A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars

Ogrin, Anita (author), Planinc, Igor (author), Bratina, Sebastjan (author)

The paper presents a novel family of strain-based beam finite elements (FE) for analysis of tensile failure of a reinforced concrete bar (RC bar), with results of the analysis being independent of the applied FE mesh. The composite bar consists of a continuous longitudinal ductile reinforcing bar(s) surrounded by brittle concrete cover, which are considered separately in the model. Longitudinal slip at the contact between the concrete cover and reinforcing bars is allowed, while their relative displacements perpendicular to the axis of the RC bar are prevented. Cracks in concrete cover occur when tensile stress in concrete exceeds its tensile strength. Propagation of partially connected crack, that is, softening of the material at the crack, is described through constitutive law in form of nonlinear relationship between stresses in concrete at the crack and the width of the crack. Each separate crack is considered discretely as a discontinuity in geometry of the element. In the analysis of cracking of concrete, it is commonly assumed that the discrete crack can occur at the nodes of FE only. However, this assumption leads to dependence of the analysis results on the employed FE mesh. The presented family of FE enables occurrence of the crack anywhere along the FE. In order to achieve this, the discrete crack is excluded from equations of FE and additional boundary conditions are introduced at the discontinuity. This approach ensures that the location of the cracks, their number and their propagation are independent of the applied FE mesh. Advantages of the novel family of FE are thoroughly presented in a parametric study which investigates influence of number of FE as well as influence of degrees of interpolation and integration on the cracking of RC bar under tensile loading. Experimental results of tensile tests on the analysed bar are available in literature. It can be concluded that the results obtained with the minimal possible number of novel FE and sufficiently high degree of numerical integration scheme, applied for solving integrals in equations of FE, are considerably more accurate than the results of previous analyses with model of discrete crack at the nodes of FE only.

• Language: English
• Keywords: civil engineering, composite element, reinforced concrete bar, tensile failure, discrete crack, excluded point, finite element, mesh-independence, localisation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2022
• Number of pages: Str. 572–584
• Numbering: Vol. 25, iss. 3
• PID: 20.500.12556/RUL-133962
• UDC: 624.07
• ISSN on article: 2048-4011
• DOI: 10.1177/13694332211058533
• COBISS.SI-ID: 90217731
• Publication date in RUL: 20.12.2021

OGRIN, Anita, PLANINC, Igor and BRATINA, Sebastjan, 2022, A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars. Advances in structural engineering [online]. 2022. Vol. 25, no. 3. [Accessed 18 May 2025]. DOI 10.1177/13694332211058533. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=133962

Record is a part of a journal

• Title: Advances in structural engineering
• Shortened title: Adv. struct. eng.
• Publisher: SAGE
• ISSN: 2048-4011
• COBISS.SI-ID: 89808643

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: gradbeništvo, kompozitni element, armiranobetonska palica, natezna porušitev, diskretna razpoka, izključena točka, končni element, neodvisnost od mreže, lokalizacija

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0158
• Name: Gradbene konstrukcije in gradbena fizika

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0260
• Name: Mehanika konstrukcij