PSI - Issue 13

Jiaming Wang et al. / Procedia Structural Integrity 13 (2018) 560–565 J. Wang et al. / Structural Integrity Procedia 00 (2018) 000–000

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or elastic-plastic-damageable material in di ff erent modelling approaches. ITZ is a very thin layer, normally 10 to 50 µ m , of highly porous mortar coating on aggregates [Tasong et al. (1999) and Xiao et al. (2013)] and appears to be the ”weakest link” in concrete, due to its low mechanical strength and high permeability to detrimental chemicals. Three main approaches to meso-structure modelling have been proposed: 1) Neglect ITZ and consider only aggregate and mortar [Du et al. (2014); Bonifaz et al. (2017)], attributing inelastic and damage behaviour of concrete to mortar; 2) Represent ITZ with a thin layer of continuum or finite thickness cohesive elements (fCE) [Huang et al. (2015); Tu and Lu (2011)], attributing the inelastic and damage behaviour to both ITZ and mortar; 3) Represent ITZ with zero-thickness cohesive elements (zCE), inserted at meshing stage [Caballero et al. (2006a); Wang et al. (2016)] or dynamically [Snozzi et al. (2012)], with behaviour similar to case 2. Voids are entrapped or entrained during casting and a number of these are of size observable at the meso-scale, i.e. comparable to smaller aggregates. Including larger pores in a meso-structural model is essential for obtaining physically realistic results [Wang et al. (2015)]. Macroscopically, concrete exhibits three well-defined regions in both tensile and compressive stress-strain response - linear elastic, relatively short inelastic region prior to peak stress (similar to hardening in metals), and long softening region after peak stress. Within finite element (FE) framework, the meso-structure regions are meshed with appropriate elements - continuum and cohesive - and assigned corresponding constitutive behaviours, tailored to reproduce the measured stress-strain behaviour of the composite. To date the majority of models have been tailored to simulate either tension [Wang et al. (2016); Caballero et al. (2006b); Lo´pez et al. (2008); Wang et al. (2015)] or compression [Song and Lu (2012); Tian et al. (2015); Grassl and Rempling (2008)]. A few models have been applied to study concrete’s behaviour in both tension and compression. The lessens learned can be seen in the following classification: a) Models without ITZ, e.g. Bonifaz et al. (2017) proposed a 3D meso-scale model with only mortar and aggregate. However, this type of modelling does not allow for simulating the post-peak softening region. b) Models with fCE for ITZ. Huang et al. (2015) used a 3D image-based model with fCE with concrete damage plasticity (CDP in Abaqus). Its success stimulated the use of CDP for mortar and fCE, but fCE used in such models is much thicker than the physical one due to meshing constraints, which questions the validity of the results; Tu and Lu (2011) compared 2D models with both fCE and zCE for ITZ using LS-DYNA, and reported that under tension both ITZ models yielded similar results with good agreement with experiments, while under compression the zCE yielded less accurate results than fCE. This outcome was attributed to the absence of shear fracture strength of zCE in LS-DYNA. The problem does not exist e.g. in Abaqus, hence zCE can be used for tension and compression studies. c) Models with zCE. Several proposals include zCE for ITZ and interface between continuum mortar elements, leaving mortar non-damagable, e.g. Lo´pez et al. (2008) and Caballero et al. (2006a) studied 2D and 3D meso-scale models, respectively, with pre-inserted zCE, but without accounting for porosity, which was shown to have significant e ff ect on deformation and failure behaviour [Wang et al. (2015)]. Other proposals include zCE for ITZ only, e.g. Unger et al. (2011) proposed 3D meso-scale concrete models with zCE for ITZ and di ff erent damage / plasticity models for mortar, without pores. The main issue is that mortar hardening is not included in the model, which makes it di ffi cult to simulate the plastic response of concrete in compression. Stepping on this background, and considering that the ITZ thickness (e.g. 10-50 µ m ) is negligible compared to aggregate sizes (e.g. 1-5 mm), it seems reasonable to exclude options with fCE. Between the remaining alternatives - zCE for ITZ only, and for ITZ as well as between mortar elements - the latter is computationally problematic due to interpenetration of mortar elements, in particular during compressive loading. Therefore, a model with zCE for ITZ only with improved constitutive relations for mortar as elastic-plastic-damageable constituent is suggested here as the most viable alternative. The improvement to mortar behaviour is based on CDP with hardening variables for both tension and compression. The combined model is solved successfully in Abaqus / Standard. Results from simulations of concrete behaviour under tension and compression are presented. Stress-strain curves and damage patterns are compared with experimental data to demonstrate very good agreement in support of the proposed model capabilities.

2. Model description

Meso-scale concrete models can be generated by either synthetic parameterisation [Wang et al. (2016)] or image based processing [Huang et al. (2015)]. In the first method, aggregate particles are randomly created and placed in a domain following prescribed size distribution. One constraint to this approach is the lack of accurate aggregate size distribution for the experiments for which macroscopic stress-strain data is available, i.e. reports on stress-strain data