Simulation Of Fracture Process Research Articles

A minimum strain energy release-based thermal–mechanical damage model for fracture process simulation of quasi-brittle materials under high temperatures

A minimum strain energy release-based thermal–mechanical damage model for fracture process simulation of quasi-brittle materials under high temperatures

Fracture process simulation and crack resistance behavior analysis of transition-layer ceramic coating based on real image reconstruction model

Due to the intricate nature of the structures and interface morphologies within transition-layer ceramic coatings, the investigation of microscopic dynamic fracture behavior presents a significant challenge. In this work, we combined the deep learning-based image recognization model with peridynamic method to analyze the dynamic process of crack propagation in transition-layer and dual-layer coatings, and evaluate their crack resistance. Through the establishment of high-precision discrete models based on the real coating morphology and simulation of fracture behavior under tensile loading conditions, it was found that the transition structure leads to more dispersed crack initiation positions, followed by forming a complex network-like crack propagation pathway which involves the connection of isolated cracks with each other. The crack resistance behavior of the coating was evaluated by quantifying the number of broken peridynamic bonds and calculating the fracture energy of the coating. The results showed that, compared with dual-layer coatings, transition-layer coatings exhibit lower fracture energy in the initial stage of failure, followed by an increase and exceeding that of the dual-layer coating. The transition structure facilitates crack initiation while impeding crack growth and delaying the failure process.

Simulation of Fracture Process of Lightweight Aggregate Concrete Based on Digital Image Processing Technology

Simulation of Fracture Process of Lightweight Aggregate Concrete Based on Digital Image Processing Technology

Parameter identification of a phase-field fracture model using integrated digital image correlation

Phase-field fracture (PFF) modeling is a popular approach to model and simulate fracture processes in solids. Accurate material parameters and boundary conditions are of utmost importance to ensure a good prediction quality of numerical simulations. In this work, an Integrated Digital Image Correlation (IDIC) algorithm is proposed to calibrate boundary conditions, Poisson’s ratio, fracture energy and internal length, all at once, by using the phase-field model itself and images of a deforming sample. The presented approach is applied to virtual experiments mimicking a single edge notched shear test and implemented in the open-source deal.II-based software pfm-cracks and the digital image correlation library Correli 3.2. The reliability of the results is investigated for different levels of acquisition noise, thereby demonstrating high robustness and accuracy for a wide range of noise levels. The conditioning of the problem is analyzed via sensitivity fields for all parameters and the eigendecomposition of the Hessian matrix used in the IDIC algorithm.

An enriched phase-field method for the efficient simulation of fracture processes

The efficient simulation of complex fracture processes is still a challenging task. In this contribution, an enriched phase-field method for the simulation of 2D fracture processes is presented. It has the potential to drastically reduce computational cost compared to the classical phase-field method (PFM). The method is based on the combination of a phase-field approach with an ansatz transformation for the simulation of fracture processes and an enrichment technique for the displacement field as it is used in the extended finite element method (XFEM) or generalised finite element method (GFEM). This combination allows for the application of significantly coarser meshes than it is possible in PFM while still obtaining accurate solutions. In contrast to classical XFEM / GFEM, the presented method does not require level set techniques or explicit representations of crack geometries, considerably simplifying the simulation of crack initiation, propagation, and coalescence. The efficiency and accuracy of this new method is shown in 2D simulations.

An Anisotropic Damage Model of Quasi-Brittle Materials and Its Application to the Fracture Process Simulation

Accurate predictions of the failure behaviors of quasi-brittle materials are of practical significance to underground engineering. In this work, a novel anisotropic damage model is proposed based on continuous damage mechanics. The anisotropic damage model includes a two-parameter parabolic-type failure criterion, a stiffness degradation model that considers anisotropic damage, and damage evolution equations for tension and shear, respectively. The advantage of this model is that the degradation of elastic stiffness only occurs in the direction parallel to the failure surface for shear damage, avoiding the interpenetration of crack surfaces. In addition, the shear damage evolution equation is established based on the equivalent shear strain on the failure face. A cyclic iterative method based on the proposed anisotropic damage model was developed to numerically simulate the fracture process of quasi-brittle materials. The developed model and method are important because the ready-made finite element software is difficult to simulate the anisotropic damage of quasi-brittle materials. The proposed anisotropic damage model was tested against a conventional damage model and validated against two benchmark experiments: uniaxial and biaxial compression tests and Brazilian splitting tests. The results demonstrate that the proposed anisotropic damage model simulates the mesoscale damage mode, macroscale fracture modes, and strength characteristics more effectively and accurately than conventional damage models.

A Hybrid Particle/Finite Element Model with Surface Roughness for Stone Masonry Analysis

Circular and spherical particle models are a class of discrete elements (DEM) that have been increasingly applied to fracture studies of quasi-brittle materials, such as rock and concrete, due to their proven ability to simulate fracture processes through random particle assemblies representing quasi-brittle materials at the grain scale. More recently, DEM models have been applied to old stone masonry fracture studies. In order to extend its applicability to structures of larger dimensions, an enhanced hybrid particle model is proposed here that allows finite elements with a given surface roughness, provided by the discretization of the element boundary with particles, to interact with the particulate media in which they are embedded. The performance of the hybrid model is compared with that of a traditional all-particle model under uniaxial testing. It is shown that similar results are obtained, namely, in the elastic phase, figures of rupture and pre-peak and post-peak behavior, while the hybrid model allows for a significant computational run time reduction of 20% to 25% in the coarse particle assemblies. Finally, the proposed hybrid model is applied in the simulation of shear tests of stone masonry walls and dry and mortared joints, providing reasonably good agreement with both the experimental results and predictions. For the rubble masonry tests, the hybrid model allows for a computation run time reduction of around 40% when compared with an all-particle model.

Extremely large deformation of tunnel induced by rock mass fracture using GPGPU parallel FDEM

AbstractIt is essential to better understand the large deformation behavior of deep tunnels in weak rock mass to improve the long‐term stability of tunnel surrounding rock mass and design effective supports for squeezing tunnels. This paper introduces two representative large deformation engineering examples to study squeezing behavior. First, new algorithms of contact search, determination of actual contact, and calculation law of contact pairs are proposed for general‐purpose computing on graphics processing units (GPGPUs), by improving the original serial algorithms and developing a compute unified device architecture (CUDA) parallel program, to satisfy the large‐scale rock fracture process simulation. Then, tunnels excavation and rock reinforcement effect including the combination of U‐shaped steel and steel fabric, spray concrete (SMC), and grouting were modeled. The verification, done by comparing the field observation data and the FDEM simulation results of progressive fracture and the tunnel wall convergence displacement, shows that stress remarkable rebalancing after excavation because of high in situ stress, low rock mass strength, and rock mass long‐term strength reduction properties, thus, the rock mass fracture progressively and the rock blocks move continuously, leading to the rock mass volume increase significantly. The result demonstrates one of the root causes of squeezing. To effectively reduce the tunnel wall displacement and maintain tunnel stability, support with higher stiffness or multifactorial combined support methods and grouting with a better bonding effect should be used together. The findings provide insights into the progress of tunnel squeezing and the basis for support design in the squeezing tunnel.

Fracture performance improvement and fracture process simulation of concrete for shotcrete use in hot and dry environments

AbstractIn order to investigate the fracture performance of concrete in hot and dry tunnel environments, the fracture parameters are tested through three‐point bending tests on notched beams. The effects of basalt and steel fibers on the fracture properties in hot and dry environments are explored, and the effects of beam height and notch length on fracture parameters of concrete are analyzed by using numerical calculations. The results show that the fracture toughness of concrete in hot and dry environments is obviously lower than that in the standard curing condition. The addition of basalt and steel fibers has little effect on the initial fracture toughness but can significantly improve the unstable fracture toughness and fracture energy. The peak load and maximum fracture process zone length decrease with the increase of the notch length and increase with the increase of the beam height, while the unstable fracture toughness is basically not affected by the size changes of concrete beams.

A strain gradient enhanced model for the phase‐field approach to fracture

AbstractPhase‐field modelling has been shown to be a powerful tool for simulating fracture processes and predicting the crack path under complex loading conditions. Note that the total energy of fracture in the classical phase‐field formulations includes the strain energy density from the linear elasticity theory resulting in singular stresses at the crack tip. Recently, we have demonstrated that integrating the strain gradient elasticity into the conventional phase‐field fracture formulations may improve the final results by alleviating the effects of a singular stress field around the crack tip [1]. The current contribution focuses on a more general formulation of strain gradient elasticity.

The Continuum Voronoi Block Model for simulation of fracture process in hard rocks

AbstractIn this paper, a numerical model is presented to represent the fracture process in hard rocks based on a pseudo‐discontinuum method called the Continuum Voronoi Block Model (CVBM). To validate this tool, numerical models for one Brazilian test, one unconfined compression test, and multiple triaxial compression tests with different confining stress were calibrated to match laboratory test results for Creighton granite. The model proved robust and matched the following macro‐properties: crack initiation (CI) stress, (CD) stress, peak strength, tensile strength, Young's Modulus, and Poisson's ratio. The calibrated model served as a basis for a sensitivity study to analyze how micro‐properties influence the rock's macroscopic responses. From the sensitivity study, a calibration methodology was proposed, which shall facilitate the use of the CVBM in future works.

A continuum damage-based three-dimensional fracture simulation method for brittle-like materials

Current numerical methods cannot simulate well three-dimensional (3D) fracture process of solids. In order to study 3D fracture process of brittle-like materials and improve crack growth path prediction accuracy, a method is developed based on continuum damage mechanics and finite element method. In the developed method, damage is computed by homogenizing stress or strain in the preset characteristic field for reducing the spurious mesh sensitivity. Meanwhile, an additional procedure is used to consider the unstable and competing fracture process, which can be used to consider stress redistribution due to local damage evolution during the fracture process simulation. In addition, a damage model of concrete is also developed and used to describe material damage. Finally, 3D fracture process of two numerical examples, were simulated and compared with the experimental results by using the developed method. The 3D crack growth path and macroscopic mechanical behaviors can be predicted by the developed method coupled with a damage model. From the comparison, the effectiveness and modeling capability of the developed method are verified, which can be used to study 3D fracture mechanisms of concrete-like materials.

Peridynamic Modeling and Simulation of Fracture Process in Fiber-Reinforced Concrete

Peridynamic Modeling and Simulation of Fracture Process in Fiber-Reinforced Concrete

Study on the characterization of rock heterogeneity and simulation of fracture process based on the mesoscopic structure

This study aims to explore the effect of rock heterogeneity caused by meso-structure differences on the macro-mechanical properties and fracture evolution process. With the help of computed tomography, the meso-structure characteristics of coarse-grained red sandstone are obtained, starting from the meso-structure level. The digital characterization of heterogeneous rocks is completed with the use of image-processing methods, and a rock equivalent crystalline model is constructed. A numerical simulation study is performed with the particle flow PFC3D 5.0 program. The results show that (1) the main form of rock heterogeneity is a meso-structure difference, and this determines the rock’s macro-mechanical properties and failure characteristics. The meso-structure difference mainly plays a role in the post-peak damage weakening stage of rock, and the slight difference leads to damage in different development modes. (2) The crack initiation starts at the cemented and crystalline grid surfaces, which is randomly distributed. The crack evolution process is selective and affected by the types and distribution of the surrounding mineral particles. The development of cracks is dominated by secondary cracks, distributed in strips, in the area of mineral particles with strong mechanical properties. In contrast, cracks are densely developed and spread around in a cluster in the area of mineral particles with weak mechanical properties.

A computational method for two/three dimensional competitive fracture process simulation of rock-like materials due to cracking

In order to study the fracture process of rock-like materials for structural safety, a method is developed to simulate two-dimensional (2D) and three-dimensional (3D) crack growth. The novelty of the developed method is that a procedure is used to consider stress redistribution due to cracking during the fracture process simulation within a loading step. Based on this way, the instable competitive and coupling fracture process can be simulated by considering the coupled interactions among cracking within rock-like materials. As case study, 2D and 3D fracture processes of a rock-like specimen containing pre-existing flaws were simulated and compared with the corresponding experimental results. From the comparison of simulation and experimental results, it can be determined that the agreement between experimental and numerical fracture modes was excellent, which supported to assess the effectiveness of the developed method. The method can be used to predict crack path of rock-like materials for studying their fracture characteristics.

A minimum Lemaitre's damage strain energy release rate-based model for competitive fracture process simulation of quasi-brittle materials

A physical damage model based on minimum Lemaitre's damage strain energy release rate is developed to describe quasi-brittle materials' softening. A modified finite element procedure together with the developed damage model is used to simulate the fracture process of quasi-brittle specimens. In the developed procedure, damage is only updated in the most dangerous element at each iteration, and mesh dependency can be reduced based on this way. Two representative numerical examples support the effectiveness of the developed damage model and procedure, which illustrate their ability to objectively simulate the mixed-mode failure process of quasi-brittle materials due to tension, compression and shear. In addition, we found that the simulation results obtained from the modified finite element procedure are insensitive to grid mesh.

Mesoscopic numerical simulation of fracture process and failure mechanism of cement mortar

AbstractCement mortar is an important part of building material and a typical cement matrix composite material. In current work, the mechanical properties and failure mechanism of cement mortar under static compression are studied by using the Base Force Element Method (BFEM). The static compression damage program of cement mortar is compiled grounded on the BFEM of the potential energy principle. An elastic polyline damage constitutive model is put forward to express the meso‐damage and evolution process of cement mortar. A 2D random circular aggregate model of cement mortar was established. The numerical simulation of the uniaxial static compression is carried out, the stress–strain curve, damage process, and damage model are obtained. The strength of the interfacial transition zone and the failure process of hardened cement mortar were discussed. A mesoscopic equivalent model is proposed to analyze the mechanical properties of cement mortar by considering the effect of initial porosity.

Numerical modeling of fracture process using a new fracture constitutive model with applications to 2D and 3D engineering cases

AbstractThe overwhelming majority of experimental and numerical tests show the dependence of mechanical response on discontinuities (such as joints, faults, and bedding plane). In this study, fracture process is numerically investigated using finite‐difference method. A quasi‐continuum model (assuming that the real rock mass represents the sum of intact rock and fracture) has been developed to describe the fracture propagation in a fractured rock. First, this model has been validated against the experimental results and was shown to simulate satisfactorily the fracture propagation in the tensile, shear as well as the mixed (tensile and shear) modes. This model then has been used to investigate the fracture processes during the 2D long‐wall mining and 3D pillar failure. According to the 2D and 3D simulations, it was found that: (a) this model can provide a new reasonable approach to simulating fracture processes in either 2D or 3D cases; (b) roof failure is mainly caused by shear fractures rather than tensile fractures during the 2D long‐wall mining.

SPH Model for Numerical Test of Heterogeneous Rock-like Material

Based on the Smoothed Particles Hydrodynamics (SPH) method, a heterogeneous material numerical model is developed for simulation of fracture process of heterogeneous rock-like material, such as rock. The self-developed SPH program is proposed to analyse the mechanical properties of rock-like materials. In the present program, the combined Mohr-Coulomb criterion is adopted. The deformation of rock-like material under uniaxial compression can be analysed, and the acoustic emission in rock-like material can also be clarified. The calculation results show that the SPH simulation model can be used for numerical test of heterogeneous rock-like material. The process of destruction of rock specimen is evolutionary process. Rock acoustic emission records the brittle failure process of rock-like material.

Coupled phase field finite element model for crack propagation in elastic polycrystalline microstructures

This paper is aimed at the development of a coupled finite element-phase field modeling framework for simulating fracture processes in anisotropic elastic materials under finite deformation conditions with tension-compression asymmetry of crack phase. A novel Helmholtz free energy density is proposed in terms of a phase field order parameter dependent elastic Green-Lagrange strain tensor. It accommodates anisotropy of the material and unilateral conditions of material damage. The paper also addresses numerical instabilities, which adversely affect computational fracture simulations. Solutions based on viscous stabilization are suggested to effectively overcome the convergence issues of nonlinear FE solvers. Numerical examples are carried out to highlight different aspects of the developed framework. Numerical results with the proposed model are successfully compared with experimental results for validation. The model admits the unilateral conditions of the crack phase and predicts the correct crack kinking in mode II fracture. Special attention is drawn to numerical details affecting the efficiency and accuracy of the phase field models.