:1589–1613] proposed by Aragón and Simone.
2017
1.
Aragón, Alejandro M., Simone, A.
The Discontinuity-Enriched Finite Element Method Journal Article
In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, vol. 112, no. 11, pp. 1589–1613, 2017.
Abstract | BibTeX | Tags: cohesive cracks, fracture mechanics, GFEM, IGFEM, strong discontinuities, XFEM | Links:
@article{Aragon2017,
title = {The Discontinuity-Enriched Finite Element Method},
author = {Alejandro M. Aragón and A. Simone},
doi = {10.1002/nme.5570},
year = {2017},
date = {2017-01-01},
journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING},
volume = {112},
number = {11},
pages = {1589–1613},
publisher = {John Wiley and Sons Ltd},
abstract = {We introduce a new methodology for modeling problems with both weak and strong discontinuities independently of the finite element discretization. At variance with the eXtended/Generalized Finite Element Method (X/GFEM), the new method, named the Discontinuity-Enriched Finite Element Method (DE-FEM), adds enriched degrees of freedom only to nodes created at the intersection between a discontinuity and edges of elements in the mesh. Although general, the method is demonstrated in the context of fracture mechanics, and its versatility is illustrated with a set of traction-free and cohesive crack examples. We show that DE-FEM recovers the same rate of convergence as the standard FEM with matching meshes, and we also compare the new approach to X/GFEM.},
keywords = {cohesive cracks, fracture mechanics, GFEM, IGFEM, strong discontinuities, XFEM},
pubstate = {published},
tppubtype = {article}
}
We introduce a new methodology for modeling problems with both weak and strong discontinuities independently of the finite element discretization. At variance with the eXtended/Generalized Finite Element Method (X/GFEM), the new method, named the Discontinuity-Enriched Finite Element Method (DE-FEM), adds enriched degrees of freedom only to nodes created at the intersection between a discontinuity and edges of elements in the mesh. Although general, the method is demonstrated in the context of fracture mechanics, and its versatility is illustrated with a set of traction-free and cohesive crack examples. We show that DE-FEM recovers the same rate of convergence as the standard FEM with matching meshes, and we also compare the new approach to X/GFEM.
