List of Journal Publications
2017
4.
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.
2015
3.
Sillem, A., Simone, A., Sluys, L. J.
The Orthonormalized Generalized Finite Element Method-OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions Journal Article
In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol. 287, pp. 112–149, 2015.
Abstract | BibTeX | Tags: Condition number, GFEM, Improved convergence, Orthonormality, SGFEM, XFEM | Links:
@article{Sillem2015,
title = {The Orthonormalized Generalized Finite Element Method-OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions},
author = {A. Sillem and A. Simone and L. J. Sluys},
doi = {10.1016/j.cma.2014.11.043},
year = {2015},
date = {2015-01-01},
journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING},
volume = {287},
pages = {112–149},
publisher = {Elsevier},
abstract = {An extension of the Generalized Finite Element Method (GFEM) is proposed with which we efficiently reduce approximation errors. The new method constructs a stiffness matrix with a conditioning that is significantly better than the Stable Generalized Finite Element Method (SGFEM) and the Finite Element Method (FEM). Accordingly, the risk of a severe loss of accuracy in the computed solution, which burdens the GFEM, is prevented. Furthermore, the computational cost of the inversion of the associated stiffness matrix is significantly reduced. The GFEM employs a set of enriched basis functions which is chosen to improve the rate at which the approximation converges to the exact solution. The stiffness matrix constructed from these basis functions is often ill-conditioned and the accuracy of the solution cannot be guaranteed. We prevent this by orthonormalizing the basis functions and refer to the method as the Orthonormalized Generalized Finite Element Method (OGFEM). Because the OGFEM has the flexibility to orthonormalize either a part or all of the basis functions, the method can be considered as a generalization of the GFEM. The method is applicable with single or multiple global and/or local enrichment functions. Problems in blending elements are avoided by a modification of the enrichment functions. The method is demonstrated for the one-dimensional modified Helmholtz and Poisson equations and compared with the FEM, GFEM and SGFEM.},
keywords = {Condition number, GFEM, Improved convergence, Orthonormality, SGFEM, XFEM},
pubstate = {published},
tppubtype = {article}
}
An extension of the Generalized Finite Element Method (GFEM) is proposed with which we efficiently reduce approximation errors. The new method constructs a stiffness matrix with a conditioning that is significantly better than the Stable Generalized Finite Element Method (SGFEM) and the Finite Element Method (FEM). Accordingly, the risk of a severe loss of accuracy in the computed solution, which burdens the GFEM, is prevented. Furthermore, the computational cost of the inversion of the associated stiffness matrix is significantly reduced. The GFEM employs a set of enriched basis functions which is chosen to improve the rate at which the approximation converges to the exact solution. The stiffness matrix constructed from these basis functions is often ill-conditioned and the accuracy of the solution cannot be guaranteed. We prevent this by orthonormalizing the basis functions and refer to the method as the Orthonormalized Generalized Finite Element Method (OGFEM). Because the OGFEM has the flexibility to orthonormalize either a part or all of the basis functions, the method can be considered as a generalization of the GFEM. The method is applicable with single or multiple global and/or local enrichment functions. Problems in blending elements are avoided by a modification of the enrichment functions. The method is demonstrated for the one-dimensional modified Helmholtz and Poisson equations and compared with the FEM, GFEM and SGFEM.
2013
2.
Vandoren, B., Proft, K. De, Simone, A., Sluys, L. J.
Mesoscopic modelling of masonry using weak and strong discontinuities Journal Article
In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol. 255, pp. 167–182, 2013.
Abstract | BibTeX | Tags: Damage, GFEM, Masonry, Mesoscopic model, Partition of unity, Weak discontinuities | Links:
@article{Vandoren2013a,
title = {Mesoscopic modelling of masonry using weak and strong discontinuities},
author = {B. Vandoren and K. De Proft and A. Simone and L. J. Sluys},
doi = {10.1016/j.cma.2012.11.005},
year = {2013},
date = {2013-01-01},
journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING},
volume = {255},
pages = {167–182},
publisher = {ELSEVIER SCIENCE SA},
abstract = {A mesoscopic masonry model is presented in which joints are modelled by weak and strong discontinuities through the partition of unity property of finite element shape functions. A Drucker-Prager damage model describes joint degradation whereas the bricks remain linear elastic throughout the simulations. Analogies and differences amongst strong and weak discontinuity models are discussed, with special emphasis on kinematic description and implementation. Mesh sensitivity and performance of the presented models are illustrated by two-brick, three-point bending and shear wall tests.},
keywords = {Damage, GFEM, Masonry, Mesoscopic model, Partition of unity, Weak discontinuities},
pubstate = {published},
tppubtype = {article}
}
A mesoscopic masonry model is presented in which joints are modelled by weak and strong discontinuities through the partition of unity property of finite element shape functions. A Drucker-Prager damage model describes joint degradation whereas the bricks remain linear elastic throughout the simulations. Analogies and differences amongst strong and weak discontinuity models are discussed, with special emphasis on kinematic description and implementation. Mesh sensitivity and performance of the presented models are illustrated by two-brick, three-point bending and shear wall tests.
2011
1.
Shabir, Z., der Giessen, E. Van, Duarte, C. A., Simone, A.
The role of cohesive properties on intergranular crack propagation in brittle polycrystals Journal Article
In: MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING, vol. 19, no. 3, 2011.
Abstract | BibTeX | Tags: brittle failure, cracks, GFEM, polycrystals | Links:
@article{Shabir2011,
title = {The role of cohesive properties on intergranular crack propagation in brittle polycrystals},
author = {Z. Shabir and E. Van der Giessen and C. A. Duarte and A. Simone},
doi = {10.1088/0965-0393/19/3/035006},
year = {2011},
date = {2011-01-01},
journal = {MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING},
volume = {19},
number = {3},
abstract = {We analyze intergranular brittle cracking of polycrystalline aggregates by means of a generalized finite element method for polycrystals with cohesive grain boundaries and linear elastic grains. Many random realizations of a polycrystalline topology are considered and it is shown that the resulting crack paths are insensitive to key cohesive law parameters such as maximum cohesive strength and critical fracture energy. Normal and tangential contributions to the dissipated energy are thoroughly investigated with respect to mesh refinement, cohesive law parameters and randomness of the underlying polycrystalline microstructure.},
keywords = {brittle failure, cracks, GFEM, polycrystals},
pubstate = {published},
tppubtype = {article}
}
We analyze intergranular brittle cracking of polycrystalline aggregates by means of a generalized finite element method for polycrystals with cohesive grain boundaries and linear elastic grains. Many random realizations of a polycrystalline topology are considered and it is shown that the resulting crack paths are insensitive to key cohesive law parameters such as maximum cohesive strength and critical fracture energy. Normal and tangential contributions to the dissipated energy are thoroughly investigated with respect to mesh refinement, cohesive law parameters and randomness of the underlying polycrystalline microstructure.
