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Tension-softening constitutive relation and numerical simulation method for mode I fatigue crack propagation in concrete

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Mengdi Jia at Dalian University of Technology
Mengdi Jia
Zhimin Wu
Zhimin Wu
Zhimin Wu
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Rena C. Yu at University of Castilla-La Mancha
Rena C. Yu
Xiaoxin Zhang at University of Castilla-La Mancha
Xiaoxin Zhang
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Abstract and Figures

This paper presents the investigations of the tension-softening constitutive relation of concrete and the numerical method for mode I fatigue crack propagation in concrete. Firstly, the static loading, fatigue loading, and fatigue–static loading were carried out on 191 notched three-point bending (TPB) beams. With the experimental results, the tension-softening constitutive relation of concrete under fatigue loading was proposed from the view of energy conservation, where the equilibrium relation between the energy dissipated by crack propagation and the external work was established. Secondly, by combining the constitutive relation with the stress intensity factor (SIF)-based crack propagation criterion, the numerical method for mode I fatigue crack propagation in concrete was developed. Finally, the applicability of the numerical method was validated by comparing the numerically derived fatigue life, fatigue crack propagation length, crack mouth opening displacement (CMOD), and SIF with the experimental results. It is concluded that the numerical method proposed in this paper is significantly helpful in evaluating the fatigue performance of concrete structures.
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ORIGINAL PAPER
Tension-softening constitutive relation and numerical
simulation method for mode I fatigue crack propagation
in concrete
Mengdi Jia .Zhimin Wu .Rena C. Yu .Xiaoxin Zhang
Received: 29 November 2021 / Accepted: 29 April 2022 / Published online: 4 August 2022
The Author(s), under exclusive licence to Springer Nature B.V. 2022
Abstract This paper presents the investigations of
the tension-softening constitutive relation of concrete
and the numerical method for mode I fatigue crack
propagation in concrete. Firstly, the static loading,
fatigue loading, and fatigue–static loading were car-
ried out on 191 notched three-point bending (TPB)
beams. With the experimental results, the tension-
softening constitutive relation of concrete under
fatigue loading was proposed from the view of energy
conservation, where the equilibrium relation between
the energy dissipated by crack propagation and the
external work was established. Secondly, by combin-
ing the constitutive relation with the stress intensity
factor (SIF)-based crack propagation criterion, the
numerical method for mode I fatigue crack propaga-
tion in concrete was developed. Finally, the applica-
bility of the numerical method was validated by
comparing the numerically derived fatigue life,
fatigue crack propagation length, crack mouth opening
displacement (CMOD), and SIF with the experimental
results. It is concluded that the numerical method
proposed in this paper is significantly helpful in
evaluating the fatigue performance of concrete
structures.
Keywords Concrete Fatigue crack propagation
Tension-softening constitutive relation Crack
propagation criterion Numerical method
1 Introduction
According to the fictitious crack model (Hillerborg
et al. 1976), the relation between the cohesive stress
and the crack opening displacement is adopted to
characterize the nonlinear behavior of concrete after
cracking. Under fatigue loading, the cohesive stress
gradually decays, resulting in the propagation of
fatigue cracks and the deterioration of mechanical
properties of concrete structures. Eventually, fatigue
failure may occur (Slowik et al. 1996; Zhang and Wu
1997; Soroushian and Elzafraney 2004; Gonza
´lez
et al. 2015). Therefore, given the importance of the
stress degradation to the fatigue failure of concrete
structures, the fatigue crack propagation in concrete
should be deeply investigated by considering the
cohesive stress under fatigue loading.
Currently, considerable investigations on the ten-
sion-softening constitutive relation of concrete under
fatigue loading were conducted, and the
M. Jia Z. Wu (&)
State Key Laboratory of Coastal and Offshore
Engineering, Dalian University of Technology,
Dalian 116024, China
e-mail: wuzhimin@dlut.edu.cn
R. C. Yu X. Zhang
ETS de Ingenieros de Caminos, Canales y Puertos,
Universidad de Castilla-La Mancha, 13071 Ciudad Real,
Spain
123
Int J Fract (2022) 238:133–163
https://doi.org/10.1007/s10704-022-00642-2(0123456789().,-volV)(0123456789().,-volV)
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