We propose a new numerical method to analyze the early-age creep of 3D printed segments with the consideration of stress history. The integral creep strain evaluation formula is first expressed in a summation form using superposition principle. The experimentally derived creep compliance surface is then employed to calculate the creep strain in the lattice model with a combination of stored stress history. These strains are then converted into element forces and applied to the analyzed object. The entire numerical analysis consists of a sequence of linear analyses, and the viscosity is modelled using imposed local forces. The model is based on the incremental algorithm and one of the main advantages is the straightforward implementation of stress history consideration. The creep test with incremental compressive loading is utilized to validate this model. The modelling results are in good agreement with experimental data, demonstrating the feasibility of the lattice model in early-age creep analysis under incremental compressive loading. To understand the impact of early-age creep on structural viscoelastic deformation during the printing process, additional analyses of a printed segment are carried out. These simulation results highlight the need to consider creep for accurate prediction of viscoelastic deformation during the printing process.

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Herein, different kinds of methods for buildability quantification of 3D concrete printing are reviewed, including experimental approaches, analytical modelling, and numerical simulations. A brief introduction on printing process is first given. This discusses the material properties in different stages. Material printability, which encompasses pumpability, extrudability and buildability, is then discussed. Subsequently, a brief review of the experimental and analytical models for buildability quantification is presented and they're discussed. An overview on the numerical tools for 3DCP is then given. These numerical models can quantify structural buildability and optimize the printing parameters, therefore, providing a more economical solution for buildability quantification. In the end, a summary and discussion on the limitations of numerical tools for buildability quantification are provided, as well as recommendations for their improvement.

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For some decades now, additive manufacturing has been a revolutionary technology which generates enormous interest in both industrial and academic applications. 3D concrete printing (3DCP), an automated construction method, is able to manufacture the computer-designed model through material deposition. This innovative technique can considerably accelerate the construction process, and make it economically and technically feasible to implement complex structural elements in practice. Although this technique shows a promising future, full adoption in construction sector is still far from possible due to the absence of fundamental knowledge about printable material and structural analysis during or after printing process....@en

Early-age stress (EAS) is an important index for evaluating the early-age cracking risk of concrete. This paper encompasses a thermo-chemo-mechanical (TCM) model and active ensemble learning (AEL) for predicting the EAS evolution. The TCM model provides the data for the AEL model. First, based on Fourier's law, Arrhenius’ equation, and rate-type creep law, a TCM model is built to simulate the heat transfer, cement hydration, and viscoelasticity, which together determine the EAS evolution. Then, a material model composed of an eXtreme Gradient Boosting model and adjusted Model Code 2010 is built to allow for parametric study and database construction. Finally, an AEL framework is built, which incorporates principal component analysis (PCA), Gaussian process, and light gradient boosting machine (LGBM). This study resulted in the following findings: (1) The dimensionality of the 672-by-1 EAS vector can be effectively reduced by PCA, and the first principal component (PC) is a global index representing the magnitude of the EAS; (2) the mechanical field of the TCM model is validated by testing data. Correlation analysis on the first PC quantifies the influence of various input parameters of the TCM model, which is in accordance with common understandings of the EAS evolution process. (3) The AEL and one-shot ensemble learning (OSEL) both achieve high prediction performance in the testing set, whose R² reaches 0.961 and 0.948, respectively. Thanks to the uncertainty-based query procedure, comparing with OSEL, AEL shows advantages in prediction performance over the whole training history. (4) AEL can significantly reduce the number of samples required for training, which can be a major improvement in efficiency considering the computational cost of the TCM model.

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This paper explores buildability quantification of randomly meshed 3D printed concrete objects by considering structural failure by elastic buckling. The newly proposed model considers the most relevant printing parameters, including time-dependent material behaviors, printing velocity, localized damage and influence of sequential printing process. The computational uniaxial compression tests were first conducted to calibrate age-dependent elastic modulus and yield stress. Subsequently, analyses of the 3D printing process of a free wall structure and a square layout were performed. The model can reproduce the asymmetry of buckling failure accurately and the predicted critical printing height is in excellent agreement with experimental data from the literature. It can be concluded the combined effect of material variability and non-uniform gravitational loading due to sequential printing process resulted in structural failure during 3D concrete printing. Using this model, printing parameters can be optimized and a suitable printing scheme can be devised to improve structure buildability.

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This study aims to provide an efficient alternative for predicting creep modulus of cement paste based on Deep Convolutional Neural Network (DCNN). First, a microscale lattice model for short-term creep is adopted to build a database that contains 18,920 samples. Then, 3 DCNNs with different consecutive convolutional layers are built to learn from the database. Finally, the performance of DCNNs is tested on unseen testing samples. The results show that the DCNNs can achieve high accuracy in the testing set, with the R² all higher than 0.96. The distribution of creep modulus predicted by the DCNNs coincides with that of the original data. Furthermore, through analyzing the feature maps, it is found that the DCNNs can correctly capture the local importance of different microstructural phases. The DCNN allows therefore prediction of the creep modulus based on microstructural input, which saves computational resources of segmentation procedure and multiple incremental FEM calculations.

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Tailoring lattice structures is a commonly used method to develop lattice materials with desired mechanical properties. However, for cementitious lattice materials, besides the macroscopic lattice structure, the multi-phase microstructure of cement paste may have substantial impact on the mechanical responses. Therefore, this work proposes a multi-scale numerical modelling method to simulate the deformation and fracture behavior of cementitious lattice materials, such that the influence of cement paste microstructure can be properly captured. On the microscale, the load–displacement response of cement paste is numerically simulated then experimentally validated. In order to rationally investigate the role of cement paste microstructure, the obtained load–displacement response was then formulated to several types of model inputs reflecting different degree of brittleness. These inputs were then used for simulating the mechanical response of macroscale cementitious lattices. By comparing the simulation to experiment, multi-linear behavior (ML) was found to an appropriate method to include the realistic pre-critical cracking and post-peak softening of cement paste in the model. Compared to ideally brittle behavior, using ML as input, the discrepancy between simulated and experimentally tested fracture energy decreases from 37.4% to 12.4%. In addition, the influence of lattice structure on the strength of cementitious lattices was also accurately captured by the proposed model. Randomized cementitious lattice has 21.6% (22.0% from simulation) lower strength than regular lattice. Moreover, the influence of fracture criterion of the proposed model is discussed and elaborated. Owning to the high simulation accuracy, the proposed multi-scale method in this work could be helpful for tailoring the fracture cementitious lattice materials for future studies.

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A good bond between the layers of 3D printed cementitious materials is a prerequisite for having high structural rigidity for the printed elements. However, the influence of printing process on an interlayer bond is still not well understood. This study investigates the influence of curing methods (i.e., air curing, plastic film covering, wet towel covering and water mist-30 min/-60 min) on the interlayer bonding characteristics of 3D printed cementitious materials for a long time interval between two printing sessions. Results showed that the interlayer bonding could be improved by covering the substrate with a plastic film or a wet towel. However, applying water mist every 60 min/30 min on the deposited layer was detrimental to the interlayer bonding. Furthermore, the interlayer bond strength of studied specimens appeared to be dominated by the mechanical strength of the cementitious matrix at the interface rather than its air void structure. Therefore, covering unfinished printed elements with plastic film or wet towels can be a practical solution to maintain a sufficiently humid environment during long waiting periods, which is vital for its interlayer adhesion.@en

Extrusion-based 3D concrete printing (3DCP) results in deposited materials with complex microstructures that have high porosity and distinct anisotropy. Due to the material heterogeneity and rapid growth of cracks, fracture analysis in these air-void structures is often complex, resulting in a high computational cost. This study proposes a convolutional neural network (CNN)-based methodology for fracture analysis using air-void structures as input. More specifically, the lattice fracture model is used to build a dataset that comprises input air-void structures as well as output fracture information, including the crack patterns and crack-width curves. To establish the relationship between crack morphology and associated microstructures, a U-net convolutional neural network is first presented. With the obtained crack pattern as input, the principal component analysis (PCA) and CNN are then integrated to predict the stress-crack width curves. The predicted results from the CNN model demonstrate a quantitative agreement with lattice numerical analyses, with 0.85 Intersection over Union for crack patterns prediction and 0.75 R2 for the stress-crack width curves prediction. This indicates that CNN models can be used as an alternative to traditional numerical analysis. The feature maps during the convolutional or deconvolutional process are given to explain why the proposed CNN models perform well on fracture analysis of the air-void system. Moreover, the model generalization is discussed using transfer learning with fine-tuning to show the model potential on microstructures expressing varied pore information. In the end, the microstructures cropped from XCT are created to explore the further application of CNN models on fracture analysis of 3D printed materials.@en

Stress evolution of restrained concrete is a significant direct index in early-age cracking (EAC) analysis of concrete. This study presents experiments and numerical modelling of the early-age stress evolution of Ground granulated blast furnace slag (GGBFS) concrete, considering the development of autogenous deformation and creep. Temperature Stress Testing Machine (TSTM) tests were conducted to obtain the autogenous deformation and stress evolution of restrained GGBFS concrete. By a self-defined material subroutine based on the Rate-type creep law, the FEM model for simulating the stress evolution in TSTM tests was established. By characterizing the creep compliance function with a 13-units continuous Kelvin chain, forward modelling was firstly conducted to predict the stress development. Then inverse modelling was conducted by Bayesian Optimization to efficiently modify the arbitrary assumption of the codes on the aging creep. The major findings of this study are as follows: 1) the high autogenous expansion of GGBFS induces compressive stress at first hours, but its value is low because of high relaxation and low elastic modulus; 2) The codes highly underestimated the early-age creep of GGBFS concrete. They performed well in prediction of stress after 200 h, but showed significant gaps in predictions of early-age stress evolution; 3) The proposed inverse modelling method with Bayesian Optimization can efficiently adjusted the aging terms which produced best modelling results. The adjusted creep compliance function of GGBFS showed a much faster aging speed at early ages than the one proposed by original codes.

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This research studies the impact of localized damage and deformed printing geometry on the structural failure of plastic collapse for 3D concrete printing (3DCP) using the lattice model. Two different approaches are utilized for buildability quantification: the (previously developed) load-unload method, which updates and relaxes the printing system after each analysis step and repeatedly applies the gravitational loading to the undeformed structure; and the incremental method, which keeps the load after each analysis step and applies the incremental loading to the deformed printing system. The former can consider the material yielding but cannot capture accurately the structural deformation during printing process. Compared to the load-unload method, the incremental method can not only consider deformed printing geometry but can also simulate the non-proportional loading conditions and disequilibrium force occurring during 3D printing. In this study, computational uniaxial compression tests are first conducted to compare two algorithms. The numerical results indicate the consideration of nonequilibrium force and deformed geometry affects the peak load and crack information for fracture analysis. Subsequently, the incremental method is incorporated into the lattice model to quantify buildability of 3DCP. The predictions are compared with previously published numerical results obtained using the load-unload method. The lattice model based on incremental method reproduces correct failure mode; better quantitative agreement about critical printing height also can be obtained. These numerical analyses demonstrate that the incremental solution is an approximate method for buildability quantification since it can account for the nonequilibrium force induced by the deformed printing geometry and localized damage.

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This study aims to provide an efficient and accurate machine learning (ML) approach for predicting the creep behavior of concrete. Three ensemble machine learning (EML) models are selected in this study: Random Forest (RF), Extreme Gradient Boosting Machine (XGBoost) and Light Gradient Boosting Machine (LGBM). Firstly, the creep data in Northwestern University (NU) database is preprocessed by a prebuilt XGBoost model and then split into a training set and a testing set. Then, by Bayesian Optimization and 5-fold cross validation, the 3 EML models are tuned to achieve high accuracy (R² = 0.953, 0.947 and 0.946 for LGBM, XGBoost and RF, respectively). In the testing set, the EML models show significantly higher accuracy than the equation proposed by the fib Model Code 2010 (R² = 0.377). Finally, the SHapley Additive exPlanations (SHAP), based on the cooperative game theories, are calculated to interpretate the predictions of the EML model. Five most influential parameters for concrete creep compliance are identified by the SHAP values of EML models as follows: time since loading, compressive strength, age when loads are applied, relative humidity during the test and temperature during the test. The patterns captured by the three EML models are consistent with theoretical understanding of factors that influence concrete creep, which proves that the proposed EML models show reasonable predictions.

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In this work, the lattice model is applied to study the printing process and quantify the buildability (i.e., the maximum height that can be printed) for 3D concrete printing (3DCP). The model simulates structural failure by incorporating an element birth technique, time-dependent stiffness and strength, printing velocity, non-uniform gravitational load, localized damage, and spatial variation of the printed object. The model can reproduce the plastic collapse failure modes reported in the literature. In this research, three main contributions for 3DCP modeling work can be found. A new failure criterion is proposed and adopted to improve the estimation of critical printing height; the element birth technique is utilized to mimic the continuous printing process and study the impact of non-uniform gravitational load; variability of a printed structure is modeled through the inclusion of disorder during mesh generation and Gaussian distributions of material properties. Using this model, parametric analyses on non-uniform gravitational load and material variation are conducted to assess their impact on the failure–deformation response and the critical printing height. Finally, the model is validated by comparison with two 3D printing experiments from the literature. The proposed lattice model can reproduce the correct failure-deformation modes of two types of structures commonly used for buildability quantification: A 3D-printed hollow cylinder and a square wall layout. Lattice modeling of the square structure yields a relative difference of around 10% with the experimental printing height. For the cylinder structure, the predicted radial deformation and corresponding height show good agreement with the experimental data; the model yields a 41.38% overprediction of the total number of printing layers, compared with the experimental data. Possible reasons for the quantitative discrepancy are discussed.

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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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In 3D concrete printing (3DCP), it is necessary to meet contradicting rheological requirements: high fluidity during pumping and extrusion, and high stability and viscosity at rest to build the layered structure. In this paper, the impact of the hydroxypropyl methylcellulose (HPMC)-based viscosity-modifying admixture (VMA) on the 3D printability and mechanical performance of a limestone and calcined clay based cementitious material is investigated. A combination of VMA and superplasticizer was used for that purpose. In this case, controlling the competitive effects between VMA and superplasticizer becomes critical. The main strategy for 3D printing in this study was to add an optimal dosage of VMA in the solid suspension that was already mixed with water and superplasticizer. A lab-scale 3DCP setup was developed and demonstrated as well. A series of tests was performed to characterize the effects of VMA on flowability, extrudability, open time, buildability, green strength, hydration, compressive strength, and air void content and distribution. Experiments performed in this study showed that the mixture containing 0.24% (of the binder mass) of VMA exhibited satisfactory 3D printability and optimal mechanical performance. Finally, the results, limitations, and perspectives of the current research were discussed.@en

A combination of laboratory experiments and numerical simulations at multiple length scales can provide in-depth understanding of fracture behaviour of hydrated cement paste (HCP). To that end, the current work presents a numerical study on compressive failure of hydrated cement paste (HCP) at the micro-scale. Virtual specimens consisting of various phases were obtained using a combination of X-ray computed tomography and image segmentation techniques. The discrete lattice fracture model was used for the deformation and fracture analysis of the specimens subjected to uniaxial compression. The input local mechanical properties of each individual phase were taken from the literature in which a micro-scale compression test was conducted for the calibration of the same type model. The influence of slenderness ratios (1 and 2), water-to-cement ratios (0.3, 0.4 and 0.5 respectively) and lateral confinement of the specimen ends (free and restricted) on the failure behaviour were investigated. It has been shown by the current study that the stress–strain response cannot be completely separated from the used boundary conditions. The proposed model provides an effective tool to understand the compressive fracture behaviour of cement paste at the micro-scale.@en

The lattice fracture model is a discrete model that can simulate the fracture process of cementitious materials. In this work, the Delft lattice fracture model is reviewed and utilized for fracture analysis. First, a systematic calibration procedure that relies on the combination of two uniaxial tensile tests is proposed to determine the input parameters of lattice elements—tensile strength, compressive strength and elastic modulus. The procedure is then validated by simulating concrete fracture under complex loading and boundary conditions: Uniaxial compression, three-point bending, tensile splitting, and double-edge-notch beam shear. Simulation results are compared to experimental findings in all cases. The focus of this publication is therefore not only on summarizing existing knowledge and showing the capabilities of the lattice fracture model; but also to fill in an important gap in the field of lattice modeling of concrete fracture; namely, to provide a recommendation for a systematic model calibration using experimental data. Through this research, numerical analyses are performed to fully understand the failure mechanisms of cementitious materials under various loading and boundary conditions. While the model presented herein does not aim to completely reproduce the load-displacement curves, and due to its simplicity results in relatively brittle post-peak behavior, possible solutions for this issue are also discussed in this work.@en

This paper reports an extended lattice model for printing process simulation of 3D printed cementitious materials. In this model, several influencing factors such as material and geometric nonlinearity are considered. Using this model, green strength of cementitious material is investigated, deformation and crack pattern can be derived, which is close to the experimental result. Subsequently, numerical analysis of 3D printing is conducted for the simulation about printing process. Imperfections arising in the printing process can be incorporated and two failure modes including the elastic buckling and plastic collapse can be simulated through this model.

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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.

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The aim of this work is to investigate the fracture process of concrete under various boundary conditions. Although numerous concrete fracture tests have been reported, showing the failure behavior of concrete, their evaluation is ambiguous due to the limitations of specimen size and experimental conditions. Therefore, it is necessary to use simulation models to better understand the fracture process. This is done herein by using a three-dimensional lattice model to simulate the failure behavior of concrete under different loading conditions ranging from uniaxial compression, tension, splitting, three point bending to shear by using a single set of input parameter. In addition, several influence factors including boundary condition and slenderness are also taken into consideration to give more detailed information about the fracture process of concrete.@en