Time-dependent tension softening

Abstract

A methodology that combines a rheological model for viscoelastic behaviour with a micromechanical model for tension softening through the effective spring concept is developed for materials exhibiting both tension softening and time‐dependent behaviour. Spring elements with softening characteristics and dashpot with varying viscosity are used for this purpose. The characteristics of the spring elements and dashpot are obtained from a micromechanical model which relates the microstructure of the material to its tension softening response. The softening‐type springs ensure gradual reduction in stiffness, whereas the dashpot with varying viscosity ensures that the retardation and relaxation times equal prescribed values. In this way, both the stress and crack opening are allowed to vary with time to reflect the real behaviour of a time‐dependent tension softening material. The methodology is illustrated on the simple Poynting– Thompson rheological model, without restricting its application to more sophisticated models.

Failure lifetime of concrete structures under creep and fracture

“…Details about the micromechanical behaviour of the process zone, the rheological model (based on the models of Santhikumar and Karihaloo (1996) and ) and the finiteelement implementation are given by Barpi and Valente (2003;2004). Attention in this paper is focused on the size effect on failure lifetime; for more details the reader is referred to the above-mentioned papers.…”

“…(a) rate-dependent softening and activation energy, developed in a series of papers by Bažant and co-workers (Bažant, 1992;Bažant and Gettu, 1992;Bažant and Jiràsek, 1992;1993;Wu and Bažant, 1993); the method was modified by van Zijl et al (2001) (b) inclusion of a standard rheological model for creep and relaxation into the fictitious crack model in order to accommodate the time dependency of crack opening, the latter in some instances being established by fitting stress relaxation results (Barpi et al, 1999;Carpinteri et al, 1995;Hansen, 1990;1991;Zhang and Karihaloo, 1992a;1992b;Zhou and Hillerborg, 1992) (c) micromechanical model for the static softening behaviour of cracked concrete in the fracture process zone (Huang and Li, 1989) combined with a rheological model for time-dependent concrete behaviour as proposed by Santhikumar and Karihaloo (1996; and .…”

A fractional order rate approach for modeling concrete structures subjected to creep and fracture

“…In each point of the fictitious process zone a micromechanical approach to tension softening is combined with rheological model described above, according to a strategy proposed in Santhikumar and Karihaloo (1996) and . Tension softening behaviour appears when the damage in the material has localized along eventual fracture planes.…”

“…In the case of integer order rate law, the related diagrams are published in Santhikumar and Karihaloo (1996) and .…”

Time-Dependent Fracture Behavior of Rock–Concrete Interface Coupling Viscoelasticity and Cohesive Stress Relaxation

“…To reflect the cohesive stress relaxation within the FPZ, various constitutive models have been proposed to express the time-varying softening relationships within the FPZ under sustained loading for concrete. These models can be divided into three groups: (i) models with combinations of rate-dependent softening and activation energy, which was established by Bažant and co-workers (Bažant and Li 1997;Li and Bažant 1997) and modified by Zijl et al (2001a); (ii) micromechanical models for the static softening relationships coupled with the rheological models for the displacement creep and stress relaxation, which were proposed by Santhikumar and Karihaloo (1996; and improved by Brapi et al (2004); (iii) time-dependent fictitious crack models including the cohesive stress relaxation detected by experiment, which was originated by Zhou (1992). The variations of the cohesive stress in the time-dependent fictitious crack model were measured by a well-designed experimental set-up.…”