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A fracture energy–based viscoelastic–viscoplastic–anisotropic damage model for rate-dependent cracking of concrete

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Abstract

A fracture energy-based constitutive model of concrete in the framework of continuum damage mechanics is formulated. Elastic, viscoelastic, and viscoplastic mechanisms are defined in a fictitious undamaged material state, the so-called effective configuration. A linear spring and a linear dashpot characterize the viscoelastic response of concrete. The viscoplastic behavior is also described using a linear spring, a nonlinear dashpot, and a slider with constant frictional resistance. The nonlinear dashpot of the viscoplastic body is formulated using a logarithmic function so that the model can reproduce valid strength magnifications under a wide range of strain rates. As a result, a consistency viscoplastic approach is obtained wherein, in contrast to the so-called overstress viscoplastic laws, the rate effects are induced in the yield surface of the model. A fracture energy-based regularization is employed to adjust the rate of damage growth to obtain mesh-objective results. The directional degradation of concrete is also characterized by a frame-independent tensorial description of damage. Next, a fully implicit return-mapping algorithm based on the Newton–Raphson scheme is proposed. The presented model is then assessed by validating its results with a series of experimental tests. In addition, the mixed-mode fracture of concrete is investigated under different strain rates, verifying the experimentally observed transition of the failure mode from a ductile flexural to a brittle diagonal failure.

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Acknowledgements

This research was funded by Iran National Science Foundation (Grant No. 97023017), the National Key Research and Development Plan, Intergovernmental Key Projects for International Scientific and Technological Cooperation (Grant No. 2018YFE0122400), and National Natural Science Foundation of China (Grant Nos. 11372098 and 51579084).

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  1. Civil Engineering Department, Sharif University of Technology, Tehran, Iran

    Alireza Daneshyar & Mohsen Ghaemian

  2. College of Mechanics and Materials, Hohai University, Nanjing, China

    Chengbin Du

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  1. Alireza Daneshyar
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Daneshyar, A., Ghaemian, M. & Du, C. A fracture energy–based viscoelastic–viscoplastic–anisotropic damage model for rate-dependent cracking of concrete. Int J Fract 241, 1–26 (2023). https://doi.org/10.1007/s10704-022-00685-5

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