Smeared Crack Model Research Articles

Study on collapse settlement and cracks of core wall rockfill dams under wetting deformation

AbstractThe safety and stability of core wall rockfill dams during impoundment are threatened by the wetting deformation of up‐stream shell materials. The serious wetting deformation not only aggravates the collapse settlement of upstream rockfill but also intensifies differential settlement of the dam crest during impoundment, and then causes cracks on the dam crest. On the basis of the proposed wetting deformation model and its simulation method of wetting deformation, this paper simulated the impoundment process of Guanyinyan core wall rockfill dam and studied the deformation characteristic of the dam during impoundment. In addition, the smeared cracking model was used to simulate the crack propagation on the dam crest, and the crack develop and spread mechanism was analysed. The results show that the simulated deformation can fit the in‐situ data well, and the simulated crack propagation is in good agreement with the actual situation. Once watered, the upstream rockfill and core wall have significant settlement, and the whole dam crest has obvious horizontal displacement towards the upstream. It is on the same order of magnitude that the increment of horizontal displacement and settlement at the top of the dam during impoundment. In the process of impoundment, the upper part of the dam tends to deform towards the reservoir area, which will lead to tensile cracks appearing in the rockfill areas on both upstream and downstream sides of the core wall of the dam crest, and the propagation direction of the cracks is basically parallel to the adjacent core wall surface. With the water level rising, the cracks on the downstream side of the dam crest mainly extend vertically, and the cracks on the upstream side of the dam crest not only extend vertically, but also extend horizontally.

A model scaling approach for fracture and size effect simulations in solids: Cohesive zone, smeared crack band and phase-field models

Despite many noteworthy contributions, the computational modeling of arbitrary fracture configurations and in particular, the quantification of size effect in quasi-brittle solids, still remains a challenging issue. In this work we proposed a model scaling approach for fracture and size effect simulations in solids. It employs only the geometric transformation relations and thus applies to any material model for fracture. Those popular models, i.e., the cohesive zone model, the smeared crack model and the phase-field cohesive zone model, are considered. With the geometric scaling factor intrinsically incorporated in the formulation, the resulting scaled models are able to predict the energetic size effect of a series of geometrically similar structures by parametric numerical simulations of the reference one. The 1-D analytical results of all the three scaled models are coincident with those from the underlying unscaled counterparts, validating the proposed model scaling approach. As it is independent of the mesh discretization and insensitive to the length scale, the scaled phase-field cohesive zone model (PF-CZM) is adopted for application to several representative benchmark tests of concrete and ice with mode-I and mixed I+II failure modes. The numerical results demonstrate that, owing to the strength-based crack nucleation criterion, the energy-based crack propagation criterion and the variational principle based path chooser, as well as the geometric scaling factor, are all incorporated into a standalone framework, the scaled PF-CZM is able to predict both the type II size effect law of pre-cracked quasi-brittle structures and the type I size effect law of intact ones. Moreover, those laborious manual manipulations in the numerical modeling of a large size range of geometrically similar structures, e.g., spatial discretization, enforcement of loading and boundary conditions, postprocessing of output data, etc., need to be done only once on the reference structure. These advantages make the scaled PF-CZM rather promising in the quantification of size effect in quasi-brittle structures.

A coupled smeared crack-plasticity model in incremental sequentially linear analysis for mixed failure modes

In this paper, a coupled smeared crack-plasticity model is proposed in incremental sequentially linear analysis (ISLA) to simulate mixed failure modes of tension, shear and compression. ISLA provides a robust and extensible solution for quasi-brittle materials. The solution search path follows damage cycles sequentially with secant stiffness corresponding to local damage increments, which traces both damage history (explicit) and displacement history (implicit). The proposed rotating smeared crack model resolves the limitations of a purely rotating crack model in the case that the smallest and the largest principal stress value are almost the same or the situation that the principal directions interchange between the beginning and the end of a load step. ISLA with the proposed constitutive model were demonstrated by mixed flure modes of the in-plane tests with large overburdens of a double clamped short wall and a cantilever long wall. Stable post-peak results were computed for large displacements, and localized crack propagation was computed robustly and correctly.

3D simulation of complex fractures with a simple mesh

AbstractRock masses are 3D in nature. The contained complex fracture networks pose great difficulty to its computer‐aided design (CAD) modeling and bring meshing burdens to classic finite element analysis (FEA). Considering the efficiency of digital images capturing complex geometries, as an extension of the previous 2D work, the 3D implementation of the image‐based simulation is carried out in this work. Continuous‐discontinuous deformations of complex rock masses are simulated in 3D with a simple structured mesh based on the numerical manifold method (NMM). Characteristics of the developed voxel crack model and its differences with discrete and smeared crack models are summarized. Based on this voxel crack model, the generating algorithm of 3D physical patches to construct the continuous‐discontinuous trial function is introduced in detail. In the developed method, the three spatial resolutions, respectively of the image model, integration voxels, and mathematical elements, are independent. These resolutions can be chosen freely by trading off the accuracy need and the computational expenses. Numerical examples investigate the accuracy and convergence of this method. Its 3D simulation capability of complex rock masses is demonstrated by calculating the continuous‐discontinuous deformation of El Capitan rock located in the Yosemite National Park with assumed complex fracture networks.

Numerical issues on brittle shear failure of pier-wall continuous vertical joints in URM dutch buildings

Terraced houses built in the Netherland after 1980 are often characterized by the use of large units connected at corners by continuous thin layer mortar joints. Unlike the running bond pattern, usually modelled as a rigid connection, the vertical continuous connection may fail in shear and influence the global seismic capacity of the entire building. This work aims at investigating and comparing different numerical modelling approaches for simulating the vertical connections. Two different constitutive models are adopted to simulate the quasi-brittle nonlinear behaviour of the continuous joint, and their advantages and limitations are pointed out in terms of robustness and accuracy. The study considers both the component level in terms of U-shaped pier-wall configuration, and the full-scale structural level in terms of the global capacity for a two-storey masonry house assemblage, characterized by a running bond arrangement. The results of this work show that the shear failure involving the continuous joint usually reduces the strength capacity of the structure. Both the selection of constitutive models for the connection interface and masonry material are demonstrated to affect the results significantly. Decoupled direct traction-displacement relations for the interfaces appear to provide more robust results than coupled plasticity-based Coulomb friction laws. The selection of either a pre-fixed orthotropic smeared crack model for the masonry or a standard isotropic concrete-like rotating smeared crack formulation is demonstrated to strongly influence the activation of the different failure mechanisms and hence the response of the structure.

Multi-fidelity progressive damage simulation of notched composite laminates with various ply thicknesses

In this study, a multi-fidelity fracture simulation scheme of composite laminates that accomplishes a seamless transition between medium- and high-fidelity crack models, namely, smeared crack models (SCMs) and discrete crack models (DCMs), is developed. The proposed scheme is based on the adaptive discrete-smeared crack (A-DiSC) method and a theoretical model for saturated crack density. The A-DiSC method first employs a DCM to model the transverse cracks in the laminates. If the crack density of each ply reaches the saturation value calculated using the theoretical model, the DCM is converted to an SCM. At this point, some cracks that are longer than a certain critical length remain explicitly modeled by the DCM, as they can significantly affect the subsequent path to final failure. By combining the two models, this method reduces the computational cost while preserving a sufficient prediction accuracy particularly in the case with numerous noncritical cracks up to failure. A simulation of the open-hole tensile test of composite laminates with various ply thicknesses was performed to verify the prediction accuracy of the developed scheme, and the predicted results were compared with the experimental results.

Nonlinear analysis method of concrete structures under cyclic loading based on the generalized secant modulus

Abstract A smeared crack model to represent cyclic concrete behavior is presented in this work. The model is based on analytical and experimental studies from the literature and proposes a numerical approach using a new concept, the generalized secant modulus. The monotonic formulation is described, followed by the changes to include the cyclic response, and the stress-strain laws to reproduce the hysteresis. Simulations adopting the proposed model were compared with experimental tests of cyclic tension and compression available in the literature, resulting in consistent load cycles. Three-point bending was simulated to display the structural response under non-elementary load. Finally, a reinforced concrete beam was studied to evaluate the model performance under usual loadings. The results show the model capacity to reproduce cyclic analyses and its potential to be extended to general loadings.

Implementation and engineering application of an improved rotating smeared crack model in rock mass fracture

Implementation and engineering application of an improved rotating smeared crack model in rock mass fracture

Numerical cracking analysis of steel-lined reinforced concrete penstock based on cohesive crack model

As the steel-lined reinforced concrete penstock is designed to allow concrete cracking, the crack propagation and bearing characteristics after the crack are the premise to evaluate the safety and stability of the penstock. However, the formulas of the steel stress and crack width are mostly semi-empirical and not in agreement with each other. Regarding numerical analysis, the crack width cannot be detected directly using the traditional smeared crack model; moreover, applying the discrete crack model is challenging because of the need for remeshing to follow the crack formation. In this study, a cohesive crack model (CCM) is implemented. An eight-node zero-thickness element is used to model the fracture separation process of the concrete. Random cracks, rather than pre-existing cracks, are achieved by inserting cohesive elements throughout the mesh. The parameters of the cohesive elements, which constitute a key for simulating concrete cracking, are extensively discussed. The concrete crack initiation time, crack propagation pattern, and stress distribution of steel are analyzed. The results of the CCM are consistent with those of the prototype model; this confirms the proposed model could provide a reference for penstock assessment and maintenance.

Numerical Analysis of Hollow Cross Section Reinforced Concrete Beams Strengthened by Steel Fibers Under Pure Torsion

This numerical study aimed to investigate the torsional behaviour of hollow cross section reinforced concrete members strengthened with steel fibers (end hooked and corrugated), subjected to pure torsion. The numerical results were compared with experimental results and show good agreement. The experimental study was conducted on ten steel fiber reinforced concrete specimens with low longitudinal reinforcement ratio to investigate the torsional behavior under pure torsion. For this analysis, a computer program (ANSYS 18.2) was used. The brick elements 8-nodes (SOLID65) were used to concrete simulation, while the steel bars simulated as axial members (link 180). The steel fibre was represented theoretically by the stress-strain relationship. The theoretical results indicated that the adopted smeared crack model is capable of making relatively acceptable estimations of cracking and ultimate torsional capacity of the members.

A state-of-the-art review of crack branching

Crack branching has important theoretical and practical significance in many natural phenomena and practical engineering problems. At present, the field of crack branching is still at an exploration stage, lacking a unified explanation of the underlying mechanisms and an effective method to predict crack branching in practical materials. This paper provides a state-of-the-art review of crack branching, including experimental observations, physics, fracture models and associated numerical methods. The experimental observations are first summarized, followed by the physics of crack branching. Then, the crack models including discrete crack models and smeared crack models are discussed, highlighting their key features, advantages and limitations. Next, a number of numerical methods that have been used to simulate crack branching are reviewed in detail, including the finite element method (FEM), extended finite element method (XFEM), boundary element method (BEM), meshfree methods (MMs), peridynamics (PD) and discrete element method (DEM). Finally, based on the information reviewed above, the future research directions of crack branching modelling are discussed.

Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation

PurposeThe aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.Design/methodology/approachThe cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.FindingsWhen compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.Originality/valueThis work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

Numerical simulation of damage patterns in the plastic hinge area of fire protected (SFRM) steel beams and its effect on their fire resistance

AbstractSprayed Fire‐Resistive Materials (SFRMs) are low strength, brittle materials used as passive fire protection on steel structural members. Their main drawback is that they can develop significant damage when the underlying steel member is subjected to mechanical deformations. The current study addresses numerically the damage patterns of the passive fire protection that could arise at the plastic hinge area of IPE steel beams and their effect on the fire resistance of the member. Initially, a numerical method that combines the smeared crack model and the discrete crack concept is implemented for the simulation of the mechanical behavior of the fire protective material and the prediction of the damage it sustains. The results of the mechanical analysis, considering the parameters of cross‐section height, SFRM thickness, monotonic or cyclic loading and presence of geometric initial imperfections, suggest that the damage pattern, which is a result of the combination of interface delamination and crack formation in the body of the material, can be categorized in two basic forms. In the sequel, a heat transfer analysis is conducted on the steel beams, under standard ISO‐834 thermal load, taking into account the damage derived by the mechanical analysis, in order to assess the reduction in the fire resistance of the beams, compared to the corresponding beams with an intact fire protection layer or without any fire protection.

A phase field model for fracture based on the strain gradient elasticity theory with hybrid formulation

In this paper, a novel phase field (PF) model for fracture is developed in the framework of strain gradient elasticity. The strain energy decomposition methods initially proposed for linear elastic fracture problems are extended to the gradient elasticity situation. The PF model is numerically implemented through Abaqus subroutine UEL (user defined element) with nine-node quatrilateral C1-continous element. The finite element implementation is validated by studying the stress field near the static crack tip. When the length-scale parameter of the gradient elasticity is zero, the stress field is consistent with the analytical solution predicted by linear elastic fracture mechanics (LEFM). For non-zero length-scale parameters, the Cauchy stress at the crack tip is found to be non-singular and the numerical results exhibit less mesh sensitivity in the crack tip region compared with the linear elastic case. After that, four different strain energy decomposition methods (Method I-IV) are compared and discussed by studying Mode I fracture behavior under tensile load. It is found that Method I can properly characterize the toughening effect of gradient elasticity. Based on Method I, the influences of the fracture length-scale parameter lc and the strain gradient length-scale parameter l on the characteristics of the smeared crack model and the load–displacement curves are systematically discussed. The specimen size effect of Mode I crack propagation is also investigated. It is found that the length-scale parameter l has a larger influence on the load–displacement curve as the specimen size decreases. Finally, crack propagation behavior in pure shear test, three point bending test and tensile test of a notched plate with hole is investigated. It is demonstrated that the proposed PF model can well predict the curvilinear crack propagation path and properly characterize the effect of gradient elasticity. Thus, the PF model developed in this paper can be applied to study complex fracture behaviors in the framework of gradient elasticity, where the effect of internal structure on the mechanical responses become significant.

Probabilistic Finite Element Modeling of Textile Reinforced SHCC Subjected to Uniaxial Tension.

The paper presents a finite element investigation of the effect of material composition and the constituents’ interaction on the tensile behavior of strain-hardening cement-based composites (SHCC) both with and without textile reinforcement. The input material parameters for the SHCC and continuous reinforcement models, as well for their bond, were adopted from reference experimental investigations. The textile reinforcement was discretized by truss elements in the loaded direction only, with the constitutive relationships simulating a carbon and a polymer textile, respectively. For realistic simulation of macroscopic tensile response and multiple cracking patterns in hybrid fiber-reinforced composites subjected to tension, a multi-scale and probabilistic approach was adopted. SHCC was simulated using the smeared crack model, and the input constitutive law reflected the single-crack opening behavior. The probabilistic definition and spatial fluctuation of matrix strength and tensile strength of the SHCC enabled realistic multiple cracking and fracture localization within the loaded model specimens. Two-dimensional (2D) simulations enabled a detailed material assessment with reasonable computational effort and showed adequate accuracy in predicting the experimental findings in terms of macroscopic stress–strain properties, extent of multiple cracking, and average crack width. Besides material optimization, the model is suitable for assessing the strengthening performance of hybrid fiber-reinforced composites on structural elements.

From diffuse damage to discrete crack: A coupled failure model for multi-stage progressive damage of composites

The multi-stage failure process and the coupled failure mechanisms have posed great challenges to damage analyses of fibre-reinforced composite laminates. In this study, a coupled failure model (CFM) is proposed which incorporates both smeared crack model (SCM) and discrete crack model (DCM) through an energy-consistent thermodynamic framework. While SCM is well suited for describing crack nucleation and diffuse damage at initial failure stage, DCM offers a great tool to model the subsequent crack growth and its interaction with other failure modes. A hybrid SCM/DCM formulation is developed for CFM, so that the progressive failure process from diffuse damage to propagation of major cracks is characterized. Furthermore, inherent limitations of each standalone model, such as convergence difficulty and computational inefficiency, are effectively resolved by the proposed approach. Performance of CFM is demonstrated through a few numerical examples, including element validation, Off-axis tensile and open-hole tension tests of composite laminates.

Modeling hydraulic fracture propagation in a saturated porous rock media based on EPHF method

Hydraulic fracture propagation in a porous rock media is complex. This paper presents an extended permeability-based hydraulic fracture (EPHF) modeling method for porous rock media. The EPHF model is a smeared crack model that is based on a fully-coupled, fluid-solid formulation. The pre-failure deformation of the solid phase is modeled by poroelasticity and the Drucker-Prager plasticity model is used for the post-fracture process. The flow liquid phase is described by Darcy's law. An extra material parameter that characterizes the onset of cracking for the brittle material is integrated into the smeared equation. Three models are integrated into the EPHF method for calculating the relative permeability when considering the mixture feature of the in-situ fluid and injected fluid. In addition to simulating fracture propagation in a homogeneous porous rock media, the EPHF model is good for simulating the fracture propagation in various heterogeneous rocks when incorporating static level set functions to describe material interfaces. An approximate method is discussed for estimating the effective hydro-fracture features; i.e., the equivalent fracture zone, fracture path and fracture aperture. Influence factors, e.g., the material properties and effective stress ratio for breakdown pressure and propagation pressure, are studied in a homogeneous fully saturated porous rock. Comparison with analytical results indicates that the EPHF method is capable of being used to model these characteristics and the hydraulic fracture propagation in a porous rock media with or without heterogeneity included.

Simplified micro-modeling of partially-grouted reinforced masonry shear walls with bed-joint reinforcement: Implementation and validation

Partially grouted reinforced masonry (PG-RM) shear walls of hollow concrete blocks (HCB) have been an object of study during the last years. The non-constant cross-section of this type of structural element and the presence of reinforcement set a challenging scenario when assessing their lateral resistance. This scenario makes simple approaches (e.g., design expressions) lacking accuracy. Besides, the most accurate existent analysis methodologies rely on user-defined sub-routines that are not available for commercial use. Therefore, proper analysis methodologies are still a need. In this regard, this research aims at reproducing the behavior of PG-RM shear walls with bed-joint reinforcement with a simple but also accurate approach. In this line, the in-plane behavior of PG-RM shear walls was reproduced by implementing 2D micro-models in a multi-purpose commercial FE code without requiring excessive work, advanced programming skills, and unaffordable hardware. The model approach was validated by reproducing two identical full-scale PG-RM shear walls. Although the model was not able to reproduce cyclic loading as in the tests, the model captured the experimental failure mode and lateral resistance with an acceptable degree of accuracy. Moreover, the distribution of cracks and deformations in horizontal reinforcement elements were appropriately reproduced at the lateral resistance, indicating the most demanded reinforcement portions. Additionally, the proposed modeling approach was compared with two alternative approaches: a 2D model that reproduced tensile failure employing interfaces and a smeared crack model and a 3D model that reproduced tensile failure utilizing a smeared crack model. The benchmark results pointed out the advantages of the reference model over the alternative modeling approaches. The first alternative model reproduced an excessive displacement capacity, and the second alternative model simulated an inaccurate crack pattern and was associated with a heavy computational burden.

Numerical simulation of GFRP-reinforced glass structural elements under monotonic loading

Several reinforcing strategies have recently been developed to overcome glass brittleness and numerical simulations are essential to investigate the structural behaviour of such hybrid systems. Based on previous experimental results from monotonic quasi-static tests, this paper presents a numerical study about the flexural behaviour of glass beams reinforced with glass fibre reinforced polymer (GFRP) laminates bonded with two different adhesives: polyurethane and epoxy. The main objective of this study is to evaluate the efficiency of different constitutive models to simulate the non-linear behaviour of glass, considering the following factors: initial stiffness, cracking load, post-cracking stiffness, crack pattern and progressive failure. The glass is simulated using smeared crack (SCM) and damaged plasticity (DPM) models with static and dynamic numerical approaches. Particular attention is paid to the influence of the several parameters that influence the structural behaviour of glass (e.g. threshold angle), as well as to the interfaces between all the materials involved (e.g. thickness of the adhesive layer). In relation to static numerical approaches, dynamic numerical approaches require more computational effort and their dynamic effects may influence the structural responses obtained; however, they also show to be able to capture all the stages of cracking in greater detail, because stability during cracking formation is guaranteed even at smaller loading stages. Since DPM models do not allow considering a maximum absolute damage factor of 1.0, the smeared crack models simulate better the non-linear behaviour of glass.

Nonlinear Mechanical Responses of Concrete Beams Reinforced with High-Performance CFRP Tendons

The nonlinear mechanical responses of concrete beams with carbon fiber-reinforced composite (CFRP) tendons were studied with the finite element model constructed within the nonlinear mechanics theory. The two typical prestressed CFRP-reinforced concrete beams were subject to nonlinear analysis, the stress behavior of the tendons was investigated, the latter and common steels were compared. Experimental data and calculated results are in good agreement. The cracking, yielding, and crushing characteristics of concrete can be well described with the smeared crack model via the Owen yielding criterion and the Hinton crushing criterion. The prestressed CFRP tendons are accurately simulated with combined nonlinear elements, and the corresponding analytical procedure was quite reliable. The CFRP tendons exhibit high strength, retaining their properties even when beam specimens are damaged. In comparison with common steels acting in the tension zone, the CFRP tendons are still in the elastic deformation region during the whole process.