Stochastic damage model for concrete based on energy equivalent strain

Abstract

a b s t r a c tStarting with the framework of conventional elastoplastic damage mechanics, a class of stochastic damage constitutive model is derived based on the concept of energy equivalent strain. The stochastic damage model derived from the parallel element model is adopted to develop the uniaxial damage evolution function. Based on the expressions of damage energy release rates (DERRs) conjugated to the damage variables thermodynamically, the concept and its tensor formulations of energy equivalent strain is proposed to bridge the gap between the uniaxial and the multiaxial constitutive models. Furthermore, a simplified coupling model is proposed to consider the evolution of plastic strain. And the analytical expressions of the constitutive model in 2-D are established from the abstract tensor expression. Several numerical simulations are presented against the biaxial loading test results of concrete, demonstrating that the proposed models can reflect the salient features for concrete under uniaxial and biaxial loading conditions.

Fatigue Performance of CRTS III Slab Ballastless Track Structure un-der High-speed Train Load Based on Concrete Fatigue Damage Constitu-tive Law

“…Specifically, the modeling of heterogeneity in the stress-strain relationship of concrete during the loading process is a key characteristic in numerical simulation. By considering the random pre-existing micro-flaws and cracks in concrete, a method named fiber bundle models (FBMs) (Wu et al 2006(Wu et al , 2013Li and Ren 2009; focus on the stochastic properties with the approach of materials' micro-mechanics is developed. In detail, with the randomly scattered micro-cracks and voids, when concrete is subjected to external loads, the evolution and the propagation of the initial damage will cause the degradation of materials' stiffness and finally results in the observation on the nonlinearity in the stress-strain relationship during the experiment.…”

A rate-dependent stochastic damage–plasticity model for quasi-brittle materials

“…Based on the damage release rate dependent damage evolution and the damage consistent condition, Li and Ren [23] further developed the damage evolution driven by the energy equivalent strain as follows…”

“…The development of damage evolution function is refer to [17] and [23]. The stochastic damage evolution functions under static loading are expressed as follows (32) where Δ(x) is the 1-D micro-fracture strain random field;…”

“…[17] investigated the stochastic damage model and developed the standard deviation of damage evolution. Li and Ren [23] further improved the results of [17] and implemented the stochastic damage model into the energy based multiaxial damage-plasticity framework.…”

Experimental and Numerical Researches on the Seismic Behavior of Tubular Reinforced Concrete Columns of Air-Cooling Structures

“…For common reinforced concrete members, lots of experimental investigations have been conducted (Nilson and Arthur 1968;Bathe and Ramaswamg 1979;Priestly and Benzoni 1996;Lehman et al 1995;Phan et al 2007;Hindi 2005;Hindi et al 2005;Wang et al 2014;Afefy and El-Tony 2016;Jiong 2004;Li and Ren 2009;Elmorsi et al 1998;Esmaeily and Shirmohammadi 2014;Shao et al 2005;Zendaoui et al 2016;Ren et al 2010). Previous studies of reinforced concrete members have demonstrated that slender ratio, material property, axial compression ratio, reinforcement ratio, detailing art and stirrups played significant roles in the seismic behavior, especially the hysteretic performance of reinforced concrete members.…”