List of Journal Publications
2021
4.
Ponson, L., Shabir, Z., Abdulmajid, M., Giessen, E. Van Der, Simone, A.
Unified scenario for the morphology of crack paths in two-dimensional disordered solids Journal Article
In: PHYSICAL REVIEW. E, vol. 104, no. 5, 2021.
Abstract | BibTeX | Tags: cracks, generalized finite element method, Hurst exponent, roughness | Links:
@article{Ponson2021,
title = {Unified scenario for the morphology of crack paths in two-dimensional disordered solids},
author = {L. Ponson and Z. Shabir and M. Abdulmajid and E. Van Der Giessen and A. Simone},
doi = {10.1103/PhysRevE.104.055003},
year = {2021},
date = {2021-01-01},
journal = {PHYSICAL REVIEW. E},
volume = {104},
number = {5},
publisher = {American Physical Society},
abstract = {A combined experimental and numerical investigation of the roughness of intergranular cracks in two-dimensional disordered solids is presented. We focus on brittle materials for which the characteristic length scale of damage is much smaller than the grain size. Surprisingly, brittle cracks do not follow a persistent path with a roughness exponent ζ≈0.6-0.7 as reported for a large range of materials. Instead, we show that they exhibit monoaffine scaling properties characterized by a roughness exponent ζ=0.50±0.05, which we explain theoretically from linear elastic fracture mechanics. Our findings support the description of the roughening process in two-dimensional brittle disordered solids by a random walk. Furthermore, they shed light on the failure mechanism at the origin of the persistent behavior with ζ≈0.6-0.7 observed for fractures in other materials, suggesting a unified scenario for the geometry of crack paths in two-dimensional disordered solids.},
keywords = {cracks, generalized finite element method, Hurst exponent, roughness},
pubstate = {published},
tppubtype = {article}
}
A combined experimental and numerical investigation of the roughness of intergranular cracks in two-dimensional disordered solids is presented. We focus on brittle materials for which the characteristic length scale of damage is much smaller than the grain size. Surprisingly, brittle cracks do not follow a persistent path with a roughness exponent ζ≈0.6-0.7 as reported for a large range of materials. Instead, we show that they exhibit monoaffine scaling properties characterized by a roughness exponent ζ=0.50±0.05, which we explain theoretically from linear elastic fracture mechanics. Our findings support the description of the roughening process in two-dimensional brittle disordered solids by a random walk. Furthermore, they shed light on the failure mechanism at the origin of the persistent behavior with ζ≈0.6-0.7 observed for fractures in other materials, suggesting a unified scenario for the geometry of crack paths in two-dimensional disordered solids.
2019
3.
Shabir, Z., der Giessen, E. Van, Duarte, C. A., Simone, A.
On the applicability of linear elastic fracture mechanics scaling relations in the analysis of intergranular fracture of brittle polycrystals Journal Article
In: INTERNATIONAL JOURNAL OF FRACTURE, vol. 220, no. 2, pp. 205–219, 2019.
Abstract | BibTeX | Tags: Brittle fracture, generalized finite element method, Linear elastic fracture mechanics, polycrystals, Scaling | Links:
@article{Shabir2019,
title = {On the applicability of linear elastic fracture mechanics scaling relations in the analysis of intergranular fracture of brittle polycrystals},
author = {Z. Shabir and E. Van der Giessen and C. A. Duarte and A. Simone},
doi = {10.1007/s10704-019-00381-x},
year = {2019},
date = {2019-01-01},
journal = {INTERNATIONAL JOURNAL OF FRACTURE},
volume = {220},
number = {2},
pages = {205–219},
publisher = {Springer},
abstract = {Crack propagation in polycrystalline specimens is studied by means of a generalized finite element method with linear elastic isotropic grains and cohesive grain boundaries. The corresponding mode-I intergranular cracks are characterized using a grain boundary brittleness criterion that depends on cohesive law parameters and average grain boundary length. It is shown that load–displacement curves for specimens with the same microstructure and for various cohesive law parameters can be obtained from a master load–displacement curve by means of simple linear elastic fracture mechanics scaling relations. This property is a consequence of the independence of intergranular crack paths from cohesive law parameters. Perfect scaling is obtained for cases characterized by the same grain boundary brittleness number, irrespective of its value, whereas scaling is approximated for cases with different but relatively large values of the grain boundary brittleness number. The former case corresponds to grain boundary traction profiles that are identical apart from a scale factor; in the latter case, a large grain boundary brittleness number implies similar, apart from a scale factor, traction profiles. By exploiting this property, it is demonstrated that computationally expensive simulations can be avoided above a certain grain boundary brittleness threshold value.},
keywords = {Brittle fracture, generalized finite element method, Linear elastic fracture mechanics, polycrystals, Scaling},
pubstate = {published},
tppubtype = {article}
}
Crack propagation in polycrystalline specimens is studied by means of a generalized finite element method with linear elastic isotropic grains and cohesive grain boundaries. The corresponding mode-I intergranular cracks are characterized using a grain boundary brittleness criterion that depends on cohesive law parameters and average grain boundary length. It is shown that load–displacement curves for specimens with the same microstructure and for various cohesive law parameters can be obtained from a master load–displacement curve by means of simple linear elastic fracture mechanics scaling relations. This property is a consequence of the independence of intergranular crack paths from cohesive law parameters. Perfect scaling is obtained for cases characterized by the same grain boundary brittleness number, irrespective of its value, whereas scaling is approximated for cases with different but relatively large values of the grain boundary brittleness number. The former case corresponds to grain boundary traction profiles that are identical apart from a scale factor; in the latter case, a large grain boundary brittleness number implies similar, apart from a scale factor, traction profiles. By exploiting this property, it is demonstrated that computationally expensive simulations can be avoided above a certain grain boundary brittleness threshold value.
2017
2.
Kim, J., Simone, A., Duarte, C. A.
Mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard FEM analysis of 3-D cohesive fractures Journal Article
In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, vol. 109, no. 2, pp. 235–258, 2017.
Abstract | BibTeX | Tags: adaptive mesh refinement, cohesive fracture, generalized finite element method, Newton-Raphson method | Links:
@article{Kim2017,
title = {Mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard FEM analysis of 3-D cohesive fractures},
author = {J. Kim and A. Simone and C. A. Duarte},
doi = {10.1002/nme.5286},
year = {2017},
date = {2017-01-01},
journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING},
volume = {109},
number = {2},
pages = {235–258},
publisher = {John Wiley and Sons Ltd},
abstract = {A robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures. This class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small-sized critical regions. The proposed approach is based on the division of a simulation into a suitable number of sub-simulations where adaptive mesh refinement is performed only once based on refinement window(s) around crack front process zone(s). The initialization of Newton-Raphson nonlinear iterations at the start of each sub-simulation is accomplished by solving a linear problem based on a secant stiffness, rather than a volume mapping of nonlinear solutions between meshes. The secant stiffness is evaluated using material state information stored/read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework. Moreover, a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software. Data transfer between sub-simulations is not required in the simplified strategy. The computational efficiency, accuracy, and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3-D.},
keywords = {adaptive mesh refinement, cohesive fracture, generalized finite element method, Newton-Raphson method},
pubstate = {published},
tppubtype = {article}
}
A robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures. This class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small-sized critical regions. The proposed approach is based on the division of a simulation into a suitable number of sub-simulations where adaptive mesh refinement is performed only once based on refinement window(s) around crack front process zone(s). The initialization of Newton-Raphson nonlinear iterations at the start of each sub-simulation is accomplished by solving a linear problem based on a secant stiffness, rather than a volume mapping of nonlinear solutions between meshes. The secant stiffness is evaluated using material state information stored/read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework. Moreover, a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software. Data transfer between sub-simulations is not required in the simplified strategy. The computational efficiency, accuracy, and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3-D.
2006
1.
Simone, A., Duarte, C. A., der Giessen, E. Van
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries Journal Article
In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, vol. 67, no. 8, pp. 1122–1145, 2006.
Abstract | BibTeX | Tags: Extended Finite Element Method, generalized finite element method, Grain boundary sliding, Partition of unity, polycrystals | Links:
@article{Simone2006,
title = {A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries},
author = {A. Simone and C. A. Duarte and E. Van der Giessen},
doi = {10.1002/nme.1658},
year = {2006},
date = {2006-01-01},
journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING},
volume = {67},
number = {8},
pages = {1122–1145},
abstract = {We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of finite element shape functions. Consequently, the finite element mesh does not need to conform to the polycrystal topology. The formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach. The proposed methodology can also be used for branched and intersecting cohesive cracks, and comparisons are made to a related approach (Int. J. Numer. Meth. Engng. 2000; 48:1741).},
keywords = {Extended Finite Element Method, generalized finite element method, Grain boundary sliding, Partition of unity, polycrystals},
pubstate = {published},
tppubtype = {article}
}
We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of finite element shape functions. Consequently, the finite element mesh does not need to conform to the polycrystal topology. The formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach. The proposed methodology can also be used for branched and intersecting cohesive cracks, and comparisons are made to a related approach (Int. J. Numer. Meth. Engng. 2000; 48:1741).
