Predicted Crack Patterns Research Articles

Applying a 2D Variational Rigid Block Modeling Method to Rubble Stone Masonry Walls Considering Uncertainty in Material Properties

ABSTRACT The computational cost of detailed micro-modeling of masonry structures can be minimized with rigid block analysis methods, where a variational formulation is particularly interesting as it allows for nonlinear pushover analysis. This work investigates the accuracy of this modeling method in predicting the response of rubble stone masonry walls in shear compression tests. To this end, we extend the mathematical programming problem by including cohesion, compressive strength, and tensile strength in the formulation and implement an improved pushover procedure, which guards compatibility of the displaced shape and crack patterns at the intersection of elastic and rigid contact models. Additionally, we reduce model uncertainty, introduced through sampling material properties with distributions estimated based on results from tests on mortar masonry joints and on mortar specimens, by correlating the predicted crack patterns with the observed ones. The findings show that (i) model falsification based on crack pattern is an effective method for reducing the parameter uncertainty of stone masonry walls; and that (ii) the improved pushover procedure predicts the pre- and post-peak response of stone masonry walls very well with analysis times of less than 20 minutes for 2D models where stones and mortar are modeled explicitly.

A smoothing gradient thermo-mechanical damage model for thermal shock crack propagation: Theory and FE implementation

This paper introduces a novel smoothing gradient-enhanced thermo-mechanical damage model to capture complex thermal crack patterns. To describe the adiabatic property of the damaged region, the scalar variable indicating the deterioration level of material, the damage variable, is employed for the heat conduction balance equation. In essence, the local heat flux and heat capacity are modified to present a decrease in heat flow. Formulations for steady state and transient heat transfer are given. The accuracy and efficiency of the coupled smoothing gradient damage model are illustrated through the numerical experiments for steady state and transient crack growth (e.g., quenching test), where the predicted crack patterns induced by thermo-mechanical loading are in good agreement with experimental data and other reference numerical solutions.

Failure analysis of underground concrete silo under near-field soil explosion

The underground concrete silo is commonly constructed severing as vertical transport passages in mining and emergency exits for buried structures like tunnels, which, however, is possible to encounter accidental or intentional soil explosions (e.g., blasting excavation). The purpose of this study is to reveal the failure mode and mechanism of an underground concrete silo (46 m in height) subjected to a near-field soil explosion. The Coupled Lagrangian-Eulerian (CEL) method, along with two well-developed material models respectively for soil and concrete, is employed to handle the violent interactions between the exploded soil and the concrete silo. The numerical framework is first validated by simulations of a soil explosion beneath a concrete slab, where the predicted crack patterns of the concrete slab accord well with the experimental results. Subsequently, comprehensive numerical simulations are conducted to investigate the failure of the concrete silo under various soil explosion scenarios. The results indicate that the concrete silo experiences successively or simultaneously tensile spalling failure, local compression-induced tensile failure, and bending-induced tensile failure, with one or two predominating. The prevailing failure mode of the concrete silo is highly dependent on the intensity of the shock wave and the loading area. Further investigations expose that with the scaled distance increasing from 0.12 to 0.4 m/kg1/3, the dominant failure mode of the concrete silo transforms from local compression-induced tensile failure to overall bending-induced tensile failure. The critical scaled distance is 0.2 m/kg1/3. Regardless of the dominant failure mode, three-dimensional fracture planes that split the silo structure are generated. Besides, the tensile spalling failure, arising from the reflected tensile stress wave, is severe on the internal surface of the silo structure, consequently, fragments with velocities up to 12 m/s are produced, posing potential risks to humans and facilities inside the silo if any. This is the first time, to the authors’ knowledge, the failure of the prototype of a large-scale underground concrete silo arising from a large-yield and near-field soil explosion has been investigated. The finding can benefit the research community and provide a reference for the protection of the underground concrete silo as well as the facilities inside it to withstand soil explosions.

Forensic assessments of the influence of reinforcement detailing in reinforced concrete half-joints: A nonlinear finite element study

This paper presents the results of forensic assessments on reinforced concrete half-joint beams tested within the literature through the application of nonlinear finite element analyses. The software package ATENA Science was utilised, in which critical evaluations were conducted into the accuracy of the software in predicting the response of reinforced concrete half-joints with inadequate reinforcement detailing. It was shown that the load capacity of the half-joints could be predicted accurately, with an average experimental-over-predicted ratio of 1.04 and a coefficient of variation of 7.3%. The predicted crack patterns and modes of failure consistently coincided with those obtained experimentally, exhibiting localised failures at the re-entrant corner of the nib, along with failures located within the full depth of section due to an inadequate amount of shear reinforcement. Moreover, the combination of bar reductions to replicate severely corroded reinforcement at critical zones highlighted the influence deterioration mechanisms have on the structural capacity, with reductions of more than 50% observed in comparison to newly constructed half-joints with no deterioration.

Phase-field modeling of electromechanical fracture in piezoelectric solids: Analytical results and numerical simulations

The optimal design, reliable manufacture and durable utilization of electromechanical systems demand objective modeling of failure under coupled electric field and mechanical actions. This is still a challenging and largely an open issue despite the large volumes of contributions from the discontinuous approach and the phase-field community for brittle fracture. In this work we propose a length scale insensitive phase-field cohesive zone model (PF-CZM) for electromechanical fracture in linear piezoelectric solids, overcoming all the issues of mesh dependence, crack tracking complexity, length scale sensitivity and crack nucleation inconsistency. More specifically, in the electromechanically coupled phase-field constitutive relations, the evolution law for the crack phase-field is established from the geometric regularization of sharp cracks and the energetic criterion in global form. In order to capture the unsymmetric mechanical and electrical fracture behavior, the mechanical energy release rate contributed from the positive cone of the effective stress in energy norm is employed as the crack driving force, resulting in a hybrid formulation. With a set of phase-field characteristic functions optimal for cohesive fracture, the critical stress upon crack nucleation and the post-peak softening regime are derived in close-form for the first time, and the experimentally observed effects of the electric field on the fracture load are predicted qualitatively. The proposed electromechanical PF-CZM is numerically implemented in the multi-field finite element method and applied to several representative examples. In all cases, as those for purely mechanical problems, the predicted crack patterns and fracture loads are insensitive to the phase-field length scale and the experimental results are well reproduced. In particular, the effect of electric field on the deflection of crack paths can be captured. These merits make the proposed PF-CZM promising in the modeling of electromechanical fracture in piezoelectric solids.

Peridynamics modelling of dynamic tensile failure in concrete

Concrete as a brittle material suffers from tensile failures such as fracture and spalling under tension. These tensile failures are believed to be associated with the initiation, propagation, and coalescence of cracks. The purpose of this study is to present a numerical investigation on the dynamic tensile failures in concrete. For this purpose, the non-ordinary state-based peridynamics (NOSB-PD) theory is employed as an analysis tool to avoid the difficulties encountered in the finite element method in dealing with discontinuities such as cracks. Furthermore, to obtain the realistic stress field in the concrete and so as to update the nonlinear relationship between the force states and the displacement vectors required in the NOSB-PD theory, a well-developed rate-dependent plastic-damage model for concrete is incorporated. This model is modified from the Kong-Fang concrete model which has been verified to be suitable for the modeling of dynamic tensile failures in concrete within the classical continuum mechanics. Several numerical examples including dynamic fracture tests and spall tests are presented to demonstrate the performance of the current model. The results reveal that the dynamic fracture and spalling in concrete can be well captured and are observed to be greatly influenced by the loading rates. The predicted crack patterns of the concrete under different loading rates are found to be comparable to the corresponding experimental results.

Crack propagation in reinforced concrete exposed to non-uniform corrosion under real climate

The aim of this study was to develop a numerical model for the process of non-uniform corrosion under realistic temperature-relative humidity variations. Non-uniform distribution of corrosion products and their expansion around the steel bar were modeled in 2D. Cohesive elements embedded in the finite element mesh were used to model concrete cracking under corrosion. The proposed model was used to predict crack patterns and crack propagation under tropical marine type and temperate marine type climatic conditions. The climates were characterized by significant variations in temperature and relative humidity that resulted in different crack patterns and crack widths.

Using Deep Learning to Predict Fracture Patterns in Crystalline Solids

Summary Fracture is a catastrophic process whose understanding is critical for evaluating the integrity and sustainability of engineering materials. Here, we present a machine-learning approach to predict fracture processes connecting molecular simulation into a physics-based data-driven multiscale model. Based on atomistic modeling and a novel image-processing approach, we compile a comprehensive training dataset featuring fracture patterns and toughness values for different crystal orientations. Assessments of the predictive power of the machine-learning model shows excellent agreement not only regarding the computed fracture patterns but also the fracture toughness values and is examined for both mode I and mode II loading conditions. We further examine the ability of predicting fracture patterns in bicrystalline materials and material with gradients of microstructural crystal orientation. These results further underscore the excellent predictive power of our model. Potential applications of this model could be widely applied in material design.

Simulating the shake table response of unreinforced masonry cavity wall structures tested to collapse or near-collapse conditions

The seismic performance of existing unreinforced masonry (URM) buildings is considerably affected by typology and level of effectiveness of both construction details and structural components, especially if not originally designed for resisting earthquakes. Within this framework, the use of advanced numerical approaches that are capable of duly accounting for such aspects might improve significantly the assessment of the global response of URM structures. In this article, the applied element method is thus employed for simulating the shake table response of a number of full-scale building specimens representative of cavity wall terraced house construction, used in a number of countries exposed to tectonic or induced seismicity, accounting explicitly for the influence of the presence of both rigid and flexible diaphragms, degree of connections among structural members, and interaction between in- and out-of-plane mechanisms. Although the models slightly underestimated the energy dissipation in some specific cycles prior to collapse, the predicted crack patterns, failure modes, and hysteretic behaviors have shown a good agreement with their experimental counterparts.

Finite strain extension of a gradient enhanced microplane damage model for concrete at static and dynamic loading

The microplane model is a constitutive formulation, which provides a straightforward approach to model quasi-brittle materials such as concrete. The material model has been developed in various formulations in the small strain framework up to now, and it has been utilized successfully to predict crack patterns by combining with nonlocal damage. However, at high pressure, strain in concrete material or structures can become very large while in the absence of high pressure, finite deformations can be indicated by concrete that forms into rubble and has no stiffness anymore. Due to these challenges, the generalization of the microplane model from small strain to finite strain is needed in order to represent largely deformed structures. The generalization to finite strains can be performed using the Green-Lagrange strain tensor instead of strain components that are obtained by small strain analysis. The volumetric-deviatoric (V-D) decomposition is simply applied similar to the existing models. In order to construct a more stable damage approach, an implicit gradient enhancement is adopted. Furthermore, rate dependency of concrete is included in this extended model to accommodate dynamic loading. Finally, numerical examples in static and dynamic cases are discussed to verify and examine the capabilities of the proposed formulation.

Deformation and fracture of 3D printed disordered lattice materials: Experiments and modeling

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.

Smeared crack modelling approach for corrosion-induced concrete damage

In this paper a smeared crack modelling approach is used to simulate corrosion-induced damage in reinforced concrete. The presented modelling approach utilizes a thermal analogy to mimic the expansive nature of solid corrosion products, while taking into account the penetration of corrosion products into the surrounding concrete, non-uniform precipitation of corrosion products, and creep. To demonstrate the applicability of the presented modelling approach, numerical predictions in terms of corrosion-induced deformations as well as formation and propagation of micro- and macrocracks were compared to experimental data obtained by digital image correlation and published in the literature. Excellent agreements between experimentally observed and numerically predicted crack patterns at the micro and macro scale indicate the capability of the modelling approach to accurately capture corrosion-induced damage phenomena in reinforced concrete. Moreover, good agreements were also found between experimental and numerical data for corrosion-induced deformations along the circumference of the reinforcement.

The possibility to predict crack patterns on dynamic fracture

The maximum energy dissipation principle (MEDP), for dynamics fracture systems far from equilibrium, proposed by Slepyan was modified. This modification includes a decoupling between the injected and dissipated energies by adding a time delay and a description of the ruggedness produced by dissipation patterns. A time delayed energy conservation equation is deduced and dynamical equations that describe the dynamical system evolution were obtained in analogous way to the Slepyan’s calculations. The conditions for the rising of the instability process were presented by a bifurcation map. These results show that the theoretical framework proposed can describe the instability process along with dissipation patterns formation. This proposal was applied to dynamics fracture where it was possible to explain the results obtained by Fineberg–Gross for the fast crack propagation in PMMA. For unstable or dynamical crack propagation it is shown the possibility to predict crack patterns using this MEDP for other experimental configurations.

3차원 확장유한요소를 사용한 철근콘크리트 휨 부재의 다중균열 해석

In this paper, the extended finite element method (XFEM) is used to simulate a crack initiation and propagation and to predict post-failure behavior of reinforced concrete flexural members. The reinforced concrete beams modeled by 2-dimension plane element and 3-dimension solid element are compared with the result of RC beam experiments. The analysis results of 2D and 3D XFEM elements are similar to experimental results. It confirmed the validity of the use of the 3D XFEM model for the analysis of RC flexural members. In this process, the locking phenomenon in enriched degree of freedoms was detected. The ways to prevent the locking phenomenon are presented; reducing the time increments or the tolerance of fracture criterion. Subsequently, a reinforced concrete slab modeled by 3-dimensional XFEM was analyzed and compared with the result of a RC slab test as well as the analysis with concrete damaged plasticity (CDP) model which can represent realistic post-failure behavior of concrete. The analysis with XFEM showed a similar load capacity and crack propagation patterns. The validity of 3D XFEM to predict crack patterns and post-failure behavior of RC members was demonstrated.

An adaptive stochastic multi-scale method for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension

An adaptive stochastic multi-scale method is developed for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension. In this method, a macro-domain is first discretised into a number of non-overlapping meso-scale elements (MeEs) each of which containing detailed micro-scale finite element meshes. Potential discrete cracks in the MeEs are modelled by pre-inserted cohesive interface elements (CIEs). Nonlinear simulations are conducted for the MeEs to obtain the crack patterns under different boundary conditions. The macro-domain with the same number of overlapped, adaptively size-increasing MeEs are then simulated, until the potential cracks seamlessly cross the boundaries of adjacent MeEs. The resultant cracks, after being filtered by a new Bayesian inference algorithm to remove spurious cracks wherever necessary, are then integrated as CIEs into a final anisotropic macro-model for global mechanical responses. A two-dimensional example of carbon fibre reinforced polymers was modelled under two types of uniaxial tension boundaries. The developed method predicted crack patterns and load–displacement curves in excellent agreement with those from a full micro-scale simulation, but consuming considerably less computation time of the latter.

Finite element simulation of crack propagation based on phase field theory

The finite element approach is applied to predict crack patterns in a single or composite material under loadings. Crack patterns are represented as variations of a field variable. These variations are determined from the solution of a coupled system of equations consisting of an Allen-Cahn or Ginzburg-Landau type field equation and elasticity equations based on phase field theory. This representation does not require tracking crack tips as in the conventional finite element approach for the modeling of crack propagation problems. For a numerical solution for the system, a finite element algorithm is proposed and implemented into the finite element program “FEAP”. Several numerical simulations are performed and analyzed to predict the crack patterns in 2D single or composite materials under the loadings.

Modeling damage in concrete caused by corrosion of reinforcement: coupled 3D FE model

Reinforced concrete structures, which are exposed to aggressive environmental conditions, such as structures close to the sea or highway bridges and garages exposed to de-icing salts, often exhibit damage due to corrosion. Damage is usually manifested in the form of cracking and spalling of concrete cover caused by expansion of corrosion products around reinforcement. The reparation of corroded structure is related with relatively high direct and indirect costs. Therefore, it is of great importance to have a model, which is able to realistically predict influence of corrosion on the safety and durability of reinforced concrete structures. In the present contribution a 3D chemo-hygro-thermo-mechanical model for concrete is presented. In the model the interaction between non-mechanical influences (distribution of temperature, humidity, oxygen, chloride and rust) and mechanical properties of concrete (damage), is accounted for. The mechanical part of the model is based on the microplane model. It has recently been shown that the model is able to realistically describe the processes before and after depassivation of reinforcement and that it correctly accounts for the interaction between mechanical (damage) and non-mechanical processes in concrete. In the present paper application of the model is illustrated on two numerical examples. The first demonstrates the influence of expansion of corrosion products on damage of the beam specimen in cases with and without accounting for the transport of rust through cracks. It is shown that the transport of corrosion products through cracks can significantly influence the corrosion induced damage. In the second example the numerically predicted crack patterns due to corrosion of reinforcement in a beam are compared with experimental results. The influence of the anode–cathode regions on the corrosion induced damage is investigated. The comparison between numerical results and experimental evidence shows that the model is able to realistically predict experimentally observed crack pattern and that the position of anode and cathode strongly influences the crack pattern and corrosion rate.

Crack patterns in clayey soils: Experiments and modeling

SUMMARYThe paper presents an experimental and numerical study to investigate the behavior of desiccated clayey soils. The performed tests permit to evaluate the crack pattern as well as the tensile strength as a function of suction. A new model that relates the porosity evolution to the suction and to the tensile strength was developed and implemented in the finite element program CODE_BRIGHT. The proposed model captured the initiation and propagation of cracks in a thin layer of desiccated clay and predicted crack patterns in terms of the Minkowski densities (i.e. average crack length and crack intensity factor). The effect of the heterogeneity of the tested specimens, modeled by random clusters, was also quantified. Copyright © 2011 John Wiley & Sons, Ltd.

Analysis of prestressed fibre-reinforced concrete beams

This paper presents the test results of 12 partially prestressed concrete flexural beams reinforced with steel fibres that failed in flexure over partial or full depth. The variables considered were strength grades of concrete (35, 65 and 85 MPa) and the presence of steel fibres in the cross-section of the beam (web, flange or full depth). Three-dimensional finite element analysis of the prestressed beams was carried out to assess the non-linear behaviour of concrete, for example post-peak softening, concrete cracking strain softening, tension stiffening, bond-slip and yielding of reinforcement. Also, the effects of the addition of steel fibres in the concrete (increase in tensile strength and control of crack width due to the bridging of fibres across the crack interface) were modelled. The bond-slip behaviour of longitudinal reinforcements (steel fibres, prestressing wire and deformed bars) was accounted for to capture the structural stiffness of the concrete beam accurately. The effects of steel fibres in the concrete beam section over partial or full depth were also modelled. All prestressed beams were analysed using Ansys. Load–deflection responses and cracks in the prestressed concrete beams were predicted and compared with experimental results. The predicted results were found to be in good agreement with the corresponding test results. The analytical model predicted crack patterns in the concrete quite accurately.

Experimental study on fatigue strength of continuously reinforced concrete pavements

A laboratory investigation was conducted to characterise and quantify fatigue life of continuously reinforced concrete pavement (CRCP) in Korea highway systems. Eight scale-sized specimens were made, based upon results of finite-element analyses and stress–strain curve comparisons. Rubber plates were used to simulate the cement-treated sub-base and the sub-grade below the concrete pavements. Initially static tests were performed to obtain magnitudes of static failure loads and to predict crack patterns before fatigue tests. The CRCP fatigue lives measured in the study were compared with the results of previous investigations by other researchers. The comparisons indicate that the fatigue lives of most specimens are very close to the results from equation of Vesic and Saxena (NCHRP Report 97, HRB, National Research Council, Washington, DC, 1970). The results obtained in the study can be used for maintenance and retrofit of the CRCP constructed in major Korea highway systems.