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• Develop concrete models based on CT images for dynamic tensile fracture mechanisms. • Propose a rate-dependent phase field model for a wide range of strain rates. • Successfully model stochastic dynamic fracture with meaningful statistical analyse. • Propose a new TDIF–strain rate–standard deviation relation based on MCS results. • Quantify influences of meso-heterogeneities, aggregate and void contents. Concrete structures are commonly exposed to dynamic loads spanning a wide range of strain rates, and the inherent mesoscale heterogeneities complicate stochastic dynamic fracture mechanisms even more. This work develops a numerical framework using mesoscale concrete models based on micro computed tomography (CT) images to investigate such mechanisms with meaningful stochastic analyses. A rate-dependent phase field model is proposed to characterise the dynamic initiation and propagation of cracks by incorporating both micro-viscosity and macroscopic viscoelasticity, which is described by two standard Maxwell elements with different relaxation times to consider a wide range of strain rates. Moreover, the viscoelastic constitutive relation is formulated in the full strain space, which allows for a spectral decomposition of the strain tensor to determine the effective damage driving force, thus effectively addressing the issue of compressive fracture. A numerical implementation scheme is developed by combining user-defined element and material subroutines in ABAQUS/Explicit solver. Extensive Monte Carlo simulations of dynamic tension up to a strain rate of 200 s−1 are performed with statistical analyses. This work reveals the intricate dynamics associated with mesoscale heterogeneities and identifies the critical transition state at 20 s−1. The transition is characterised by changing modes of fracture patterns, stress wave propagation, and load-carrying capacities. A new TDIF–strain rate–standard deviation relation is also proposed and aligns well with the increasing dispersion of experimental data. The relationship between void content and tensile strength reflects the formation characteristics of crack networks, with the void content exhibiting a positive correlation with the TDIF from 20 s−1 to 100 s−1. [ABSTRACT FROM AUTHOR]

• Propose an arbitrary polygon-based CSFEM-PFCZM to investigate quasi-brittle fracture of concrete-like materials. • Successfully simulate macroscale and mesoscale heterogeneous problems. • Show evident flexibility and efficiency over traditional FEM-PFCZM. • Hold promise to increase the acceptance and momentum of both the CSFEM and PFCZM in the research communities. In recent years, engineering and research communities have shown a growing interest in polygon elements due to their adaptability to complex geometries. However, their applicability for investigating the quasi-brittle damage and fracture of concrete structures is still an open question. This work thus develops a numerical framework to integrate the phase-field regularized cohesive zone model (PFCZM) with the cell-based smoothed finite element method (CSFEM) using arbitrary polygon elements. The techniques of centroidal Voronoi tessellation and polytree decomposition are adopted to discretize the computational domains and efficiently refine the potential cracking areas in a multi-level manner. This allows fast transition of the mesh density and direct elimination of the hanging-node issue using the CSFEM. To calculate the displacements and the damage variables, only Wachspress shape functions and boundary geometries are needed, eliminating the need for coordinate mapping and Jacobian inversion. For each CSFEM subcell, crack-driving forces are determined at the integration point and stored as history variables. Typical concrete structures under different loading conditions are validated with respect to the crack path and load-carrying capacity, exhibiting good coarse-mesh accuracy. A mesoscale test-piece under uniaxial tension is also modelled using the developed framework, showing significant computational efficiency when compared to the conventional FEM. [ABSTRACT FROM AUTHOR]

Accurate prediction of fracture in concrete depends on the characterization of real meso-structures. Micro X-ray computed tomography (CT) can fulfil this task but is still too expensive and time-consuming to repetitively generate numerical models, also with massive degrees of freedom (DOFs) that prohibit nonlinear computations. To address such problems, we develop a novel computational framework driven by only one CT image for 3D fracture investigation of realistic mesoscale concrete models. The voxelized CT data of aggregates is first processed to obtain spatially continuous surfaces. A number of aggregates with real shapes from a created library are then randomly packed into containers through compaction and vibration simulated by a dynamic physics engine. In this way, realistic concrete models with various aggregate contents (up to 60%) can be achieved without performing extra CT tests and image processing. To capture potential micro-cracks, cohesive interface elements with zero-thickness are automatically inserted between solid elements. The proposed models with more than 15 million DOFs are well validated through typical uniaxial tension tests, elucidating complex formation mechanisms of micro-cracking, pre-peak nonlinearity, softening behaviour and 3D fracture networks. Quantitative analyses indicate that with the increase of aggregate content, the coupling effect of aggregate blocking and interfacial cracking becomes stronger to make the crack surfaces more tortuous with higher ITZ-mortar area ratios and lower load-carrying capacities, although more aggregates are often required to enhance overall elastic modulus and compressive strength, and reduce carbon footprints of concrete. [ABSTRACT FROM AUTHOR]

• Develop a numerical approach integrating random fields and the CSFEM-PFCZM for the first time. • Successfully model quasi-brittle fracture of typical concrete structures. • Perform extensive Monte Carlo simulations (MCSs) with parametric analyses. • The MCSs include more statistical information than deterministic studies. Design and maintenance of concrete structures require efficient methods for predicting quasi-brittle fracture while incorporating mesoscale-induced structural uncertainties. Toward this aim, a phase field cohesive zone model combined with the cell-based smoothed finite element method (CSFEM-PFCZM) is developed in the study, with mesoscale heterogeneity of concrete characterised by Weibull random fields. An automatic quadtree decomposition technique is presented to adaptively refine meshes around mesoscale areas, in which the hanging-node problem is tackled by treating hierarchical quadtree elements as CSFEM polygons. The crack driving forces are evaluated as history variables at the integration points of CSFEM subcells, and only the boundary geometry and Wachspress shape functions are needed to calculate strain matrices and stiffness matrices without the Jacobian inversion problems. The developed method is validated by extensive Monte Carlo simulations of typical nonlinear fracture benchmarks of concrete structures, demonstrating that the well-captured variability of crack paths and load–displacement curves can supplement the limited statistical results obtained from a small number of experiments. It is also found that larger correlation length and higher variance underline higher heterogeneity that leads to more dispersed responses. The developed method holds promise for the efficient evaluation of structural reliability taking into account stochastic mesoscale effects, due to the fast generation of random field samples in large quantities and flexible simulation of complicated fracture through the CSFEM-PFCZM. [ABSTRACT FROM AUTHOR]

In this work, a localizing gradient damage model (LGDM) based on the generalized micromorphic theory is adopted to investigate the quasi-brittle fracture behaviour of concrete at mesoscale for the first time. Micro Computed Tomography (CT) image-based realistic concrete models are generated including aggregates, mortar, pores, and aggregate-mortar interfacial transition zones (ITZs). In the LGDM, an additional micro-force equilibrium equation is formulated with a damage-dependent interaction function to prevent spurious energetic interactions during the softening stage. The damage driving forces are evaluated as history variables through the maximum nonlocal equivalent strains at the integration points. The stiffness matrices and residual vectors for displacement and nonlocal equivalent strain fields are formulated through the conventional shape function and strain matrices of finite elements, by using the user-defined element (UEL) subroutine implemented with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to improve numerical performance. Typical nonlinear fracture benchmarks are presented to investigate the variability of mesoscale fracture evolution, crack trajectories, and load–displacement curves as well as numerical performance. It is found that the LGDM significantly improves the computational efficiency over the conventional phase-field cohesive zone model (PFCZM) with 60% savings of CPU time, and holds great potential for multiscale fracture evaluation of quasi-brittle composite materials, through the high-fidelity representation of real materials' microstructures, and flexible simulation of the complicated nonlinear fracture without the need for re-meshing or mesh enrichments. • Simulate mesoscale fracture of concrete using a localizing gradient damage model (LGDM) for the first time. • Enable a robust and efficient monolithic framework by the BFGS quasi-Newton algorithm. • Successfully capture quasi-brittle fracture behaviour of mesoscale concrete using CT images with high fidelity. • Demonstrate considerable reduction (60%) in computational time over the phase-field cohesive zone model. • Widen the applicability and acceptability of the LGDM among researchers. [ABSTRACT FROM AUTHOR]

In this work, a phase field cohesive zone model (PFCZM) combined with the cell-based smoothed finite element method (CSFEM) is presented to investigate the quasi-brittle fracture behaviour of concrete at mesoscale. An automatic quadtree decomposition technique is employed to discretise the CT image-based meso-structures including aggregates, mortar and pores, with local mesh adaptively refined at material boundaries. The resultant quadtree elements with hanging nodes are naturally treated as CSFEM polygons. In the proposed CSFEM-PFCZM, the stiffness matrices and residual vectors for displacement and damage fields are formulated by the Wachspress shape function and smoothed strain matrices. The crack driving forces are evaluated as history variables at the integration points of CSFEM subcells. Four nonlinear fracture benchmarks are presented to validate the proposed method regarding the variability of mesoscale fracture processes, crack topology and load–displacement curves. It is found that the CSFEM-PFCZM combined with the quadtree decomposition significantly improves the computational efficiency over the traditional FEM counterparts, and shows great potential for multiscale fracture evaluation of quasi-brittle composite materials. This is due to the fast mesh generation and flexible simulation of complicated nonlinear fracture using the CSFEM-PFCZM without the need for remeshing or mesh enrichments. • Integrate the PFCZM with CSFEM (CSFEM-PFCZM) for the first time. • Develop a user defined element subroutine (UEL) in ABAQUS for the CSFEM-PFCZM. • Successfully model quasi-brittle fracture behaviour of concrete at mesoscale using CT images with high fidelity. • Demonstrate considerable reduction (70%) in degrees of freedom and computational time. • The CSFEM-PFCZM is very flexible and efficient using quadtree meshes to conduct multiscale fracture simulations. [ABSTRACT FROM AUTHOR]

• Generate continuous random fields (RFs) of material properties from micro CT images of concrete. • Increase the application and acceptability of CT image modelling and the phase-field model. • Successful validation by Monte Carlo simulations for benchmarks of quasi-brittle failure. • It is promising to use only one CT image slice to generate a sufficient number of RF-based models. The damage and fracture mechanisms of concrete are complicated due to the material's inherent meso-scale heterogeneities. In this study, continuous random fields for selected properties, such as the tensile strength, are first generated on the basis of real microscale X-ray Computed Tomography (CT) images of concrete, using statistical reconstruction algorithms and the Karhunen-Loève expansion technique. The random fields are then assigned to finite element models with mesoscale crack initiation and propagation simulated by a phase-field regularized cohesive zone model (PF-CZM) with softening laws. The proposed two-step modelling method is validated by Monte Carlo simulations of a square test-piece under uniaxial tension and an L-shaped panel under mixed-mode fracture. It is found that the method can capture the variability of mesoscale fracture processes, crack paths and load-displacement curves, in good agreement with measured experimental variations. The method holds promise for the efficient evaluation of structural reliability by Monte Carlo simulations taking into account stochastic microstructural variability, thanks to the fast generation of a large number of random samples, through the high-fidelity representation of real materials' microstructures, and flexible simulation of complicated nonlinear fracture of phase-field models without the need for remeshing or mesh enrichments. [ABSTRACT FROM AUTHOR]

• Propose a rate-dependent phase field model considering both viscoelasticity and micro-viscosity;. • Develop VUEL and VUMAT subroutines to integrate the model through explicit numerical solution schemes;. • Successfully predict dynamic tensile behaviour of quasi-brittle concrete material;. • Elucidate complicated dynamic fracture mechanisms using CT image-based real meso‑structures. To investigate dynamic fracture mechanisms of quasi-brittle materials, this work proposes a rate-dependent phase field model that integrates both macroscopic viscoelasticity and micro-viscosity to reflect the rate effects by free water and unhydrated inclusions. Based on the unified phase field theory, the model introduces a linear viscoelastic constitutive relation in effective stress space to consider the macro-viscosity of the bulk material. Additionally, the micro-force balance concept is utilized with the micro-viscosity to derive a parabolic phase field evolution law that accurately describes the dynamic micro-crack development. Explicit numerical solution schemes are established for the governing equations by developing VUEL and VUMAT subroutines in ABAQUS. This eliminates the convergence issue in implicit phase field modelling. Four typical benchmarks are investigated to validate the proposed model for macroscale and mesoscale heterogeneous problems. It is found that the proposed model can well capture the crack branching, delaying characteristic of micro-crack growth, and increase of macroscopic strength under higher strain rates. Using real meso‑structures from CT images, the complicated dynamic behaviour of concrete is investigated which yields deeper insight into stress wave propagation, crack evolution and load-carrying capacities. [ABSTRACT FROM AUTHOR]

• Integrate dynamics and image slicing to generate mesoscale models of concrete composites realistically and efficiently. • Successfully model stochastic phase-field fracture and conduct meaningful statistical analyses. • Quantify influences of heterogeneities, aggregate content, and key fracture parameters. • Elucidate complex dual impact of aggregates regarding crack blocking and interfacial channels. The accurate prediction of concrete composites' fracture behaviour requires precise meso-structural characterization, appropriate fracture modelling, and pivotal uncertainty assessment. Towards this goal, we adopt a dynamics approach with CT images to generate numerical concrete models using real aggregates with 30%-60% contents. An image slicing method is then developed to obtain a large number of realistic models in 2D, whose heterogeneity is characterised by aggregates, mortar and interfaces. Monte Carlo simulations of uniaxial tension are performed, incorporating cross-scale fracture evolution through a phase-field cohesive zone model. Statistical analyses reveal that the stochasticity of crack patterns and stress-displacement curves, especially post-peak softening responses, is inherently dependent on the random meso-structures. It is observed that increasing aggregate content accelerates the deterioration rate of peak stress, decreases the softening curve, and leads to more tortuous crack paths, considering the ITZ crack channels. On the other hand, the tensile strength of mortar has significant impacts on the load-carrying capacity, while the fracture energy primarily influences the ductility and has negligible effects on the peak stress and the pre-peak nonlinear part. Besides, the ratios of mortar-ITZ tensile strength and fracture energy are found to affect the crack paths. The proposed numerical framework holds promise to reveal complex fracture mechanisms of concrete with more insights into other loading or environmental conditions. [ABSTRACT FROM AUTHOR]

• Propose an explicit phase field model to tackle complex 3D quasi-brittle fracture problems; • Develop VUEL and VUMAT subroutines for element formulations and constitutive equations; • Successfully simulate I, I+II and I+III failure modes without convergence concerns; • The CPU time is in an acceptable range of 12 h even for the large-scale model. Phase field models can effectively capture complicated crack evolution characteristics such as propagation, bifurcating, intersecting and merging. However, the simulation of three-dimensional (3D) quasi-brittle fracture remains a challenge due to large nonlinear equation systems and significant computational costs, which are often intractable by iteration-based implicit approaches, especially in complex mixed-mode fracture. This work presents an efficient explicit phase field model based on the unified phase field theory in order to overcome the above issues. In this model, the displacement field is second-order time dependent while the damage-phase field follows a first-order time dependence with a viscosity term. Efficient explicit central- and forward-difference algorithms for each field are developed by combining VUEL and VUMAT subroutines in the software ABAQUS/Explicit; hence, the convergence issue in the implicit phase field modelling is avoided. Several typical 3D fracture benchmarks with different failure modes are analysed for verification purposes and compared with the available experimental data. The results indicate that the developed model and computational implementation method can simulate complex 3D fracture of brittle/quasi-brittle materials with salient accuracy and efficiency, and are promising to meet the requirements in structural-level engineering practices. [Display omitted] [ABSTRACT FROM AUTHOR]