Advanced Modeling Methods-Applications to Bone Fracture Mechanics.

PURPOSE OF REVIEW: The goal of this review is to summarize recent advances in modeling of bone fracture using fracture mechanics-based approaches at multiple length scales spanning nano- to macroscale. RECENT FINDINGS: Despite the additional information that fracture mechanics-based models provide over strength-based ones, the application of this approach to assessing bone fracture is still somewhat limited. Macroscale fracture models of bone have demonstrated the potential of this approach in uncovering the contributions of geometry, material property variation, as well as loading mode and rate on whole bone fracture response. Cortical and cancellous microscale models of bone have advanced the understanding of individual contributions of microstructure, microarchitecture, local material properties, and material distribution on microscale fracture resistance of bone. Nano/submicroscale models have provided additional insight into the effect of specific changes in mineral, collagen, and non-collagenous proteins as well as their interaction on energy dissipation and fracture resistance at small length scales. Advanced modeling approaches based on fracture mechanics provide unique information about the underlying multiscale fracture mechanisms in bone and how these mechanisms are influenced by the structural and material constituents of bone at different length scales. Fracture mechanics-based modeling provides a powerful approach that complements experimental evaluations and advances the understanding of critical determinants of fracture risk.

An Equivalent Constitutive Model of Cancellous Bone With Fracture Prediction.

To simulate the mechanical and fracture behaviors of cancellous bone in three anatomical directions and to develop an equivalent constitutive model. Microscale extended finite element method (XFEM) models of a cancellous specimen were developed with mechanical behaviors in three anatomical directions. An appropriate abaqus macroscale model replicated the behavior observed in the microscale models. The parameters were defined based on the intermediate bone material properties in the anatomical directions and assigned to an equivalent nonporous specimen of the same size. The equivalent model capability was analyzed by comparing the micro- and macromodels. The hysteresis graphs of the microscale model show that the modulus is the same in loading and unloading; similar to the metal plasticity models. The strength and failure strains in each anatomical direction are higher in compression than in tension. The microscale models exhibited an orthotropic behavior. Appropriate parameters of the cast iron plasticity model were chosen to generate macroscale models that are capable of replicating the observed microscale behavior of cancellous bone. Cancellous bone is an orthotropic material that can be simulated using a cast iron plasticity model. This model is capable of replicating the microscale behavior in finite element (FE) analysis simulations without the need for individual trabecula, leading to a reduction in computational resources without sacrificing model accuracy. Also, XFEM of cancellous bone compared to traditional finite element method proves to be a valuable tool to predict and model the fractures in the bone specimen.

Probabilistic Model Updating for Sizing of Hole-Edge Crack Using Fiber Bragg Grating Sensors and the High-Order Extended Finite Element Method.

This paper presents a novel framework for probabilistic crack size quantification using fiber Bragg grating (FBG) sensors. The key idea is to use a high-order extended finite element method (XFEM) together with a transfer (T)-matrix method to analyze the reflection intensity spectra of FBG sensors, for various crack sizes. Compared with the standard FEM, the XFEM offers two superior capabilities: (i) a more accurate representation of fields in the vicinity of the crack tip singularity and (ii) alleviation of the need for costly re-meshing as the crack size changes. Apart from the classical four-term asymptotic enrichment functions in XFEM, we also propose to incorporate higher-order functions, aiming to further improve the accuracy of strain fields upon which the reflection intensity spectra are based. The wavelength of the reflection intensity spectra is extracted as a damage sensitive quantity, and a baseline model with five parameters is established to quantify its correlation with the crack size. In order to test the feasibility of the predictive model, we design FBG sensor-based experiments to detect fatigue crack growth in structures. Furthermore, a Bayesian method is proposed to update the parameters of the baseline model using only a few available experimental data points (wavelength versus crack size) measured by one of the FBG sensors and an optical microscope, respectively. Given the remaining data points of wavelengths, even measured by FBG sensors at different positions, the updated model is shown to give crack size predictions that match well with the experimental observations.

Numerical Study of Crack Prediction and Growth in Automotive Wheel Rims.

Finite element analysis has become an essential tool for simulating and understanding crack growth. This technique holds significant importance in the field of mechanical engineering, where it finds wide application in the design and optimization of structural components and material properties. This work began with the identification of critical zones and estimated the number of load life repeats through fatigue analysis, specifically applied to automotive rims utilizing innovative finite element methods. To investigate crack behavior, we are used the Extended Finite Element Method (XFEM) with the volumetric approach to compute the Stress Intensity Factor (SIF). The results obtained by our study align closely with experimental tests in terms of detecting the critical zone where a crack can appear. Our findings contribute to the understanding of fatigue behavior in automotive rims, offering new insights into their structural integrity and performance under various load conditions.

A Revised Abaqus® Procedure for Fracture Path Simulation Based on the Material Effort Criterion.

This paper presents the results of computer simulations of fracture in three laboratory tests: the three-point bending of a notched beam cut from sandstone, the pull-out test of a self-undercutting anchor fixed in sandstone, and the pull-out test of a bar embedded in concrete. Five material failure criteria were used: Rankine, Coulomb-Mohr, Drucker-Prager, Ottosen-Podgórski, and Hoek-Brown. These criteria were implemented in the Abaqus® FEA system to work with the crack propagation modeling method-extended finite element method (X-FEM). All criteria yielded similar force-displacement relationships and similar crack path shapes. The improved procedure gives significantly better, close-to-real crack propagation paths than can be obtained using the standard subroutines built into the Abaqus® system.

XFEM for Composites, Biological, and Bioinspired Materials: A Review.

The eXtended finite element method (XFEM) is a powerful tool for structural mechanics, assisting engineers and designers in understanding how a material architecture responds to stresses and consequently assisting the creation of mechanically improved structures. The XFEM method has unraveled the extraordinary relationships between material topology and fracture behavior in biological and engineered materials, enhancing peculiar fracture toughening mechanisms, such as crack deflection and arrest. Despite its extensive use, a detailed revision of case studies involving XFEM with a focus on the applications rather than the method of numerical modeling is in great need. In this review, XFEM is introduced and briefly compared to other computational fracture models such as the contour integral method, virtual crack closing technique, cohesive zone model, and phase-field model, highlighting the pros and cons of the methods (e.g., numerical convergence, commercial software implementation, pre-set of crack parameters, and calculation speed). The use of XFEM in material design is demonstrated and discussed, focusing on presenting the current research on composites and biological and bioinspired materials, but also briefly introducing its application to other fields. This review concludes with a discussion of the XFEM drawbacks and provides an overview of the future perspectives of this method in applied material science research, such as the merging of XFEM and artificial intelligence techniques.

Research on ultrasonic bone cutting mechanism based on extended finite element method.

The research on the crack propagation mechanism of bone has important research significance and clinical medical value for the selection of cutting parameters and the development of new surgical tools. In this paper, an extended finite element method (X-FEM) model of ultrasonic bone cutting considering microstructure was developed to further study the ultrasonic bone cutting mechanism and to quantitatively analyze the effects of cutting direction, ultrasonic parameters, and cutting parameters on the mechanism of ultrasonic bone cutting crack propagation. The results show that ultrasonic bone cutting is essentially a controlled crack propagation process, in which brittle crack and fatigue crack are the main crack propagation mechanisms. In order to improve the efficiency of ultrasonic bone cutting, large amplitude and high-frequency ultrasonic vibration are preferred. Compared with the other two cutting directions, the crack propagation deflection angle in the transverse cutting direction is the largest, resulting in the worst cutting surface. Therefore, in the path planning of orthopedic surgical robots, the transverse cutting direction should be avoided as much as possible. Frequency only has a significant effect on the crack propagation rate and has a positive correlation. There is a positive correlation between the deflection angle, propagation length, propagation rate, and amplitude, which provides the possibility to control the direction and length of crack propagation by controlling the amplitude of ultrasonic. The feed speed is much lower than the ultrasonic vibration speed, which makes the influence of ultrasonic vibration speed on the crack propagation characteristics dominant. The X-FEM model of ultrasonic bone cutting provides an effective method for selecting reasonable machining parameters of orthopedic robot and optimize the design of ultrasonic osteotome.

Enhancement Effect of Aggregates on the Low-Temperature Cracking Resistance of Asphalt Mixtures.

Aggregates' configurations result in different stress fields, which change the fracture mode and mechanical properties of an asphalt mixture. To reveal the enhancing effect of aggregates with different particle sizes on the low-temperature cracking resistance of an asphalt mixture, an indirect tensile (IDT) test was carried out to analyze the aggregates' influence on crack propagation and low-temperature cracking resistance from a macroscopic perspective. And combined with the test results, mesostructure models of an asphalt mixture with different aggregates' spatial distributions were established through the extended finite element method (XFEM) to analyze changes in the crack propagation path and crack tip configuration force from a mesoscopic perspective. The main results showed that the crack tip configurational force was reduced due to the aggregate size increasing, demonstrating the inhibitory effect of aggregates on crack propagation. This contributes to enhancing asphalt mixtures' low-temperature cracking resistance. Compared to single-grain aggregates, multi-grain aggregates exhibit a greater inhibitory effect on crack propagation. Nonetheless, an excessive disparity in particle sizes compromises particle continuity, leading to the formation of more branching cracks. Meanwhile, the aggregates' inhibitory effect on crack propagation is influenced by the crack deflection angle. In particular, when the crack deflection angle, ß, equals 45°, the crack tip's configurational force is notably larger, leading the crack to enter an unstable state conducive to the expansion and formation of macrocracks. The research results reveal aggregates' inhibitory effect on crack propagation from a macro- and microperspective and reveal the relationship between aggregate configurations and the low-temperature cracking resistance of asphalt mixtures.

Numerical Fatigue Crack Growth on Compact Tension Specimens under Mode I and Mixed-Mode (I+II) Loading.

This study focused on standard Compact Tension (CT) specimens and two loading modes during the numerical analyses carried out, namely: pure mode I and mixed-mode loading (Modes I+II). Numerical stress intensity factors, KI, were calculated using Abaqus® 2022 and compared with those given analytically under pure mode I loading, showing very good agreement. Additionally, KI, KII, and KIII results obtained from Abaqus® were presented for mixed-mode loading, analyzing crack growth and variation through the thickness of the CT specimen. Moreover, fatigue crack growth simulations under mode I loading were conducted on standard CT specimens using the Extended Finite Element Method (XFEM) and the Paris Law parameters of an AISI 316L stainless steel. It was shown that XFEM effectively determines crack propagation direction and growth, provided that an appropriate mesh is implemented.

Effect of Initial Crack Position on Crack Propagation Behaviors of Heavy-Duty Transmission Gear.

The tooth bending fatigue fracture is caused by the alternating loads for the heavy-duty transmission gears. The crack initiation and propagation are the two major parts in the failure process. The crack propagation behavior is mainly affected by initial crack position except for the load and material properties. In this paper, the crack propagation model of a gear is established under the considering of crack initiation location by using extended finite element method (XFEM). The model accuracy is verified by testing results of strain and fractography by conducting the single-tooth bending fatigue experiment. The influence of crack initiation locations on subsequent crack propagation behavior is analyzed. The crack length in the tooth width direction and depth direction is faster when the initial crack is located in the middle of root surface. The crack growth rate is lower for the initial crack located in the surface close to the end surface of the gear.

Extended Finite Element Method (XFEM) Model for the Damage Mechanisms Present in Joints Bonded Using Adhesives Doped with Inorganic Fillers.

The use of adhesive bonding in diverse industries such as the automotive and aerospace sectors has grown considerably. In structural construction, adhesive joints provide a unique combination of low structural weight, high strength and stiffness, combined with a relatively simple and easily automated manufacturing method, characteristics that are ideal for the development of modern and highly efficient vehicles. In these applications, ensuring that the failure mode of a bonded joint is cohesive rather than adhesive is important since this failure mode is more controlled and easier to model and to predict. This work presents a numerical technique that enables the precise prediction of the bonded joint's behavior regarding not only its failure mode, but also the joint's strength, when inorganic fillers are added to the adhesive. To that end, hollow glass particles were introduced into an epoxy adhesive in different amounts, and a numerical study was carried out to simulate their influence on single lap joint specimens. The numerical results were compared against experimental ones, not only in terms of joint strength, but also their failure pattern. The neat adhesive, which showed 9% and 20% variations in terms of failure load and displacement, respectively. However, looking at the doped configurations, these presented smaller variations of about 2% and 10% for each respective variable. In all cases, by adding glass beads, crack initiation tended to change from adhesive to cohesive but with lower strength and ductility, correctly modeling the general experimental behavior as intended.

Numerical Simulation of Fatigue Cracking of Diaphragm Notch in Orthotropic Steel Deck Model.

Orthotropic steel deck (OSD) are widely used in steel bridges because of their many advantages, but the structures and stresses of OSD are complex and sensitive to fatigue. Based on the model test, the structural fatigue analysis of OSD is carried out by using the extended finite element method (XFEM) to understand and reveal the causes of fatigue detail cracks and the generation and propagation of fatigue cracks at the welding ends of diaphragms, U-ribs, and diaphragms, which are the main structural fatigue details of the deck. The results show that: the fatigue crack at the diaphragm opening is not caused by a single factor, but the horizontal relative displacement is the root-cause of the fatigue crack; the contribution of out-of-plane displacement to the fatigue crack is more significant than that of vertical displacement or in-plane stress, which often leads to the initiation and propagation of the fatigue crack; the crack-propagation direction is perpendicular to the contour of principal stress, and the crack propagates into the plate along the high-stress area in the horizontal direction, which is in accordance with the basic theory of crack propagation. The research methods can provide technical support for the design of similar structures.

Fracture Toughness and Fatigue Crack Growth Analyses on a Biomedical Ti-27Nb Alloy under Constant Amplitude Loading Using Extended Finite Element Modelling.

The human body normally uses alternative materials such as implants to replace injured or damaged bone. Fatigue fracture is a common and serious type of damage in implant materials. Therefore, a deep understanding and estimation or prediction of such loading modes, which are influenced by many factors, is of great importance and attractiveness. In this study, the fracture toughness of Ti-27Nb, a well-known implant titanium alloy biomaterial, was simulated using an advanced finite element subroutine. Furthermore, a robust direct cyclic finite element fatigue model based on a fatigue failure criterion derived from Paris' law is used in conjunction with an advanced finite element model to estimate the initiation of fatigue crack growth in such materials under ambient conditions. The R-curve was fully predicted, yielding a minimum percent error of less than 2% for fracture toughness and less than 5% for fracture separation energy. This provides a valuable technique and data for fracture and fatigue performance of such bio-implant materials. Fatigue crack growth was predicted with a minimum percent difference of less than nine for compact tensile test standard specimens. The shape and mode of material behaviour have a significant effect on the Paris law constant. The fracture modes showed that the crack path is in two directions. The finite element direct cycle fatigue method was recommended to determine the fatigue crack growth of biomaterials.

Effect of plasticity of the cladding with different thicknesses on the bearing capacity of the brittle base wall of RPV under PTS loads.

In the research field of reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), the traditional linear elastic analytical method generally ignores the plastic properties of cladding. In fact, the neutron irradiation in RPV is easy to cause the embrittlement of the base material rather than cladding. So the elastic-plastic parameters of cladding are introduced into the FE model of the RPV with a sub-clad crack. The stress distributions in the thermal-mechanical coupling fields related to the base wall and cladding of different thicknesses are then obtained. The XFEM is used to simulate the crack growth in the nozzle area. The allowable internal pressure in the dangerous moment of the PTS is calculated to show the ultimate bearing capacity of the structure. The numerical results are compared with those only considering the elasticity of cladding. Furthermore, the law of the effect of plasticity of cladding on the structural safety is summarized.

Isolating the Role of Bone Lacunar Morphology on Static and Fatigue Fracture Progression through Numerical Simulations.

Currently, the onset of bone damage and the interaction of cracks with the surrounding micro-architecture are still black boxes. With the motivation to address this issue, our research targets isolating lacunar morphological and densitometric effects on crack advancement under both static and cyclic loading conditions by implementing static extended finite element models (XFEM) and fatigue analyses. The effect of lacunar pathological alterations on damage initiation and progression is evaluated; the results indicate that high lacunar density considerably reduces the mechanical strength of the specimens, resulting as the most influencing parameter among the studied ones. Lacunar size has a lower effect on mechanical strength, reducing it by 2%. Additionally, specific lacunar alignments play a key role in deviating the crack path, eventually slowing its progression. This could shed some light on evaluating the effects of lacunar alterations on fracture evolution in the presence of pathologies.

Fatigue Life Prediction of Notched Details Using SWT Model and LEFM-Based Approach.

The fatigue crack initiation life of unwelded steel components accounts for the majority of the total fatigue life, and the accurate prediction of it is of vital importance. In this study, a numerical model utilizing the extended finite element method (XFEM) and Smith-Watson-Topper (SWT) model is established to predict the fatigue crack initiation life of notched details extensively used in orthotropic steel deck bridges. Using the user subroutine UDMGINI in Abaqus, a new algorithm was proposed to calculate the damage parameter of SWT under high-cycle fatigue loads. The virtual crack-closure technique (VCCT) was introduced to monitor crack propagation. Nineteen tests were performed, and the results were used to validate the proposed algorithm and XFEM model. The simulation results show that the proposed XFEM model with UDMGINI and VCCT can reasonably predict the fatigue lives of the notched specimens within the regime of high-cycle fatigue with a load ratio of 0.1. The error for the prediction of fatigue initiation life ranges from -27.5% to 41.1%, and the prediction of total fatigue life has a good agreement with the experimental results with a scatter factor of around 2.

An X-FEM technique for numerical simulation of variable-density flow in fractured porous media.

Solute transport is one of the major topics in geological studies. Fracture is a significant characteristic of natural porous media, where the solute can transport due to its higher density with respect to the density of fluid. As the solute migrates in the medium, the density of the fluid changes with time. In this paper, the mass transport problem in the fractured porous media is modeled using the extended finite element method (X-FEM). An advection-diffusion equation is adopted to define the transport phenomenon in conjunction with the continuity equation of fluid. Transport regimes including diffusion, dispersion and advection are taken into the computational model. The presence of fractures within a porous medium substantially affects the transport behavior. In order to resolve the issue of discontinuity in the field variables, the X-FEM is implemented to discretize the discontinuity of medium. The Newmark integration scheme is adopted to discretize the governing equations in time domain. The nonlinear equations are solved by the Newton-Raphson iterative technique in a fully coupled manner. Finally, in order to illustrate the performance of the proposed computational model, two conventional problems, including the Schincariol problem and the Elder problem as well as the fractured Elder problem are solved numerically. Different patterns of fractures including horizontal and vertical intersecting cracks are adopted to study the effect of fracture density as well as the capability and versatility of the proposed computational model. The method is described in details and the pitfalls of the whole approach are demonstrated. •The density-driven fluid flow in naturally fractured porous media is modeled using an enhanced-FEM technique.•The effect of fractures (faults) in the porous medium is investigated by modeling the transport of saltwater in the fractured Elder problem.•The proposed computational model provides an accurate prediction of subsurface hydrology for a field-scale closed desert basin.

Analysis of Crack Propagation Behaviors in RPV Dissimilar Metal Welded Joints Affected by Residual Stress.

In severe service environments, the presence of high local residual stress, significant organizational gradient, and nonlinear changes in material properties often leads to stress corrosion cracking (SCC) in dissimilar metal welded (DMW) joints. To accurately predict the crack growth rate, researching the initiation and propagation behavior of SCC cracks in DMW joints under residual stress (RS) is one of the most important methods to ensure the safe operation of nuclear power plants. Using the extended finite element method (XFEM), the crack propagation behaviors in DMW joints under different RS states are predicted and compared. The effects of RS, crack location, and initial crack length on crack propagation behavior are investigated. The crack in a DMW joint without RS deflects to the material of low yield strength. High residual stress urges the crack growing direction to deflect toward the material of high yield strength. Young's modulus has little impact on the crack deflection paths. The distance between the specimen symmetric line and the boundary line has little effect on the crack initiation and propagation within the RS field. A long initial crack is more likely to initiate and propagate than a short crack. To a long crack and the crack that is far from the interface of two materials, the impact of residual stress on the crack propagation path is significant when it is located in a material with high yield strength, while when the initial crack is located in the material with low yield strength, RS has a great influence on the deflection of a short crack growth direction on the condition that the crack is adjacent to the interface.

An integrated experimental-computational framework to assess the influence of microstructure and material properties on fracture toughness in clinical specimens of human femoral cortical bone.

Microstructural and compositional changes that occur due to aging, pathological conditions, or pharmacological treatments alter cortical bone fracture resistance. However, the relative importance of these changes to the fracture resistance of cortical bone has not been quantified in detail. In this technical note, we developed an integrated experimental-computational framework utilizing human femoral cortical bone biopsies to advance the understanding of how fracture resistance of cortical bone is modulated due to modifications in its microstructure and material properties. Four human biopsy samples from individuals with varying fragility fracture history and osteoporosis treatment status were converted to finite element models incorporating specimen-specific material properties and were analyzed using fracture mechanics-based modeling. The results showed that cement line density and osteonal volume had a significant effect on crack volume. The removal of cement lines substantially increased the crack volume in the osteons and interstitial bone, representing straight crack growth, compared to models with cement lines due to the lack of crack deflection in the models without cement lines. Crack volume in the osteons and interstitial bone increased when mean elastic modulus and ultimate strength increased and mean fracture toughness decreased. Crack volume in the osteons and interstitial bone was reduced when material property heterogeneity was incorporated in the models. Although both the microstructure and the heterogeneity of the material properties of the cortical bone independently increased the fracture toughness, the relative contribution of the microstructure was more significant. The integrated experimental-computational framework developed here can identify the most critical microscale features of cortical bone modulated by pathological processes or pharmacological treatments that drive changes in fracture resistance and improve our understanding of the relative influence of microstructure and material properties on fracture resistance of cortical bone.

On the fracture behavior of cortical bone microstructure: The effects of morphology and material characteristics of bone structural components.

Bone encompasses a complex arrangement of materials at different length scales, which endows it with a range of mechanical, chemical, and biological capabilities. Changes in the microstructure and characteristics of the material, as well as the accumulation of microcracks, affect the bone fracture properties. In this study, two-dimensional finite element models of the microstructure of cortical bone were considered. The eXtended Finite Element Method (XFEM) developed by Abaqus software was used for the analysis of the microcrack propagation in the model as well as for local sensitivity analysis. The stress-strain behavior obtained for the different introduced models was substantially different, confirming the importance of bone tissue microstructure for its failure behavior. Considering the role of interfaces, the results highlighted the effect of cement lines on the crack deflection path and global fracture behavior of the bone microstructure. Furthermore, bone micromorphology and areal fraction of cortical bone tissue components such as osteons, cement lines, and pores affected the bone fracture behavior; specifically, pores altered the crack propagation path since increasing porosity reduced the maximum stress needed to start crack propagation. Therefore, cement line structure, mineralization, and areal fraction are important parameters in bone fracture. The parameter-wise sensitivity analysis demonstrated that areal fraction and strain energy release rate had the greatest and the lowest effect on ultimate strength, respectively. Furthermore, the component-wise sensitivity analysis revealed that for the areal fraction parameter, pores had the greatest effect on ultimate strength, whereas for the other parameters such as elastic modulus and strain energy release rate, cement lines had the most important effect on the ultimate strength. In conclusion, the finding of the current study can help to predict the fracture mechanisms in bone by taking the morphological and material properties of its microstructure into account.