The classically lattice model assumes the local elements behave elastic brittle, neglecting the ductility of the mortar matrix. This leads to the simulated load⁃displacement response more brittle than the realistic. To solve the aforementioned issue, a piece⁃wise approach was introduced to describe the elastic⁃plastic constitutive relation of lattice element. The fracture process and the load⁃displacement response were obtained through the sequentially⁃linear solution approach. The model was calibrated using the uniaxial tension and compression tests. It is found that the model can precisely simulate the fracture process and load⁃displacement response. Moreover, the model was used to model the size effect in uniaxial tension and the influence of the specimen’s slenderness and boundary confinement on the fracture behavior under compression. It offers a new theoretical method and approach for studying the fracture of concrete.

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Cementitious materials are widely used in construction. For their low ductility, they typically need to be reinforced by steel rebars, which cause potential corrosion problems. Polymeric reinforcement, which does not have corrosion problems, has been used to replace steel rebars. However, a relatively high reinforcing ratio is usually required for the cementitious composites reinforced by conventional polymeric reinforcement. Owing to the customizability of 3D printing technology, polymeric reinforcement with a functionally graded structure is able to be manufactured, which significantly reduces the reinforcing ratio of the reinforced cementitious composites meanwhile improves their mechanical properties. In this present study, 3D printed polymeric octet lattice structures were used as reinforcement to develop cementitious composites with enhanced ductility. Four-point bending experiments were performed on the plain mortar, and the reinforced specimens and a finite element model was used to simulate the experiments numerically. A good agreement between experiments and simulations was found: the reinforced specimens have a significantly increased flexural ductility comparing to plain mortar. Composites reinforced by vertically functionally graded lattice structures have a significantly lower reinforcing ratio while exhibiting obviously higher normalized ductility. In addition, the fracture behavior of the reinforced cementitious composites was evaluated using a fracture energy based analytical model. The analysis shows that, from the perspective of fracture energy release, the steady state cracking criteria were not satisfied by the cementitious composites developed in this study so that multiple cracking and strain hardening behavior was not obtained. However, according to numerical predictions, increasing strength of the printed reinforcement material by 40% would allow these behaviors to be potentially achieved. This work shows that additive manufacturing has great potential for developing reinforcement for cementitious materials to reduce the reinforcing ratio and enhance ductility.

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Considering the application scenarios of rubber granules from waste tires in the bitumen modification process (wet or dry process), both aerobic and anaerobic aging of rubber may occur. The current study aims to investigate the thermal aging behavior of waste tire rubber samples using nanoindentation and environment scanning electron microscopy (ESEM) tests. Both aerobic and anaerobic aging tests with different durations were conducted on rubber samples. The complex moduli of aged rubber samples were measured by nanoindentation tests. The surface morphology and elemental composition of aged samples were obtained by ESEM tests together with the energy dispersive X-ray analysis. Results have shown that for both aerobic and anaerobic aging, the equilibrium modulus derived from the complex modulus curve first increases and then decreases with aging time. However, the time needed for the aerobically aged sample to reach the maximum equilibrium modulus is shorter than the anaerobic case. Aging results in crack propagation and an increase of sulfur content on the rubber surface until it reaches the peak. The degree of crosslinking reflected by sulfur content for anaerobic aging is higher than aerobic aging. The morphological change and elemental change of rubber correlate well with the change of mechanical properties. The aging of rubber from the waste truck tire at 180°C can generally be separated into two stages: crosslinking dominant stage and chain scission dominant stage.@en

Application of micromechanical modelling of hydrated cement paste (HCP) gains more and more interests in the field of cementitious materials. One of the most promising approaches is the use of so-called microstructure informed micromechanical models, which provides a direct link between microstructure and mechanical properties. In order to properly model the micromechanical properties of HCP, advanced mechanical models, well-characterised microstructures and proper input parameters are required. However, due to the complex material structure of HCP, this is not an easy to achieve for any of the three aforementioned aspects. Therefore, this paper aims at reviewing of the techniques that have been developed to contribute to the micromechanical modelling. Basic principles, corresponding research results, recent advances and limitations are given. It is expected that this review can help researchers make reasonable choices on techniques for the micromechanical modelling of cementitious materials.

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For a single batch material, time intervals and nozzle standoff distances between two subsequent layers are two critical printing parameters that influence the mechanical performance of the printed concrete. This paper presents an experimental and numerical study to investigate the impacts of these printing parameters on the interlayer bond strength of the 3D printed limestone and calcined clay-based cementitious materials. All samples were manufactured by a lab-scale 3D printer equipped with a hybrid back- and down-flow nozzle (rectangular opening). The uniaxial tensile test was employed to quantify the interface adhesion of printed specimens. Moreover, the greyscale value image of microstructure, as well as the air void content and distribution of the printed specimens were acquired by X-ray computed tomography and characterized by image analysis. The experimental results showed that extending the time interval between construction of two layers could decrease the bond strength, whereas only increasing the nozzle standoff distance exhibited limited effects on that. The weak bond strength could be attributed to the high local porosity at the interface of the specimen. Additionally, numerical simulations of the uniaxial tensile test were conducted using a 2D lattice fracture model, which can predict the bond strength of printed specimens for different void content in the interface layer.

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Auxetic behavior refers to material with negative Poisson's ratio. In this research, a new type of cementitious auxetic material is developed. A novel crack bridging auxetic mechanism is discovered which is in contrast with a local buckling mechanism commonly employed to trigger auxetic behavior. Taking advantage of 3D printing techniques, cementitious cellular composite (CCC) specimens with auxetic cellular structures were produced. Meanwhile, cementitious materials with different fiber content were used as constituent material. Uniaxial compression and cyclic loading tests were performed on the CCCs. Experiments show that with proper constituent material, CCCs can exhibit auxetic behavior which is induced by crack bridging process of the cementitious constituent material. In addition, strain hardening behavior can be identified in the stress-strain curve under uniaxial compression and consequently high specific energy absorption is obtained. Furthermore, 2.5% of reversible deformation which is significantly higher than conventional cementitious materials under cyclic loading is obtained within 25,000 cycles. Obvious fatigue damage is observed in the first 3000 cycles, afterwards signs of mechanical properties recovering can be found. The discovered auxetic mechanism indicates a new designing direction for brittle materials to achieve auxetic behaviors.@en

Carbonation of hydrated cement paste (HCP) causes numerous chemo-mechanical changes in the microstructure, e.g., porosity, strength, elastic modulus, and permeability, which have a significant influence on the durability of concrete structures. Due to its complexity, much is still not understood about the process of carbonation of HCP. The current study aims to reveal the changes in porosity and micromechanical properties caused by carbonation using micro-beam specimens with a cross-section of 500 μm x 500 μm. X-ray computed tomography and micro-beam bending tests were performed on both noncarbonated and carbonated HCP micro-beams for porosity characterization and micromechanical property measurements, respectively. The experimental results show that the carbonation decreases the total porosity and increases micromechanical properties of the HCP micro-beams under the accelerated carbonation. The correlation study revealed that both the flexural strength and elastic modulus increase linearly with decreasing porosity.

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This paper presents a validation process of the developed multi-scale modelling scheme on mortar composites. Special attention was paid to make the material structure of real and virtual mortar specimens comparable at the meso-scale. The input mechanical parameters of cement paste (both bulk cement paste and interfacial transition zone) at the meso-scale were derived from results of micromechanical modelling through a volume averaging approach. Two constitutive relations for local elements were assumed and tested. By comparing with the experiments, the model using linear-elastic constitutive relation showed to be capable to reproduce the experimental load-displacement response satisfactorily in terms of the elastic stage and peak load. However, in the non-elastic stage a more realistic load-displacement curve can be simulated by considering the softening of cement paste using a step-wise approach. More importantly, the proposed multi-scale modelling scheme is validated by the experimental measurements. The proposed development offers the opportunity for the meso-scale model to become fully predictive.@en

A method is presented to model deformation and fracture behavior of 3D printed disordered lattice materials under uniaxial tensile load. A lattice model was used to predict crack pattern and load-displacement response of the printed lattice materials. To include the influence of typical layered structures of 3D printed materials in the simulation, two types of printed elements were considered: horizontally and vertically printed elements. Strengths of these elements were measured: 3 mm cubic units consist of lattice elements with two printing directions were printed and their strengths were tested in uniaxial tension. Afterwards, the measured element strengths and bulk material strength, respectively, were used as model input. Uniaxial tensile tests were also performed on the printed lattice materials to obtain their crack pattern and load-displacement curves. Simulations and experimental results were comparatively analyzed. For both levels of disorder considered, only when measured strengths were assigned to the elements with identical printing direction, are the predicted crack patterns and load-displacement curves in agreement with experimental results. The results emphasize the importance of considering printing direction when simulating mechanical performance of 3D printed structures. The influence of disorder on lattice material mechanical properties was discussed based on the experiments and simulations.

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This work proposes a method for numerically investigating the fracture mechanism of cement paste at the microscale based on X-ray computed tomography and nanoindentation. For this purpose, greyscale level based digital microstructure was generated by X-ray microcomputed tomography with a resolution of 2 μm/voxel length. In addition, statistics based micromechanical properties (i.e. Young's modulus and hardness) were derived from the grid nanoindentation test which was set to have an interaction volume the same as the resolution of the digital microstructure. A linear relationship between the two probability density functions of greyscale level and local Young's modulus was assumed and verified by the two-sample Kolmogorov-Smirnov (K–S) statistic. Based on this assumption, the fracture and deformation of a digital cubic volume with a dimension of 100 μm under uniaxial tension was simulated using a lattice fracture model. In addition, the influence of heterogeneity on fracture response was studied. Furthermore, the proposed method was compared with the results obtained from a traditional approach used previously by the authors in which discrete phases (capillary pore, anhydrous cement clinker, outer and inner hydration products) were considered. The two methods show similar crack patterns and stress-strain responses. The proposed method is regarded more promising as it captures also the gradient of material properties (within the discrete phases) in the cement paste.

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One of the major problems with the bone implant surfaces after surgery is the competition of host and bacterial cells to adhere to the implant surfaces. To keep the implants safe against implant-associated infections, the implant surface may be decorated with bactericidal nanostructures. Therefore, fabrication of nanostructures on biomaterials is of growing interest. Here, we systematically studied the effects of different processing parameters of inductively coupled plasma reactive ion etching (ICP RIE) on the Ti nanostructures. The resultant Ti surfaces were characterized by using scanning electron microscopy and contact angle measurements. The specimens etched using different chamber pressures were chosen for measurement of the mechanical properties using nanoindentation. The etched surfaces revealed various morphologies, from flat porous structures to relatively rough surfaces consisting of nanopillars with diameters between 26.4 ± 7.0 nm and 76.0 ± 24.4 nm and lengths between 0.5 ± 0.1 μm and 5.2 ± 0.3 μm. The wettability of the surfaces widely varied in the entire range of hydrophilicity. The structures obtained at higher chamber pressure showed enhanced mechanical properties. The bactericidal behavior of selected surfaces was assessed against Staphylococcus aureus and Escherichia coli bacteria while their cytocompatibility was evaluated with murine preosteoblasts. The findings indicated the potential of such ICP RIE Ti structures to incorporate both bactericidal and osteogenic activity, and pointed out that optimization of the process conditions is essential to maximize these biofunctionalities.@en

The aim of this work is to investigate the mechanical performance of hardened cement paste (HCP) under compression at the micrometre length scale. In order to achieve this, both experimental and numerical approaches were applied. In the experimental part, micrometre sized HCP specimens were fabricated and subjected to uniaxial compression by a flat end tip using nanoindenter. During the test, the load-displacement curves can be obtained. In the modelling part, virtual micrometre sized specimens were created from digital material structures obtained by X-ray computed tomography. A computational compression test was then performed on these virtual specimens by a discrete lattice fracture model using the local mechanical properties calibrated in the authors' previous work. A good agreement is found between the experimental and numerical results. The approach proposed in this work forms a general framework for testing and modelling the compression behaviour of cementitious material at the micrometre length scale.@en

Properties of concrete are, to a large extent, dependent on the properties of its binding constituent, hydrated cement paste. Therefore, knowledge of properties of hydrated cement paste is crucial for predicting concrete behavior. This paper presents an experimentally informed approach for modeling elastic and transport properties of cement paste. The models used realistic microstructural information—obtained by X-ray computed tomography—as input for property determination. The properties were then determined using discrete numerical models, namely, models based on a lattice approach. Modeling results were compared with literature data, showing excellent correlations. Furthermore, dependence of properties of cement paste on the total porosity, based on the modeling results, was explored. Finally, a correlation between elastic and transport properties for the explored range of portland cement pastes was established. It is seen that the models can be used for property prediction, but also for exploring correlations between different parameters.@en

Cementitious materials are heterogeneous on mutliple length scales, from nanometres to metres. Consequently, their macroscopic mechanical properties are affected by material structures at all length scales. In pursuit of fundamental understanding the relationship between their multiscale heterogeneous material structure and mechanical properties, testing and modelling are required at all length scales. In this thesis, a series of experimental and modelling techniques for cementitious materials on multiple length scales (micrometre to millimetre) has been developed. This forms an experimentally validated modelling scheme in which experimental results are used to provide input and validation for numerical model at each length scale. The approach on micro-scale sized specimen preparation has been developed by combining thin-sectioning and micro-dicing techniques. Mechanical measurements on the prepared micro-scale sized specimens were performed using a nanoindenter under various test configurations. The micromechanical model has been developed by combining the micro X-ray computed tomography and discrete lattice fracture model. In terms of hardened cement paste (HCP), the micro-cube indentation splitting test technique offers experimental results for the calibration of the micromechanical model. The one-sided micro-cube splitting test was used to validate the calibrated model. Moreover, the one-sided splitting test can offer the nominal splitting strength of HCP. The micro-cube compression test was developed to validate the modelling results and to provide the compressive strength and Young’s modulus measurements of HCP at the micro-scale. The experimentally validated micromechanical model was further used to predict the uniaxial tensile fracture behaviour of HCP at the micro-scale. It is confirmed by both numerical modelling and experimental measurements that the micromechanical properties (such as compressive strength, tensile strength) of HCP are much higher than at the meso-scale properties. With respect to the interfacial transition zone (ITZ), micro-scale sized HCP-aggregate cantilever beams were fabricated and loaded by the nanoindenter. The measured load-displacement response was used to calibrate the microstructure informed lattice fracturemodel. This model was further used to predict the fracture behaviour of the ITZ under uniaxial tension. The volume averaging up-scaling approach has been adopted as a tool to pass the outcome from the micro-scale to the higher scale as input. The micro-beam three-point bending test has been developed to validate this modelling scheme on HCP. The good agreement between modelling and testing shows that this modelling approach can reproduce the experimental results in terms of fracture pattern, strength and elasticity well. This up-scaling approach was further validated by comparing the modelling and testing results of the 10 mm cubic mortar under uniaxial tension. As strength and fracture properties of cementitious materials are size dependent, a size effect study on HCP has been carried out using both one-sided splitting test configurations and the multiscale modelling approach. The size range of specimens that can be experimentally measured and numerically simulated are significantly improved by using these techniques. The experimentally validated multi-scalemodelling scheme developed in this thesis is fully quantitatively predictable at the meso-scale. This modelling scheme is generic. It can be used in the same or similar way for studying systems utilizing other binders or aggregates. @en

Within pavement engineering community, Open Graded (OG) mixes are regarded as mixes capable of reducing noise and improving wet skid resistance. Due to the formation of interconnected aggregate network, aggregate packing plays an important role in the overall response of OG mixes. However, some of the models developed in the past do not consider the effect of aggregate packing in their predictions which leads to unreliable predicted results. Thus, it is important to understand the contribution of packed aggregates in the prediction of mechanical properties of OG mixes. In this paper, a procedure for obtaining the stiffness of packed aggregates in OG mixes was proposed by mean of micromechanics (the Mori-Tanaka model) and it was verified on the basis of laboratory tests. The results showed that the calculated stiffness of packed aggregates is frequency dependent which needs to be considered in the prediction of mechanical properties of OG mixes.@en

Cement paste is the main binding component in concrete and thus its fundamental properties are of great significance for understanding the fracture behaviour as well as the ageing process of concrete. One major aim of this paper is to characterize the micromechanical properties of cement paste with the aid of a nanoindenter. Besides, this paper also presents a preliminary study on the fatigue behaviour of cement paste at the micrometer level. Miniaturized cantilever beams made of cement paste with different water/cement ratios were statically and cyclically loaded. The micromechanical properties of cement paste were determined based on the measured load-displacement curves. The evolution of fatigue damage was evaluated in terms of the residual displacement, strength, and elastic modulus. The results show that the developed test procedure in this work is able to produce reliable micromechanical properties of cement paste. In addition, little damage was observed in the cantilever beams under the applied stress level of 50% to 70% for 1000 loading cycles. This work may shed some light on studying the fatigue behaviour of concrete in a multiscale manner.@en

Mercury intrusion porosimetry (MIP) measurements are widely used to determine pore throat size distribution (PSD) curves of porous materials. The pore throat size of porous materials has been used to estimate their compressive strength and air permeability. However, the effect of sample size on the determined PSD curves is often overlooked. In pursuit of a better understanding of the effect of sample size on mercury intrusion into porous materials, a combined experimental and numerical approach was applied. Quartz sand and epoxy resin were mixed to form artificial sandstone. Digital microstructures of the sandstone were obtained by using X-ray computed tomography (CT scan) technique. PSD curves of the artificial sandstone with different sample sizes were determined both by MIP measurement and by simulation of mercury intrusion (i.e., MIP simulation). Percolation analysis was performed on mercury-intruded pores in the digital microstructures. The PSD curves determined both by MIP measurements and by MIP simulations show that there was a significant effect of sample size on mercury intrusion before percolation of mercury-intruded pores. The effect of sample size decreased with the increasing pressure. After the mercury-intruded pores percolated through the samples, the effect of sample size on mercury intrusion became minor. The pore throat size of the artificial sandstone was used to estimate the air permeability using the relation proposed in the literature. The calculated air permeability of the smaller sandstone sample was higher. However, in principle, the air permeability of sandstone samples should be independent of the sample size. Two main conclusions can be drawn: (1) a fixed sample size should be used in MIP measurements or MIP simulation so that the PSD curves of different samples can be properly compared, (2) sample size needs to be considered when the pore throat size determined by MIP measurement is used for estimating air permeability.@en

This work presents a study of stochastic fracture properties of cement paste at the micro length scale based on a combination of X-ray computed tomography (XCT) technique and discrete lattice type fracture model. Thirty virtual specimens consisting of pore, outer hydration products, inner hydration products and anhydrous cement particles were extracted from 3D images obtained through XCT from real cement paste samples. These virtual specimens were subjected to a computational uniaxial tension test to calculate their tensile strengths and elastic moduli. The predicted stochastic strengths were analysed using Weibull statistics, showing that specimens with lower w/c ratio yield higher strength and less variability. The strength-porosity and modulus-porosity relations were investigated based on existing empirical models. It was shown that existing models can predict the properties in the studied porosity range quite accurately, with the exponential model having the highest determination coefficient among all the models for both relations. Finally, by comparing the existing data in the literate, it is found that the smaller cement paste specimens have higher modulus/tensile strength ratio, which indicates that they are able to have more strain at the peak load.

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Cement paste possesses complex microstructural features including defects/pores over a range of length-scales, from nanometres to millimetres in size. As a consequence, it exhibits different behaviour under loading depending on the size. In this work, cubic specimens in a size range of 1: 400 were produced and tested by a one-sided splitting concept using different testing instruments. The smallest specimen with size of 100 μm showed a high nominal splitting strength (18.81 MPa), an order of magnitude higher than the measured strength of 40 mm specimen (1.8 MPa). The test results were used to fit existing analytical size effect models. Although a good fit can be found for the existing size effect models, special attention should be given to the physical meaning behind these empirical parameters. In addition, a multi-scale modelling strategy that considers microstructural features at different length scales was adopted to model the trend of decreasing strength with specimen size observed in experiments. A good agreement between experimental observations and modelling results indicates that the featured material structure dominates the observed size effect on measured strength in the size range considered.@en

This work aims to provide a method for numerically and experimentally investigating the fracture mechanism of cement paste at the microscale. For this purpose, a new procedure was proposed to prepare micro cement paste cubes (100 × 100 × 100 µm3) and beams with a square cross section of 400 × 400 µm2. By loading the cubes to failure with a Berkovich indenter, the global mechanical properties of cement paste were obtained with the aid of a nano-indenter. Simultaneously the 3D images of cement paste with a resolution of 2 µm3/voxel were generated by applying X-ray microcomputed tomography to a micro beam. After image segmentation, a cubic volume with the same size as the experimental tested specimen was extracted from the segmented images and used as input in the lattice model to simulate the fracture process of this heterogeneous microstructure under indenter loading. The input parameters for lattice elements are local mechanical properties of different phases. These properties were calibrated from experimental measured load displacement diagrams and failure modes in which the same boundary condition as in simulation were applied. Finally, the modified lattice model was applied to predict the global performance of this microcube under uniaxial tension. The simulated Young’s modulus agrees well with the experimental data. With the method presented in this paper the framework for fitting and validation of the modelling at microscale was created, which forms a basis for multi-scale analysis of concrete.@en