Node-to-segment and node-to-surface interface finite elements for fracture mechanics

authored by: M. Paggi, P. Wriggers
Abstract: The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets (in 3D) belonging to the opposite crack faces and enforce the cohesive traction-separation relation. In the present work we propose a novel type of interface element for fracture mechanics sharing some analogies with the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact elements. The displacement gap of a node belonging to the finite element discretization of one crack face with respect to its projected point on the opposite face is used to determine the cohesive tractions, the residual vector and its consistent linearization for an implicit solution scheme. The following advantages with respect to classical interface finite elements are demonstrated: (i) non-matching finite element discretizations of the opposite crack faces is possible; (ii) easy modeling of cohesive cracks with non-propagating crack tips; (iii) the internal rotational equilibrium of the interface element is assured. Detailed examples are provided to show the usefulness of the proposed approach in nonlinear fracture mechanics problems.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): IMT School for Advanced Studies Lucca
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 300
Pages: 540-560
No. of pages: 21
ISSN: 0045-7825
Publication date: 28.11.2015
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2015.11.023 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{7600293dd865482c8438ecf1ffaa1d33,
title = "Node-to-segment and node-to-surface interface finite elements for fracture mechanics",
abstract = "The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets (in 3D) belonging to the opposite crack faces and enforce the cohesive traction-separation relation. In the present work we propose a novel type of interface element for fracture mechanics sharing some analogies with the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact elements. The displacement gap of a node belonging to the finite element discretization of one crack face with respect to its projected point on the opposite face is used to determine the cohesive tractions, the residual vector and its consistent linearization for an implicit solution scheme. The following advantages with respect to classical interface finite elements are demonstrated: (i) non-matching finite element discretizations of the opposite crack faces is possible; (ii) easy modeling of cohesive cracks with non-propagating crack tips; (iii) the internal rotational equilibrium of the interface element is assured. Detailed examples are provided to show the usefulness of the proposed approach in nonlinear fracture mechanics problems.",
keywords = "Cohesive zone model, Finite element discretization, Interface cracks, Interface finite elements, Nonlinear fracture mechanics",
author = "M. Paggi and P. Wriggers",
note = "Funding information: The research leading to these results has received funding from the European Research Council under the European Union{\textquoteright}s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement no. 306622 (ERC Starting Grant “Multi-field and multi-scale Computational Approach to Design and Durability of PhotoVoltaic Modules”—CA2PVM; PI: Prof. M. Paggi).",
year = "2015",
month = nov,
day = "28",
doi = "10.1016/j.cma.2015.11.023",
language = "English",
volume = "300",
pages = "540--560",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}