What is the physical origin of the gradient flow structure of variational fracture models?

We investigate a physical characterization of the gradient flow structure of variational fracture models for brittle materials: a Griffith-type fracture model and an irreversible fracture phase field model. We derive the Griffith-type fracture model by assuming that the fracture energy in Griffith's theory is an increasing function of the crack tip velocity. Such a velocity dependence of the fracture energy is typically observed in polymers. We also prove an energy dissipation identity of the Griffith-type fracture model, in other words, its gradient flow structure. On the other hand, the irreversible fracture phase field model is derived as a unidirectional gradient flow of a regularized total energy. We have considered the time relaxation parameter a mathematical approximation parameter, which we should choose as small as possible. In this research, however, we reveal the physical origin of the gradient flow structure of the fracture phase field model (F-PFM) and show that the small time relaxation parameter is characterized as the rate of velocity dependence of the fracture energy. It is verified by comparing the energy dissipation properties of those two models and by analysing a travelling wave solution of the irreversible F-PFM. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

XFVM modelling of fracture aperture induced by shear and tensile opening.

In reservoir simulation, it is important to understand the mechanical behaviour of fractured rocks and the effect of shear and tensile displacements of fractures on their aperture. Tensile opening directly enhances the fracture aperture, whereas shear of a preexisting rough-walled fracture creates aperture changes dependent on the local stress state. Since fracture dilatation increases reservoir permeability, both processes must be included in a realistic and consistent manner into the mechanical reservoir simulation model. Here, we use the extended finite volume method (XFVM) to conduct flow and geomechanics simulations. In XFVM, fractures are embedded in a poroelastic matrix and are modelled with discontinuous basis functions. On each fracture segment the tractions and compressive forces are calculated, and one extra degree of freedom is added for both the shear and tensile displacement. In this particular XFVM implementation we assume that linear elasticity and steady state fluid pressure adequately constrain the effective stress. In this paper, shear dilation is not calculated a posteriori, but it enters the equations such that aperture changes directly affect the stress state. This is accomplished by adding shear dilation to the displacement gradients and therefore ascertains a consistent representation in the stress-strain relations and force balances. We illustrate and discuss the influence of this extra term in two simple test cases and in a realistic layer-restricted two-dimensional fracture network subjected to plausible in situ stress and pore pressure conditions.

Crack-Resistant and Tissue-Like Artificial Muscles with Low Temperature Activation and High Power Density.

Constructing soft robotics with safe human-machine interactions requires low-modulus, high-power-density artificial muscles that are sensitive to gentle stimuli. In addition, the ability to resist crack propagation during long-term actuation cycles is essential for a long service life. Herein, a material design is proposed to combine all these desirable attributes in a single artificial muscle platform. The design involves the molecular engineering of a liquid crystalline network with crystallizable segments and an ethylene glycol flexible spacer. A high degree of crystallinity can be afforded by utilizing aza-Michael chemistry to produce a low covalent crosslinking density, resulting in crack-insensitivity with a high fracture energy of 33 720 J m-2 and a high fatigue threshold of 2250 J m-2. Such crack-resistant artificial muscle with tissue-matched modulus of 0.7 MPa can generate a high power density of 450 W kg-1 at a low temperature of 40 °C. Notably, because of the presence of crystalline domains in the actuated state, no crack propagation is observed after 500 heating-cooling actuation cycles under a static load of 220 kPa. This study points to a pathway for the creation of artificial muscles merging seemingly disparate, but desirable properties, broadening their application potential in smart devices.

Fracture mechanics modeling of aortic dissection.

Aortic dissection, a critical cardiovascular condition with life-threatening implications, is distinguished by the development of a tear and its propagation within the aortic wall. A thorough understanding of the initiation and progression of these tears, or cracks, is essential for accurate diagnosis and effective treatment. This paper undertakes a fracture mechanics approach to delve into the mechanics of tear propagation in aortic dissection. Our objective is to elucidate the impact of geometric and material parameters, providing valuable insights into the determinants of this pivotal cardiovascular event. Through our investigation, we have gained an understanding of how various parameters influence the energy release rate for tear propagation in both longitudinal and circumferential directions, aligning our findings with clinical data.

Mechanical properties of clot made from human and bovine whole blood differ significantly.

Thromboembolism - that is, clot formation and the subsequent fragmentation of clot - is a leading cause of death worldwide. Clots' mechanical properties are critical determinants of both the embolization process and the pathophysiological consequences thereof. Thus, understanding and quantifying the mechanical properties of clots is important to our ability to treat and prevent thromboembolic disease. However, assessing these properties from in vivo clots is experimentally challenging. Therefore, we and others have turned to studying in vitro clot mimics instead. Unfortunately, there are significant discrepancies in the reported properties of these clot mimics, which have been hypothesized to arise from differences in experimental techniques and blood sources. The goal of our current work is therefore to compare the mechanical behavior of clots made from the two most common sources, human and bovine blood, using the same experimental techniques. To this end, we tested clots under pure shear with and without initial cracks, under cyclic loading, and under stress relaxation. Based on these data, we computed and compared stiffness, strength, work-to-rupture, fracture toughness, relaxation time constants, and prestrain. While clots from both sources behaved qualitatively similarly, they differed quantitatively in almost every metric. We also correlated each mechanical metric to measures of blood composition. Thereby, we traced this inter-species variability in clot mechanics back to significant differences in hematocrit, but not platelet count. Thus, our work suggests that the results of past studies that have used bovine blood to make in vitro mimics - without adjusting blood composition - should be interpreted carefully. Future studies about the mechanical properties of blood clots should focus on human blood alone.

Temperature-dependent failure of atomically thin MoTe2.

CONTEXT: In this study, we investigated the mechanical responses of molybdenum ditelluride (MoTe2) using molecular dynamics (MD) simulations. Our key focus was on the tensile behavior of MoTe2 with trigonal prismatic phase (2H-MoTe2) which was investigated under uniaxial tensile stress for both armchair and zigzag directions. Crack formation and propagation were examined to understand the fracture behavior of such material for varying temperatures. Additionally, the study also assesses the impact of temperature on Young's modulus and fracture stress-strain of a monolayer of 2H-MoTe2. METHOD: The investigation was done using molecular dynamics (MD) simulations using Stillinger-Weber (SW) potentials. The tensile behavior was simulated for temperature for 10 K and then from 100 to 600 K with a 100-K interval. The crack propagation and formation of 10 K and 300 K 2H-MoTe2 for both directions at different strain rates was analyzed using Ovito visualizer. All the simulations were conducted using a strain rate of 10-4 ps-1. The results show that the fracture strength of 2H-MoTe2 in the armchair and zigzag direction at 10 K is 16.33 GPa (11.43 N/m) and 13.71429 GPa (9.46 N/m) under a 24% and 18% fracture strain, respectively. The fracture strength of 2H-MoTe2 in the armchair and zigzag direction at 600 K is 10.81 GPa (7.56 N/m) and 10.13 GPa (7.09 N/m) under a 12.5% and 12.47% fracture strain, respectively.

On Cyclic-Fatigue Crack Growth in Carbon-Fibre-Reinforced Epoxy-Polymer Composites.

The growth of cracks between plies, i.e., delamination, in continuous fibre polymer matrix composites under cyclic-fatigue loading in operational aircraft structures has always been a very important factor, which has the potential to significantly decrease the service life of such structures. Whilst current designs are based on a 'no growth' design philosophy, delamination growth can nevertheless arise in operational aircraft and compromise structural integrity. To this end, the present paper outlines experimental and data reduction procedures for continuous fibre polymer matrix composites, based on a linear elastic fracture mechanics approach, which are capable of (a) determining and computing the fatigue crack growth (FCG) rate, da/dN, curve; (b) providing two different methods for determining the mandated worst-case FCG rate curve; and (c) calculating the fatigue threshold limit, below which no significant FCG occurs. Two data reduction procedures are proposed, which are based upon the Hartman-Schijve approach and a novel simple-scaling approach. These two different methodologies provide similar worst-case curves, and both provide an upper bound for all the experimental data. The calculated FCG threshold values as determined from both methodologies are also in very good agreement.

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.

A Literature Review of Incorporating Crack Tip Plasticity into Fatigue Crack Growth Models.

This paper presents an extensive literature review focusing on the utilisation of crack tip plasticity as a crucial parameter in determining and enhancing crack growth models. The review encompasses a comprehensive analysis of various methodologies, predominantly emphasising numerical simulations of crack growth models while also considering analytical approaches. Although experimental investigations are not the focus of this review, their relevance and interplay with numerical and analytical methods are acknowledged. The paper critically examines these methodologies, providing insights into their advantages and limitations. Ultimately, this review aims to offer a holistic understanding of the role of crack tip plasticity in the development of effective crack growth models, highlighting the synergies and gaps between theoretical, experimental, and simulation-based approaches.

Estimation of the Deformation Gradient Tensor by Particle Tracking Near a Free Boundary with Quantified Error.

Background: Obtaining accurate displacement measurements for large material deformation and/or rotation presents a distinct challenge to digital image correlation (DIC) due to cumulative and decorrelation errors, particularly near material boundaries. Objective: We aim to accurately measure the deformation gradient tensor near boundary discontinuities in situations of large deformation and large deformation gradients. Methods: To achieve this goal, the locations of randomly distributed particles are tracked using an open-source particle-tracking software, Trackpy. A least-squares estimate of the deformation gradient tensor field uses nearest-neighbor material vectors and a first-order Finite Difference (FD) approximation, circumventing common errors in other methods. The error caused by FD approximation and that incurred by measurement are derived and tested with exhaustive numerical simulations. Furthermore, a uniaxial tensile test and mode-I fracture experiment are conducted with particle-embedded hydrogels to validate the method. Results: Numerical results corroborate a theoretical expression of measurement error. They show that the FD error increases while the measurement error decreases for a growing estimating radius. Moreover, measurement error is linearly correlated to displacement noise. A benchmark uniaxial tensile test validates the accuracy of the proposed estimator, and the near-crack-tip measurements in a tensile fracture experiment demonstrate the estimator's capabilities near a free surface, when a material undergoes large deformation and rotation. The results of the displacement and strain data are benchmarked against kinematic data obtained using an open-source DIC software, Ncorr. Computation time for both methods is compared. Conclusions: A deformation gradient tensor estimator is developed based on a particle tracking technique and a least squares routine. Theoretical error bounds on the estimator are verified by numerical simulations, and the method's capability is confirmed by physical experiments in evaluating large deformation and rotation near a free boundary. The proposed estimator is expected to open a door towards future material tests and experimental mechanics studies, especially in large deformation and large rotation scenarios.

Recycled Fine and Coarse Aggregates' Contributions to the Fracture Energy and Mechanical Properties of Concrete.

This paper investigates the fracture mechanical properties of concrete, using crushed concrete aggregates (CCA) and granulated blast furnace slag (GGBS) for partial cement replacement. CCAs made from prefabricated concrete replace 100% of the fine and coarse fractions in concrete recipes with w/c ratios of 0.42 and 0.48. Two pre-treatment methods, mechanical pre-processing (MPCCA) and accelerated carbonation (CO2CCA), are investigated for quality improvements in CCA. The resulting aggregates show an increased density, contributing to an increase in the concrete's compressive strength. The novelty of this paper is the superposition of the effects of the composite parts of concrete, the aggregate and the cement mortar, and their contributions to concrete fracture. Investigations are directed toward the influence of fine aggregates on mortar samples and the influence of the combination of coarse and fine aggregates on concrete samples. The physical and mechanical properties of the aggregates are correlated with mortar and concrete fracture properties. The results show that CCA concrete achieves 70% of the fracture energy values of concrete containing natural aggregates, and this value increases to 80% for GGBS mixes. At lower w/c ratios, MPCCA and CO2CCA concretes show similar fracture energies. CO2CCA fine aggregates are the most effective at strengthening the mortar phase, showing ductile concrete behavior at a w/c ratio of 0.48. MPCCA aggregates contribute to higher compressive strengths for w/c ratios of 0.42 and 0.48. Thus, mechanical pre-processing can be improved to produce CCA, which contributes to more ductile concrete behavior.

Intrinsic Fatigue Limit and the Minimum Fatigue Crack Growth Threshold.

In the field of long-life fatigue, predicting fatigue lives and limits for mechanical components is crucial for ensuring reliability and safety. Fracture mechanics tools have enabled the estimation of fatigue lives for components with small cracks or defects. However, when dealing with defects larger than the microstructural characteristic size, estimating the fatigue resistance of a material requires determining the cyclic resistance curve for the defect-free matrix, which depends on knowledge of the material's intrinsic fatigue limit. This study focuses on the experimental evidence regarding the intrinsic fatigue limit and its correlation with naturally nucleated non-propagating cracks. Fracture mechanics models for small crack propagation are introduced, and their disparities and limitations are analyzed. The concept of intrinsic fatigue limit is then introduced and applied to reanalyze a recent publication. Methods for estimating the intrinsic fatigue limit are explored and applied to experimental results reported in the literature. The need to clarify and accurately predict the intrinsic fatigue limit is highlighted in alloys where the processing generates defects larger than the microstructural size of the matrix, as often observed in materials and components produced using additive manufacturing.

Defect driven physics-informed neural network framework for fatigue life prediction of additively manufactured materials.

Additive manufacturing (AM) has attracted many attentions because of its design freedom and rapid manufacturing; however, it is still limited in actual application due to the existing defects. In particular, various defect features have been proved to affect the fatigue performance of components and lead to fatigue scatter. In order to properly assess the influences of these defect features, a defect driven physics-informed neural network (PiNN) is developed. By embedding the critical defects information into loss functions, the defect driven PiNN is enhanced to capture physical information during training progress. The results of fatigue life prediction for different AM materials show that the proposed PiNN effectively improves the generalization ability under small samples condition. Compared with the fracture mechanics-based PiNN, the proposed PiNN provides physically consistent and higher accuracy without depending on the choice of fracture mechanics-based model. Moreover, this work provides a scalable framework being able to integrate more prior knowledge into the proposed PiNN. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Fatigue strength and life prediction of lower limb venous stents under three-stage loading conditions.

After the implantation of lower limb artery stents, the complex loading conditions imposed on the limb can lead to fatigue failure, which may induce inflammation and restenosis. To investigate the effect of multi-axial loading conditions on the fatigue performance of stents, five stents, namely APsolute Pro (APbott Vascular, USA), Complete SE (Medtronic, USA), Protégé EverFlex (PE3, USA), Pulsar-35 (Biotronik, Germany), and E-luminexx-B (Bard, USA), were analyzed based on the finite element method (FEM). Besides, their fatigue strength was determined under three levels of loading conditions, including tension-bending-torsion and compression-bending-torsion. Based on that, the fatigue life of these stents was predicted. The results showed that based on the nominal stress method, tension-bending-torsion loading had a more significant impact on the fatigue life of stents than compression-bending-torsion loading. Besides, two different types of initial cracks were analyzed by the fracture mechanics method. The results suggested that both the initial crack and the external load were the main causes of stent fatigue fractures. Compared with the loading nature, the influence of the initial crack on stent fatigue life was more significant. Under the same loading condition, the APsolute Pro stent had the longest fatigue life, while the E-luminexx-B stent had the shortest. Moreover, the mechanism of stent fatigue failure was revealed by exploring the fatigue performance and life prediction of stents under complex loading conditions. These findings have important implications for improving the structural design of stents and their clinical selection.

Predicting the Effect of Surface Waviness on Fatigue Life of a Wire + Arc Additive Manufactured Ti-6Al-4V Alloy.

This paper reports the effect of as-deposited surface conditions on the fatigue strength of an additively manufactured titanium alloy, Ti-6Al-4V (WAAM Ti64). First, the local stress concentration caused by the surface waviness was quantified using a metrology technique and computer modelling. Fatigue tests were conducted under bending loads at a cyclic load ratio of 0.1. The applicability of two predictive methods was the focus of this study. The traditional notch stress method was unable to predict the correct S-N curve trend slope, which could be attributed to the early crack initiation from the troughs on the as-built surface, with crack propagation being the dominant failure mechanism. By treating the troughs as small cracks, the fracture mechanics approach delivered good predictions at every applied stress level. Surface machining and polishing may not always be practical or required; it depends on the applications and service load levels. This research demonstrated that the fracture mechanics approach can be used for predicting the fatigue life of WAAM titanium alloys in as-built conditions and, hence, can be a tool for decision making on the level of surface machining.

Effect of Surface Finishing State on Fatigue Strength of Cast Aluminium and Steel Alloys.

The endurance limit of structural mechanical components is affected by the residual stress state, which depends strongly on the manufacturing process. In general, compressive residual stresses tend to result in an increased fatigue strength. Post-manufacturing processes such as shot peening or vibratory finishing may achieve such a compressive residual stress state. But within complex components, manufacturing-process-based imperfections severely limit the fatigue strength. Thus, the interactions of imperfections, residual stress state and material strength are key aspects in fatigue design. In this work, cast steel and aluminium alloys are investigated, each of them in vibratory finished and polished surface condition. A layer-based fatigue assessment concept is extended towards stable effective mean stress state considering the elastic-plastic material behaviour. Murakami's concept was applied to incorporate the effect of hardness change and residual stress state. Residual stress relaxation is determined by elastic-plastic simulations invoking a combined hardening model. If the effective stress ratio within the local layer-based fatigue strength is evaluated as critical distance value, a sound calculation of fatigue strength can be achieved. Summing up, the layer-based fatigue strength design is extended and features an enhanced understanding of the effective stabilized mean stress state during cyclic loading.

Differential Energy Criterion for Brittle Fracture: Conceptualization and Application to the Analysis of Axial and Lateral Deformation in Uniaxial Compression of Rocks.

This paper discusses modeling the behavior and prediction of fracture of brittle materials. Numerous publications show that progress in this area is characterized by the emergence of a number of new models that meet the requirements of the mining industry, construction and other engineering practices. The authors focus only on one class of models, paying special attention to the compromise between simplicity of solution and versatility of the model. A new version of the model is proposed, taking into account the advantages of previous models. We present a differential energy criterion for brittle fracture substantiated, according to which, fracture occurs at a certain ratio of dissipated and stored (elastic) energy. Fracture is considered as the end of the deformation process with a virtual transformation of the initial material almost without cracks into a real material with cracks. The highest and lowest elastic moduli are analytically determined, respectively, on the ascending and descending branches of the stress-strain curve. A graphical version of the algorithm for determining the brittle fracture point on the post-peak branch of the stress-strain curve is proposed. The modeling results are consistent with the experimental data known from the literature.

Study on Elastic Mixed Mode Fracture Behavior and II-III Coupling Effect.

Mixed mode fracture is a widely studied topic, while the coupling effects of mixed mode cracking are unclear. In this paper, elastic fracture behaviors and the coupling effects of the mixed mode cracks are studied in detail based on the finite element method, experimental study and linear elastic fracture mechanics. Results show that there always exist II-III coupling effects at the crack tips of mixed mode cracks, which have many effects on the crack tip field and crack propagation behavior. It is found that a mode II component at the tip of a mixed mode crack is the main reason for crack deflection, while the mode III components show no effect. For any mixed mode crack, mode II components at the crack tip can be divided as that by mode II loading which causes plane crack propagation, and by the coupling effect which causes spatial crack propagation. On this basis, a new fracture criterion suitable for any mixed mode crack is proposed, combined with the coupling effect and the linear elastic superposition principle. The research in this paper provides a solution to the problem of an II-III coupling effect in mixed mode fracture research and further promotes the development of fracture mechanics.

The biomechanics of tooth strength: testing the utility of simple models for predicting fracture in geometrically complex teeth.

Teeth must fracture foods while avoiding being fractured themselves. This study evaluated dome biomechanical models used to describe tooth strength. Finite-element analysis (FEA) tested whether the predictions of the dome models applied to the complex geometry of an actual tooth. A finite-element model was built from microCT scans of a human M3. The FEA included three loading regimes simulating contact between (i) a hard object and a single cusp tip, (ii) a hard object and all major cusp tips and (iii) a soft object and the entire occlusal basin. Our results corroborate the dome models with respect to the distribution and orientation of tensile stresses, but document heterogeneity of stress orientation across the lateral enamel. This implies that high stresses might not cause fractures to fully propagate between cusp tip and cervix under certain loading conditions. The crown is most at risk of failing during hard object biting on a single cusp. Geometrically simple biomechanical models are valuable tools for understanding tooth function but do not fully capture aspects of biomechanical performance in actual teeth whose complex geometries may reflect adaptations for strength.

Stochastic Propagation of Fatigue Cracks in Welded Joints of Steel Bridge Decks under Simulated Traffic Loading.

The fatigue cracking of orthotropic steel bridge decks (OSDs) is a difficult problem that hinders the development of steel structures. The most important reasons for the occurrence of fatigue cracking are steadily growing traffic loads and unavoidable truck overloading. Stochastic traffic loading leads to the random propagation behavior of fatigue cracks, which increases the difficulty of the fatigue life evaluations of OSDs. This study developed a computational framework for the fatigue crack propagation of OSDs under stochastic traffic loads based on traffic data and finite element methods. Stochastic traffic load models were established based on site-specific, weigh-in-motion measurements to simulate fatigue stress spectra of welded joints. The influence of the transverse loading positions of the wheel tracks on the stress intensity factor of the crack tip was investigated. The random propagation paths of the crack under stochastic traffic loads were evaluated. Both ascending and descending load spectra were considered in the traffic loading pattern. The numerical results indicated that the maximum value of KI was 568.18 (MPa·mm1/2) under the most critical transversal condition of the wheel load. However, the maximum value decreased by 66.4% under the condition of transversal moving by 450 mm. In addition, the propagation angle of the crack tip increased from 0.24° to 0.34°-an increase ratio of 42%. Under the three stochastic load spectra and the simulated wheel loading distributions, the crack propagation range was almost limited to within 10 mm. The migration effect was the most obvious under the descending load spectrum. The research results of this study can provide theoretical and technical support for the fatigue and fatigue reliability evaluation of existing steel bridge decks.