Fracture Problems Research Articles

Meso-scale simulation of thermal fracture in concrete based on the coupled thermal–mechanical phase-field model

Temperature-induced concrete fracture is a multi-field coupled process and the propagation of crack is complex because of the nonhomogeneity of materials. In this paper, the mesoscale concrete containing aggregate, interfacial transition zone (ITZ), and mortar is established using the random generation algorithm. The governing equations of the coupled thermal–mechanical phase-field model are established, and the finite element method is implemented to solve these equations. Several representative numerical samples are solved by the proposed coupled model, such as concrete under tension after high temperature, concrete spalling caused by high temperature, concrete cracking caused by the temperature rise of a circular hole, and cracking of confined concrete. Numerical results have shown that concrete cracks first appear at the ITZs and eventually develop into one or more major cracks. Most numerical results indicate that the influence of the length scale in the proposed phase-field model on crack propagation is little. It has shown that the application of the phase-field model to simulate mesoscale concrete fracture problems under multi-field coupling is feasible.

Kinking prohibition enhancement of interface crack in artificial periodic structures with local resonators

In this study, the propagation and kinking of an interface crack between two dissimilar artificial periodic structures with local resonators is investigated. By Fourier transform, the dynamic fracture problem is derived as an equation with Wiener–Hopf type. An additional band gap can be created by local resonators. During the dynamic failure, elastic waves will be excited continuously from the crack tip and result in the energy dissipation. Moreover, the energy release ratio which characterizes the fracture resistance is obtained. The meta-arrest property of the artificial periodic structure with local resonators is illustrated. Based on inverse Fourier transform, the displacement field is given to further understand the deformation and oscillation of crack faces. Based on the crack-tip field, the maximum energy release rate criterion is presented to discuss about whether the crack can propagate through kinking out of the interface. Comparing with the model without local resonators, we find that crack kinking can be prohibited in the proposed artificial periodic structures. Finally, finite element simulation and experiment are performed to show the good agreement with the theoretical predictions.

A micromorphic phase-field model for brittle and quasi-brittle fracture

In this manuscript, a robust and variationally consistent technique is proposed for local treatment of the phase-field fracture irreversibility. This technique involves an extension of the phase-field fracture energy functional through a micromorphic approach. Consequently, the phase-field is transformed into a local variable, while a micromorphic variable regularizes the problem. The local nature of the phase-field variable enables an easier implementation of its irreversibility using a pointwise ‘max’ with system level precision. Unlike the popular history variable approach, which also enforces local fracture irreversibility, the micromorphic approach yields a variationally consistent framework. The efficacy of the micromorphic approach in phase-field fracture modelling is demonstrated in this work with numerical experiments on benchmark brittle and quasi-brittle fracture problems in linear elastic media. Furthermore, the extensibility of the micromorphic phase-field fracture model towards multiphysics problems is demonstrated. To that end, a theoretical extension is carried out for modelling hydraulic fracture, and relevant numerical experiments exhibiting crack merging are presented. The source code as well as the data set accompanying this work would be made available on GitHub (https://github.com/ritukeshbharali/falcon).

Robust line segment mismatch removal using point-pair representation and Gaussian-uniform mixture formulation

Line segment matching (LSM) plays an important role in image matching, while it is always a challenging problem due to line fracture and high geometric complexity. In this paper, we propose a line segment mismatch removal to address the sensitivity to segment length and the fracture problem. The mismatch removal removes the massive false matches obtained by the descriptors like LBD. Specifically, we suggest calculating the endpoint error in LSM rather than the direction error in considering the error band and segment length. We propose a point-pair representation, and transform the LSM problem to be an intuitive point-pair alignment problem with a mixture model. The point-pair representation is more robust on the segment length than the linear equation representation used in RANSAC, which significantly preserves short line segments. Then, based on the point-pair representation, we propose a novel Directed Endpoint Drift method to solve the inherent fracture problem of line segments by allowing the endpoints to move along the line to complement the fracture. Compared with the recent learning-based method, the proposed method nearly doubles the number of correct matches on the remote sensing dataset. Especially, the recall is improved by 10% to 30% for both the short segments and the slightly fractured segments, compared with the popular RANSAC and MAGSAC++ methods. The code is available at https://github.com/shenliang16/DEpD.

The Rising Problem of Hip Fractures in Geriatric Patients-Analysis of Surgical Influences on the Outcome.

Hip fractures in geriatric patients often have a poor outcome in terms of mortality, mobility as well as independence. Different surgical influence factors are known that improve the outcome. In this observational cohort study, 281 patients of a geriatric trauma unit were analyzed prospectively. Demographic factors, as well as data regarding the trauma mechanism and perioperative treatment, were recorded. The nutritional status was also analyzed. The follow-up was set to 120 days. The key conclusion of this study is that a high ASA classification, the use of anticoagulatory medicine and malnutrition are significantly associated with higher mortality together with worse independence (p < 0.05). There is no significant difference in outcome concerning the time to surgery within the first 24 h. Malnutrition seems to be an important risk factor for an adverse outcome of geriatric patients and therefore warrants a focus in multidisciplinary treatment. The risk factor ASA cannot be improved during the pre-surgery phase, but requires intensified care by a multidisciplinary team specialized in orthogeriatrics.

Memory effects on the thermal fracture behavior of cracked plates via fractional heat conduction models

Studies have shown that fractional derivatives have important memory effect on the thermal shock fracture of structures. In the present work, four generalized fractional models are applied to investigate the thermal fracture problem of cracked plates. Laplace transform and finite sine transform are employed to obtain transient temperature and thermal stresses. Stress intensity factors around the crack tips are evaluated through the weight function method for edge and center cracks. Numerical results show that memory effects on the thermoelastic fields are different with different fractional derivative definition and fractional orders, and the effects will vary accordingly with crack geometry parameters.

An acceleration scheme for the phase field fatigue fracture simulation with a concurrent temporal homogenization method

The phase field approach for fracture has been adapted for fatigue fracture in recent years. In this work, we propose an efficient acceleration scheme for this approach based on concurrent time-scale homogenization. In this scheme, the fatigue fracture problem is decomposed into a macrochronological problem and a microchronological problem, and is accelerated with the macrochronological time steps adaptively determined. The macrochronological time step is monitored during the whole simulation, and is corrected by a predictor–corrector strategy if necessary. Numerical examples demonstrate that this scheme is able to accelerate fatigue fracture simulations without sacrificing much accuracy, and can be up to 200 times faster than direct numerical simulations in some cases. For certain force-controlled examples, the proposed scheme, equipped with the arc-length control, is able to reproduce Paris’ law with a correlation coefficient higher than 0.91 in the logarithmic scale.

A phase-field lattice model (PFLM) for fracture problem: Theory and application in composite materials

In the present work, a phase-field lattice model (PFLM) is proposed to model fracture problems. The element deletion process and oversimplified failure criterion of the classical lattice model not only lead to a strong mesh sensitivity but also limit the method’s application to various materials and fracture modes. Hence, a smeared form of crack is introduced into the lattice model to deal with these problems. The model exploits discontinuous discrete methods to model the propagation of three-dimensional cracks by characterizing the crack with a phase-field variable. Moreover, by regarding the crack propagation process as a multi-field problem composed of a displacement field and a phase-field, a flexible and robust algorithm is established, in which the crack path can be obtained directly by resolving the governing equations. Numerical simulations were performed and compared with the experimental results and other numerical models. It is shown that the PFLM can capture the main features of the fracture for both brittle and quasi-brittle materials. To further demonstrate the performance of the model, a mesoscale system of cement composite generated by computed tomography scanning technology was examined. The result demonstrates that the fracture of composite materials can also be well predicted.

Generalization of Mvcci Approach for Lefm Problems Using Numerical Integration

Modified Virtual Crack Closure Integral (MVCCI) has become a valuable tool for estimation of mixed-mode fracture parameters in Linear Elastic Fracture Mechanics (LEFM) problems. When finite elements with fewer nodes and using polynomial shape functions are employed at the crack tip for fracture analysis, the expressions for MVCCI can easily be derived and many times also be expressed in closed form. For higher order elements they become unwieldy and so a numerical integration scheme is proposed and this can be used with any type of element. The scheme requires a two-step numerical integration: one to evaluate nodal forces exerted by the solid below the crack extension line on the portion above and the second to evaluate Strain Energy Release Rates. This development makes the post-processing for fracture parameters easy and computationally economical for 3-dimensional fracture problems. The technique is used to estimate fracture parameters in certain practical problems using higher order elements and typical numerical results are presented.

Reliability analysis of the stress intensity factor using multilevel Monte Carlo methods

This paper presents a reliability analysis for fracture toughness using a multilevel refinement on a hierarchy of computational models. A 2D finite element model discretized by quadrilateral elements is developed to analyze the stress intensity with the presence of an initial edge crack. The multilevel simulations are obtained considering a non-uniform sequence of mesh refinement in the vicinity of the crack tip. We set the probabilistic problem accounting for applied stress and crack size uncertainties. We analyze several error tolerances using the standard and multilevel Monte Carlo methods combined with the selective refinement procedure. The probability of failure is estimated by expanding it in a telescoping sum of an initial approximation at the coarsest mesh and a series of incremental corrections between the subsequent levels. In our analysis, we take on two common fracture problems; a single-edge notched tension to investigate the pure mode-I and an asymmetric four-points bending to consider the mixed mode-I/II. The results show significant savings in the computation cost.

Simulation analysis of effect of wheel out-of-roundness on dynamic stress of coil springs in metro vehicles

Many Chinese metros experienced numerous fatigue failures of the coil springs in the suspension of vehicles. The field test results presented in our previous work showed that wheel out-of-roundness (OOR) was responsible for the failure of the coil springs. It is believed that the most effective countermeasure to eliminate wheel OOR is to reprofile wheel. The fatigue life of coil springs is an important reference for determining the reprofiling parameters. A sophisticated vibration model for train and track with flexible coil springs and flexible track was established and validated with field test results. The effects of wheel OOR and P2 resonance on the coil spring can be evaluated with this model. The relationship between wheel OOR and coil spring dynamic stresses was determined using multibody simulation (MBS). The fatigue life of the coil springs was evaluated using the parameters of the amplitude of the wheel OOR and the mileage. Under the premise of finding a balance between improving the service life of the coil springs and reducing the cost of reprofiling the wheel, viable proposals were made to solve the problem of coil spring fracture.

Advancements in Phase-Field Modeling for Fracture in Nonlinear Elastic Solids under Finite Deformations

The prediction of failure mechanisms in nonlinear elastic materials holds significant importance in engineering applications. In recent years, the phase-field model has emerged as an effective approach for addressing fracture problems. Compared with other discontinuous fracture methods, the phase-field method allows for the easy simulation of complex fracture paths, including crack initiation, propagation, coalescence, and branching phenomena, through a scalar field known as the phase field. This method offers distinct advantages in tackling complex fracture problems in nonlinear elastic materials and exhibits substantial potential in material design and manufacturing. The current research has indicated that the energy distribution method employed in phase-field approaches significantly influences the simulated results of material fracture, such as crack initiation load, crack propagation path, crack branching, and so forth. This impact is particularly pronounced when simulating the fracture of nonlinear materials under finite deformation. Therefore, this review outlines various strain energy decomposition methods proposed by researchers for phase-field models of fracture in tension–compression symmetric nonlinear elastic materials. Additionally, the energy decomposition model for tension–compression asymmetric nonlinear elastic materials is also presented. Moreover, the fracture behavior of hydrogels is investigated through the application of the phase-field model with energy decomposition. In addition to summarizing the research on these types of nonlinear elastic body fractures, this review presents numerical benchmark examples from relevant studies to assess and validate the accuracy and effectiveness of the methods presented.

Coupling Explicit Phase-field MPM for Two-Dimensional Hydromechanical Fracture in Poro-elastoplastic Media

In this paper, a novel coupling explicit phase-field material point method with the convected particle domain interpolation (ePF-CCPDI) is proposed to predict the large deformation elastoplastic failure behavior in two-dimensional fully saturated porous media. This method provides a new thermodynamic derivation for the explicit phase-field modeling of multi-physical fracture problems. To account for the coupling effect of pore fluid flow on fractured porous solids, the pressure energy is included in the coupled system energy balance equation. The constitutive relationship of saturated porous media indicates that the pore pressure has a direct effect on the deformation of the solid skeleton. For achieving the fluid pressure smoothly distributed in damaged porous media under large deformation, exponential indicator functions are constructed to interpolate the fluid properties from the intact medium to the fully broken one. Meanwhile, the crack-opening-dependent permeability is introduced to estimate fluid flow inside the crack. The coupled explicit phase-field plasticity model is adopted to characterize the elastoplastic failure behavior of the solid skeleton. Moreover, a mixed explicit-implicit staggered solution scheme is developed to effectively solve the governing equations of the coupled system. To eliminate the numerical noises while material points cross the cell boundaries in large deformation simulation, the improved convected particle domain interpolation technique (CPDI) is adopted to enhance the computational accuracy. Two solution schemes are also proposed based on the extended material point penalty method to handle the specified pressure boundary condition. Finally, several representative two-dimensional numerical examples are conducted to validate the accuracy and capability of the proposed method.

An enhanced adaptive coupling strategy of peridynamics and finite element method via variable horizon approach for simulating quasi-static fracture problems

An enhanced adaptive coupling method of peridynamic (PD) theory and the finite element method (FEM) is performed that combines the advantages of both approaches and can be used to simulate quasi-static fracture problems. In the proposed model, PD is used to simulate crack initiation and propagation, whereas the FEM is used to simulate domains without damage to improve efficiency. The influence of ghost forces is reduced by introducing a transition subregion with a variable horizon, thereby significantly improving the accuracy of the model, which is verified by application to a plane stress problem. The conventional coupling model requires pre-partitioning of the solution domain, which is difficult to achieve when modeling certain problems, such as the initiation of cracks at unknown locations. Hence, the adaptive conversion criterion is introduced to ensure that subregions automatically evolve as cracks grow, thereby obviating the need for prior knowledge of crack propagation paths. The proposed model is applied to three standard laboratory tests of quasi-static fracture and its performance is validated by the good agreement of its results with reference solutions or experimental observations. The model accurately simulates complex fracture problems involving crack initiation, irregular crack propagation, and crack coalescence.

A mixed-mode dependent interface and phase-field damage model for solids with inhomogeneities

The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular situation of a solid with inhomogeneities. Description of the fracture processes are based on the theory of material damage. It introduces two independent damage parameters to distinguish between interface and internal cracks. The parameter responsible for interface cracks is defined in a thin adhesive layer of the interface and renders relation between stress and strain quantities in fashion of cohesive zone models. The second parameter is defined inside material domains and it is founded on the theory of phase-field fracture guaranteeing the material damage to occur in a thin material strip introducing a regularised model of internal cracks. Additional property of both interface and phase-field damage is their capability to distinguish between fracture modes which is useful if the structures is subjected to combined loading. The solution methodology is based on a variational approach which allows implementation of non-linear programming optimisation into standard methods of finite-element discretisation and time stepping method. Computational implementation is prepared in MATLAB whose numerical data validate developed formulation for analysis of problems of fracture in multi-domain elements of structures.

Three-dimension mesoscale model of concrete by random placement algorithm and its failure mechanism analysis

This contribution presents the development and application of a 3D numerical concrete model for investigating the fracture behavior of concrete at the mesoscale. The reconstruction of actual geometric models of pebble and crushed aggregates is carried out using a 3D laser scanner. An aggregate and pore library were then constructed, and a 3D random placement method is developed to generate the realistic mesostructure of concrete. Additionally, the cohesive zone model-based numerical computation approach was employed to simulate the fracture problem in concrete. Then, the numerical concrete model is applied to investigate the mechanical response and fracture behavior of cylindrical concrete specimens under uniaxial compression and concrete beams under three-point bending. Results show that the 3D mesoscale concrete model effectively captures the complex fracture process and nonlinear mechanical behavior. This methodology can be used for investigating the effect of mesostructure on macroscopic behavior of concrete and also has potential applications in studying the behavior of particulate composites under various conditions.

Phase field model for brittle fracture in multiferroic materials

Multiferroic materials, which simultaneously possess piezomagnetic, piezoelectric, and electromagnetic coupling effects, have a wide range of applications in various fields. Multiferroic materials are generally brittle with low fracture toughness, and accurate prediction of the fracture behaviors of multiferroics is challenging. In this work, a phase field model for brittle fracture in multiferroic materials is developed with the help of the Hamilton principle. In light of the second law of thermodynamics, the constitutive equations are derived in the context of the phase field method. The present theoretical framework unifies two classical phase field models and four combinations of the electric and magnetic boundary conditions. The residual controlled staggered algorithm, which enjoys a higher accuracy and lower computational cost, is extended to the fracture problems in the context of magneto-electro-elasticity. Systematic numerical simulations are performed in both 2D and 3D cases. The influences of the external magnetic field, electric field, and electric and magnetic boundary conditions on fracture behaviors of multiferroic materials are studied in detail. The applied magnetic field may not only accelerate or delay the fracture, but also influence the crack path. The present work is beneficial to assess the safety of multiferroic-based devices in engineering applications.

A coupled axisymmetric peridynamics with correspondence material model for thermoplastic and ductile fracture problems

A coupled axisymmetric peridynamics with correspondence material model for thermoplastic and ductile fracture problems

Convergence study of stabilized non-ordinary state-based peridynamics for elastic and fracture problems

Non-ordinary state-based peridynamics simulates crack propagation while avoiding the imposition of additional criteria to describe the responses at discontinuities. However, an incomplete coverage by the sphere of a horizon near the boundaries and crack surfaces could cause the boundary effect. In this study, the boundary effects occurring in the stress concentration region are investigated in δ- and m-convergence tests for elastic deformation and crack propagation. Three types of boundary imposition methods are investigated in m-convergence and the method showing the fastest convergence is applied to fracture problems. The weighted average stress estimation is proposed for the damage criterion to reduce the variation in the crack paths in the convergence test, and the weight function is defined as a parameter that can change the shape of the function into three different forms: linear, bilinear, and constant. The fracture simulation is performed in an L-shaped panel with varying geometrical parameters. As a result, the bilinear weighted average stress estimation reduces the variation in the crack path compared to the conventional arithmetic average estimation method. Therefore, the proposed weighted average stress estimation method increases the accuracy of the crack path prediction and will enlarge the application area for fracture simulation using peridynamics.

A phase-field model for thermo-elastic fracture in quasicrystals

In this paper, a thermo-elastic phase-field model for brittle fracture in quasicrystals is developed. The kind of quasicrystals is not preset, so this model is suitable for almost all thermo-elastic quasicrystal solids. The phonon force and thermal load trigger the variation of the phonon elastic energy, and then drive crack initiation and propagation. The thermal conductivity in the cracked region is assumed to be degraded, which means cracks are adiabatic. For the static penny-shaped crack problem, the results based on the present model agree well with the existing analytical solution. For the quasi-static crack problems, both the tensile/shear fracture in a thermal environment and the thermal shock cracking failure can be dealt with by the present model. Several examples of 1D hexagonal and 2D decagonal quasicrystals are performed to evaluate the effects of thermal load and phason elastic field. The simulation results show that the thermal load can influence the peak force and fracture displacement. For the single-edge notched tension test, the effect of the thermal load on the peak force is small, but it on the fracture displacement is obvious. For the single-edge notched shear test, the thermal load has an obvious influence on both the peak force and fracture displacement. For the thermal shock cracking problem, the phason elastic field has a significant effect on the cracking time and crack number. The present model can serve as a powerful tool to simulate various thermo-elastic fracture problems in quasicrystals.