Structural Engineering and Mechanics

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A new formulation of cracking in concrete structures based on lumped damage mechanics

  • Daniel V.C. Teles (Laboratory of Mathematical Modelling in Civil Engineering, Post-graduate Program in Civil Engineering, Federal University of Sergipe) ;
  • Rafael N. Cunha (Post-graduate Program in Civil Engineering, Federal University of Alagoas) ;
  • Ricardo A. Picon (Departamento de Obras Civiles y Geologia, Facultad de Ingenieria, Universidad Catolica de Temuco) ;
  • David L.N.F. Amorim (Laboratory of Mathematical Modelling in Civil Engineering, Post-graduate Program in Civil Engineering, Federal University of Sergipe) ;
  • Yongtao Bai (School of Civil Engineering, Chongqing University) ;
  • Sergio P.B. Proenca (Department of Structural Engineering, Engineering School of Sao Carlos, University of Sao Paulo) ;
  • Julio Florez-Lopez (School of Civil Engineering, Chongqing University)
  • Received : 2023.03.18
  • Accepted : 2023.11.16
  • Published : 2023.12.10
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Abstract

Lumped Damage Mechanics (LDM) is a theory proposed in the late eighties, which assumes that structural collapse may be analyzed as a two-phase phenomenon. In the first (pre-localization) stage, energy dissipation is a continuous process and it may be modelled by means of the classic versions of the theory of plasticity or Continuum Damage Mechanics (CDM). The second, post-localization, phase can be modelled assuming that energy dissipation is lumped in zones of zero volume: inelastic hinges, hinge lines or localization surfaces. This paper proposes a new LDM formulation for cracking in concrete structures in tension. It also describes its numerical implementation in conventional finite element programs. The results of three numerical simulations of experimental tests reported in the literature are presented. They correspond to plain and fiber-reinforced concrete specimens. A fourth simulation describes also the experimental results of a new test using the digital image correlation technique. These numerical simulations are also compared with the ones obtained using conventional Cohesive Fracture Mechanics (CFM). It is then shown that LDM conserves the advantages of both, CDM and CFM, while overcoming their drawbacks.

Keywords

Acknowledgement

The authors acknowledge the Laboratory of Mathematical Modelling in Civil Engineering (LAMEC) of the Post-graduate Program in Civil Engineering of the Federal University of Sergipe (PROEC/UFS) and the Laboratory of Building Materials and Structures (LAMCE/UFS) for the physical support during the development of this work. The first and the second authors acknowledge CAPES (Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior) for the financial support of their M.Sc. and D.Sc. studies, respectively. The first and the fourth author acknowledge the PROAP/CAPES grants 23113.058556/2019-31, 23113.064080/2019-78, 23113.025644/2020-58 and 23113.031287/2022-78 provided by the PROEC/UFS. The fourth author acknowledges CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico), Brazil, for the grant 436523/2018-3 (Chamada Universal CNPq MCTIC).

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