A modified cyclic constitutive model for engineered cementitious composites

Highlights

• A new cyclic constitutive model for ECC materials is proposed.

• The model improves the prediction of hysteretic stress-strain behavior of ECC.

• The model more accurately predicts residual deformation than existing models.

• The model is validated by experiments on various versions of ECCs and R/ECC.

Abstract

Residual strain is a key parameter reflecting the damage condition of engineered cementitious composite (ECC) structural components after experiencing cyclic loads. A new cyclic constitutive model is proposed for ECC materials to accurately capture their hysteretic responses and residual strains for numerically simulating the seismic response of structural systems. Companion to the modeling, experiments were conducted on different versions of ECC with various mechanical properties, and on reinforced ECC specimens. The experimental data are used to calibrate and validate the proposed model. The discrepancies between the predicted and measured unloading residual deformations are found to be generally less than 6%.

Introduction

Engineered cementitious composite (ECC) has emerged as a type of high-performance structural material in the past two decades. The microstructure and fiber/matrix interfaces within ECC are tailored to favor sequentially-formed steady-state cracking under tension [1]. As a result, ECC features a pseudo-strain-hardening tensile behavior with a strain capacity as high as 5% [2], [3]. This unique material property leads to extraordinary damage tolerance, high tensile ductility and energy dissipation capacity under extreme loads, and desired durability under service conditions [4]. Large-scale monotonic, cyclic, and impact loading tests on various types of structural elements made of ECC (e.g. beams, columns, walls, and connections) proved the superior structural performance of ECC as compared with conventional concrete [5], [6], [7], [8], [9], [10], [11]. Accordingly, ECC has been applied to the construction or repair of critical structural components in bridges, buildings, dams and tunnels [12], [13], [14], [15], [16], [17], [18].

Despite the increasing applications of ECC materials in practice, constitutive models needed to numerically simulate the behavior of ECC-based structural elements are few. Two categories of ECC constitutive models exist. The first one was developed based on micromechanics using a bottom-up multi-scale modeling approach [19], [20], [21]. The tensile response of ECC was modeled by linking the single fiber debonding and pullout behavior from cementitious matrix (microscale), to single steady-state crack opening bridged by numerous fibers with statistically distributed orientation and embedment length (mesoscale), and further to the sequential multiple microcracking process (macroscale) [19]. Although capable of describing the micromechanics mechanisms of ECC behavior, the models are not suitable for the numerical simulations of structural systems due to their complexity [22] or for cyclic loading conditions due to their emphasis on monotonic behavior under tension. The other type of ECC constitutive model, normally used for structural behavior predictions, considers smeared cracking, a continuum representation of the multiple microcracking generated during ECC strain-hardening stage in a volume element [23], [24], [25], [26], [27]. Some of the smeared crack models, such as those suggested by Li et al. [25] and Suryanto et al. [23], were developed for monotonic loading conditions only.

To date, only a limited number of constitutive models have been created for ECC cyclic loading behavior. Han et al. [28] developed a total-strain-based rotating crack model capable of simulating the cyclic loading response of ECC. To employ this model in the numerical simulations of structural components, a user needs the cyclic loading experiment data for the considered ECC material to input the key hysteretic modeling parameters such as residual strain for each loading cycle. Hung et al. [29], [30] proposed an improved version of ECC constitutive model where, in addition to the rotating crack model, a fixed crack model was also incorporated, leading to a better prediction of crack orientation. These models do not consider the scenarios that ECC can carry compressive stress when the material experiences a tensile strain or tensile stress when the material is subjected to a compressive strain. Therefore, the models do not fully represent the transitional behavior of ECC between cyclic tension and compression. In this sense, the models may overestimate the pinching effect of reinforced ECC structural elements under cyclic loading [22]. Gencturk and Elnashai [22], [31] suggested a model on the basis of the work by Han et al. [28]. Improvements included the use of a higher order reloading stress-strain relationship and an explicit definition of plastic residual strains upon unloading based on test data.

Although these models were developed mainly to predict the overall hysteretic response and strength of structural components, the residual deformation upon unloading was not a major focus. For instance, the model suggested by Gencturk and Elnashai [22], [31] assumed that residual deformation caused by unloading in tension is identical to that caused by unloading in compression, which is inconsistent with experimental observations. However, a proper prediction of ECC residual deformation is necessary for the numerical simulation of a structural system in several senses. First, the residual deformation can be accumulated over the loading cycles, thereby elongating a flexural component such as a beam. The elongation can dramatically alter the seismic response of a structure [32]. Second, the residual strain is an important indicator for the extent of local damage after a structure made of ECC material has suffered severe loading such as a major earthquake. Moreover, the residual strain may strongly affect the post-event condition of a structural system such as residual inter-story drift that impacts the post-earthquake functionality of a building.

It is further noted that the existing cyclic models for ECC [22], [28], [29] were tested by the experimental data of ECCs with a tensile strain capacity no more than 2%. The applicability of these models to ECCs with much higher ductility is largely unknown. In ECC, a large tensile ductility is achieved through higher density of microcracking before a localized fracture occurs, rooting in a difference in the behaviors of material microstructure, fiber/matrix interfaces, and pore network. These microscopic differences may lead to a discrepancy in the macroscopic hysteretic behavior between lower- (e.g. 2% tensile strain capacity) and higher-ductility ECCs (e.g. 4% tensile strain capacity). Also, microcracking density under each loading cycle influences the damage level in the material, consequently affecting the residual strain upon each unloading cycle. Therefore, it is of significance to validate the cyclic constitutive model with a wide range of ECC material designs that possess various tensile ductilities.

This paper presents a uniaxial hysteretic model for ECC formulated based on its behavior observed in experiments at various loading stages and modified from the existing models. Efforts are made particularly to improve the prediction of residual strains of ECC upon unloading by better modeling the transitional behavior between tension and compression. As a major advancement, the new model defines different residual strains caused by compression unloading and tension unloading to accurately reflect the experimental observations. The new model defines residual strains as a function of the maximum experienced strains. Therefore, the user only needs monotonic loading data of ECC rather than cyclic loading test data. Companion to the mechanical modeling, cyclic tension and bending tests were conducted on ECC specimens of different versions and with a wide range of mechanical properties, and were used to validate the proposed model.