Resulting Fracture Patterns Research Articles

Numerical Modelling of the Influence of Tidal Stresses on Fracture Patterns on the Surface of Europa

AbstractJupiter’s satellite Europa is covered by an ice shell exhibiting many surface features, including linear structures called lineae, which in this work are treated as fractures. A three-dimensional finite-element simulator is used to numerically model fracture nucleation, growth, and interaction, assuming the ice is an isotropic, linear elastic medium. Tidal stresses are exerted upon the ice through the Jovian orbital relationship. These stresses are calculated using a closed-form model derived from first principles. The fractures grow in response to stress concentration around their tips, and a damage criterion models the weakening of the ice matrix. Three-dimensional non-planar multiple fracture growth is modelled as a function of geometric multi-modal stress intensity factors computed at the fracture tips. Fracturing is evaluated over multi-scale periods, from days to millions of years, thus capturing multiple tidal effects. Fracture behaviour is modelled across the Europan surface in one domain. The patterns are dense clusters of lineae about the stress maxima with diffuse fracturing in outlying regions. Fractures are also modelled in the vicinity of subsurface meltwater lenses, where fractures form parallel to the surface in contrast to the usual perpendicular orientation. The resultant fracture patterns are qualitatively compared against images from NASA’s Galileo mission. This work contributes to the understanding of Europan lineae by illustrating how they behave in a fracture mechanics framework, and suggests interesting results regarding lineae interaction with meltwater lenses. This work is also a proof of concept for this modelling approach, and will serve as the framework for future work.

Effect of a singular planar heterogeneity on tensile failure

Many rocks contain planar heterogeneities, in the form of open fractures, veins and/or stylolites, but scarce data exist on how strength and fracture pattern formation is affected by the presence of a singular planar heterogeneity in an otherwise uniform matrix. The mechanics of stylolite-bearing and/or fractured limestone is of interest to several engineering applications, from quarries to subsurface gas or geothermal reservoirs. We have performed Brazilian Disc tests on pre-fractured Indiana limestone samples and Treuchtlinger Marmor discs which contain cohesive stylolites, investigating Brazilian test Strength and the resulting fracture pattern. All experiments were filmed, and where possible analyzed with particle image velocimetry. When viewed in 2D, the planar discontinuity was set at different rotation angles compared to the principal loading direction, where perpendicular to the loading direction is defined as 0⁰. The results show that all samples are weaker than their intact counterparts. For the pre-fractured Indiana limestone, there is 10–75% angle-dependent weakening. However, in the samples with a stylolite, strength is weakened by 35–75%, independent of direction. Several new cracks appeared when fracturing a stylolite-sample, where the orientation is heavily influenced by the stylolite orientation. The fracture pattern and associated stress drops are more complex for high angles. In these samples always more than one fracture formed, whereas in pre-fractured samples usually only one new fracture formed. This suggests a potential for more permeability increase when hydrofracturing a stylolite-rich interval. Comparison with Finite Element Models indicates that this difference in fracture pattern is caused by the strength contrast between the anastomosing stylolite zone and the matrix material, leading to stress concentrations effects. This causes (micro-) fracture nucleation to occur locally, promotes fracture coalescence and fracture growth at lower overall sample-load conditions compared to intact samples.

Gradual fracture of layers in laminated glass plates under low-velocity impact

Modeling of gradual fracture of individual layers of laminated glass produced by successive low-velocity impacts is presented. This subject is first examined experimentally focusing on fracture sequence of the laminate composed of three or four glass layers bonded by polyvinyl butyral (PVB) interlayers. While both laminate geometries, limited to four test samples, show a significant scatter in impact energies and breakage forces causing fracture as well as differences in fracture sequence with increasing impact height, they consistently support ability of partially damaged samples to withstand contact forces exceeding those leading to fracture of the previous glass layer. Also, the four-glass layer laminates seem to provide the post-fracture response consistent with the concept of a sacrificial-glass-ply design. However, many questions remain concerning stochastic behavior of glass laminates further promoted by the present experimental results. To open the door to probabilistic modeling, the present topic is addressed also computationally adopting the LS-DYNA software. It is illustrated that properly tuned computational model may provide results, which are comparable to experimental observations both in terms of contact forces and the resulting fracture patterns.

Crack nucleation and propagation of electromagneto-thermo-mechanical fracture in bulk superconductors during magnetization

Bulk high-temperature superconductors (HTS) like REBCO (RE: rare earth element or Y) have been widely adopted in a variety of engineering applications. With high magnetic flux applied in a short time of milliseconds, significant tensile stresses are induced during pulsed field magnetization by the Lorentz electromagnetic forces and Joule heating thermal expansions. Consequently, potential damage and fracture may occur in bulk HTS, leading to degradation of the capacity in trapping the magnetic field. In this multi-physical problem, due to the complex stress distribution even in the elastic stage and the intensive redistribution once crack nucleation occurs, the resulting fracture pattern is very complicated. Accordingly, it is a challenging issue to model crack nucleation and propagation of such electromagneto-thermo-mechanical fracture involving both the Lorentz electromagnetic forces and the Joule heating. In this work, the mechanical stresses and multi-physical fracture in bulk HTS during magnetization are studied systematically by the phase-field cohesive zone model (PF-CZM). The governing equations and the involved constitutive relations for the electromagnetic, thermal and cracking-mechanical sub-problems are given together with the numerical implementation. The elastic semi-analytical solutions for the Lorentz forces and thermal expansions induced stresses in an infinitely long cylindrical bulk HTS during magnetization are derived for the determination of crack nucleation. Numerical results are then discussed in details regarding the whole fracture process in bulk HTS under isothermal and non-isothermal cases. It is found that the first crack nucleation occurs at a certain interior position along the circumferential direction after which a couple of cracks nucleate and propagate outwards along the radial direction. The effects of Joule heating and cracking on the electromagnetic performances are quantified, and those of the inhomogeneity in the critical current density are also briefly discussed. Moreover, extension of the proposed PF-CZM to more complex cases is straightforward, making it a promising tool in optimizing the fabrication and practical application of bulk HTS.

Cortical bone continuum damage mechanics constitutive model with stress triaxiality criterion to predict fracture initiation and pattern.

A primary objective of finite element human body models (HBMs) is to predict response and injury risk in impact scenarios, including cortical bone fracture initiation, fracture pattern, and the potential to simulate post-fracture injury to underlying soft tissues. Current HBMs have been challenged to predict the onset of failure and bone fracture patterns owing to the use of simplified failure criteria. In the present study, a continuum damage mechanics (CDM) model, incorporating observed mechanical response (orthotropy, asymmetry, damage), was coupled to a novel phenomenological effective strain fracture criterion based on stress triaxiality and investigated to predict cortical bone response under different modes of loading. Three loading cases were assessed: a coupon level notched shear test, whole bone femur three-point bending, and whole bone femur axial torsion. The proposed material model and fracture criterion were able to predict both the fracture initiation and location, and the fracture pattern for whole bone and specimen level tests, within the variability of the reported experiments. There was a dependence of fracture threshold on finite element mesh size, where higher mesh density produced similar but more refined fracture patterns compared to coarser meshes. Importantly, the model was functional, accurate, and numerically stable even for relatively coarse mesh sizes used in contemporary HBMs. The proposed model and novel fracture criterion enable prediction of fracture initiation and resulting fracture pattern in cortical bone such that post-fracture response can be investigated in HBMs.

Blunt force trauma in the human mandible: An experimental investigation

There exist sparse data associating known points of mandibular impact with resultant fracture patterns. These data may provide an important foundation for interpreting mandible fractures in forensic cases. The current study illustrates results of experimental blunt force impacts to five locations on the mandible: the ramus, posterior body, mid-body, anterior body, and midline. The experimental sample comprised thirteen intact heads from non-edentulous, unembalmed human adult male cadavers. Three key findings resulted from this study: (1) each impact produced a fracture at or adjacent to the impact site; (2) ramus and midline impacts produced more fractures than mandibular body impacts; and (3) fracture locations varied among mandibles impacted at the same location and exhibited similarities among mandibles impacted at different locations, suggesting there are limitations in estimating mandibular impact sites based on fracture location alone. Overall, these results contribute a comparative sample of known blunt force trauma cases for practitioners evaluating mandibular fractures in forensic cases.

Relaxation damage control via fatigue-hydraulic fracturing in granitic rock as inferred from laboratory-, mine-, and field-scale experiments

The ability to control induced seismicity in energy technologies such as geothermal heat and shale gas is an important factor in improving the safety and reducing the seismic hazard of reservoirs. As fracture propagation can be unavoidable during energy extraction, we propose a new approach that optimises the radiated seismicity and hydraulic energy during fluid injection by using cyclic- and pulse-pumping schemes. We use data from laboratory-, mine-, and field-scale injection experiments performed in granitic rock and observe that both the seismic energy and the permeability-enhancement process strongly depend on the injection style and rock type. Replacing constant-flow-rate schemes with cyclic pulse injections with variable flow rates (1) lowers the breakdown pressure, (2) modifies the magnitude-frequency distribution of seismic events, and (3) has a fundamental impact on the resulting fracture pattern. The concept of fatigue hydraulic fracturing serves as a possible explanation for such rock behaviour by making use of depressurisation phases to relax crack-tip stresses. During hydraulic fatigue, a significant portion of the hydraulic energy is converted into rock damage and fracturing. This finding may have significant implications for managing the economic and physical risks posed to communities affected by fluid-injection-induced seismicity.

A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation

We present a new derivation for a phase-field model of cohesive fracture that allows for fully-damaged surfaces to properly transmit tractions under frictionless contact conditions. The model is derived from an energy minimization standpoint, and the governing equations are presented in a general Allen–Cahn form, unifying both brittle and cohesive fracture models. A novel elastic energy split is proposed to enforce frictionless contact conditions along the regularized crack set. A fixed-point iterative algorithm is used to solve the system of equations, and an active-set strategy is incorporated to enforce the crack set irreversibility. The model is then applied to study the mechanical-fracture coupling in the fracture of thin films and soil desiccation problems in which intricate crack networks form. We present results for one-dimensional, two-dimensional, and fully three-dimensional configurations, and examine the relationship between the generalized driving energies for fracture and the resulting fracture patterns. We also investigate the impact of stochastic spatial variations in material parameters on fragment statistics and fracture network morphology. To this end, we develop a random field model for fracture properties and address a forward propagation problem. The versatility offered by the probabilistic framework is finally highlighted by considering a statistical inverse problem based on physical experiments. It is shown, in particular, that the formulation allows key characteristics of observed crack patterns to be reproduced with reasonable accuracy.

Experimental hydraulic fracturing of Berea sandstone under triaxial stress state

In this work, a newly designed experimental setup is used to perform in-lab fracking under controlled triaxial loading on cylindrical cores of Berea sandstone. Fracking tests are conducted at 10 MPa confining pressure, with vertical compressive loading, as well as two horizontal stresses that simulate reservoir triaxial stress state. Multiple injection scenarios are tested to investigate the effect of the pore fluid injection conditions on the fracking and failure mechanisms. In-situ micro-seismic monitoring via eight acoustic emissions sensors is used for logging the fracking events evolution with time. Post-experimental characterization included computational tomography (CT) scanning to characterize the resulting fracture patterns.

Development and commissioning of an instrumented pneumatic device to simulate blunt- and sharp-force trauma

Forensic investigators commonly interpret bone fracture patterns to estimate the force required to generate that trauma. Unfortunately, these estimates are limited to qualitative values such as “mild”, “moderate” or “extreme” force. This work presents a new experimental forensic device developed to simulate blunt- and sharp-force trauma injuries, while recording the forces and velocities involved, so that a more quantitative relationship between force and trauma can be established. The machine design is described in some detail, its capabilities are outlined, and the results of the commissioning and validation tests are presented. Preliminary results for both blunt- and sharp-force testing of porcine ribs, conducted at 3.8m/s, indicate the average peak force (733±95N versus 392±73N), average force (334±49N versus 101±24N), and work (2.34±0.26J versus 0.68±0.09J) are significantly higher in the blunt case. The experimental data generated by this instrumented device will allow forensic investigators to create a better quantitative link between incident conditions (velocity, force, work) and the resulting fracture patterns.

Orbital Trauma.

The orbit is contained within a complex bony architecture with overlying soft tissue that involves many important anatomical structures. Orbital trauma is a frequent cause of damage to these structures. The authors review the literature on reconstructive techniques focusing on fractures of the orbital rim, orbital roof, orbital floor, medial orbital wall, and naso-orbito-ethmoid complex. A thorough literature review was conducted using PubMed analyzing articles relevant to the subject matter. Various search terms were used to identify articles regarding orbital trauma presentation, diagnosis, management, as well as postoperative complications. Articles were examined by all authors and pertinent information was gleaned for the purpose of generating this review. Orbital trauma can result in a wide variety of complications in form and function. Not all orbital fractures require operative repair. However, bony disruption can cause enophthalmos, hypophthalmos, telecanthus, epiphora, cerebrospinal fluid leaks, orbital hematoma, and even blindness to name a few. Timing of operative repair as well as reconstructive method is dictated by the patient's individual presentation. Successful fracture management requires a detailed understanding of the anatomy and pathophysiology to ensure restoration of the patients' preoperative state. Orbital trauma encompasses a wide variety of mechanisms of injury and resulting fracture patterns. A variety of surgical approaches to the orbit exist as has been discussed allowing the surgeon access to all area of interest. Regardless of the fracture complexity, the principles of atraumatic technique, anatomic reduction, and stable fixation apply in all cases.

Biomechanical analysis of likelihood of optic canal damage in peri-orbital fracture

Purpose: Detection of optic canal fractures is often difficult because of the subtleness of the fracture. If we could clarify impact on which region around the orbit is likely to accompany the fracture of the optic canal, the knowledge should be useful to make early diagnosis of optic canal fractures. The present study was conducted to elucidate this issue.Methods: Ten finite element models were produced simulating the skulls of ten humans (8 males and 2 females; 43.8 ± 10.2 y/o). The peri-orbital area of each of the ten models was divided into eight regions in a clockwise fashion per 45 degrees. These regions were defined as Superior-Medial (0–45 degrees), Medial-Superior (45–90 degrees), Medial-Inferior (90 to 135 degrees), Inferior-Medial (135 to 180 degrees), Inferior-Lateral (180–225 degrees), Lateral-Inferior (225 to 270 degrees), Lateral-Superior (270–315 degrees), and Superior-Lateral regions (315–360 degrees), respectively. Dynamic simulation of applying traumatic energy on each of these regions was conducted. Resultant fracture patterns were evaluated using finite element analyses. Thereafter, frequencies of fracture involvement of the optic canal were evaluated for each of the eight regions.Results: The involvement of the optic canal was most frequent for the Superior-Medial region (7/10), followed by the Medial-Superior region (5/10).Conclusion: Optic canal fracture is likely to occur when the area between the supra-orbital notch and the medial canthus are strongly impacted. When evident fracture or serious damage of soft tissue is observed in this area, occurrence of optic canal fracture should be suspected.

Does preliminary optimisation of an anatomically correct skull-brain model using simple simulants produce clinically realistic ballistic injury fracture patterns?

Ballistic head injury remains a significant threat to military personnel. Studying such injuries requires a model that can be used with a military helmet. This paper describes further work on a skull-brain model using skulls made from three different polyurethane plastics and a series of skull ‘fills’ to simulate brain (3, 5, 7 and 10% gelatine by mass and PermaGel™). The models were subjected to ballistic impact from 7.62 × 39 mm mild steel core bullets. The first part of the work compares the different polyurethanes (mean bullet muzzle velocity of 708 m/s), and the second part compares the different fills (mean bullet muzzle velocity of 680 m/s). The impact events were filmed using high speed cameras. The resulting fracture patterns in the skulls were reviewed and scored by five clinicians experienced in assessing penetrating head injury. In over half of the models, one or more assessors felt aspects of the fracture pattern were close to real injury. Limitations of the model include the skull being manufactured in two parts and the lack of a realistic skin layer. Further work is ongoing to address these.

Modeling propellant-based stimulation of a borehole with peridynamics

A non-local formulation of classical continuum mechanics theory known as peridynamics is used to study fracture initiation and growth from a wellbore penetrating the subsurface within the context of propellant-based stimulation. The principal objectives of this work are to analyze the influence of loading conditions on the resulting fracture pattern, to investigate the effect of in-situ stress anisotropy on fracture propagation, and to assess the suitability of peridynamics for modeling complex fracture formation.It is shown that the loading rate significantly influences the number and extent of fractures initiated from a borehole. Results show that low loading rates produce fewer but longer fractures, whereas high loading rates produce numerous shorter fractures around the borehole. The numerical method is able to predict fracture growth patterns over a wide range of loading and stress conditions. Our results also show that fracture growth is attenuated with increasing in-situ confining stress, and, in the case of confining stress anisotropy, fracture extensions are largest in the direction perpendicular to the minimum compressive stress. Since the results are in broad qualitative agreement with experimental and numerical studies found in the literature, suggesting that peridynamics can be a powerful tool in the study of complex fracture network formation.

Multi-branched growth of fractures in shales for effective reservoir contact: A particle based distinct element modeling study

The complexity of a stimulated fracture network is important for hydrocarbon extraction from tight shales. Branched-interconnected-complex fracture networks are preferable for a better production due to a larger contact area compared to unconnected-single fractures. The presented numerical modeling study aims for a better understanding of the hydraulic fracturing process in shale formations to eventually achieve these kinds of fracture networks. In this study, a two dimensional particle based distinct element method (DEM) is used to systematically investigate the influence of specific model parameters on the resulting fracture patterns. The applicability of the model is critically discussed and technical measures to increase hydraulic fracture complexity are proposed.

Arthroscopic Bullet Removal From the Central and Peripheral Compartments of the Hip Joint

Recent advances in hip arthroscopy offer an approach for treating an uncommon but highly disabling injury from intra-articular missile injury to the hip. Hip arthroscopy affords the patient the benefit of minimally invasive surgery while allowing for the diagnosis and treatment of concomitant pathology, which may be either acute, from the trauma of the missile, or chronic. We present a technique for the removal of projectiles from the central and peripheral compartments of the hip joint. Through a surgical series of a variety of gunshot wounds, we detail the unique aspects of retrieval for the various missile endpoints. We describe this technique for bullets or pieces of bullets lodged within the hip joint space, bone of the acetabulum, or femoral head. Furthermore, we provide an example in which hip arthroscopy is not a suitable option for treatment because of the resulting fracture pattern, which necessitates open reduction along with internal fixation.

Numerical investigation of the effect of preexisting discontinuities on hydraulic stimulation

The present work aims to investigate the effect of the orientation and spacing of preexisting planes of weakness (discontinuities) on the process of hydraulic stimulation. Structured assemblies of spheropolyhedra were created and a constant water inflow was applied at their center. The hydraulic pressure and the resulting fracture pattern were monitored during each simulation. Both showed a strong dependence on the geometry of the preexisting discontinuities and the orientation of the stress field. The dependence of the maximum hydraulic pressure in each simulation on the geometry of the preexisting discontinuities was found to be compatible with continuum considerations.

A grain based modeling study of fracture branching during compression tests in granites

In a previous study we used a the grain based modeling approach (GBM) to carry out a sensitivity analysis of mineral size and random distribution of minerals and particles and their influence on elastic properties, strength and fracture types in Aue Granite. In the present study, the same calibrated model is used to further evaluate the influence of these parameters as well as the particle, parallel-bond, and smooth joints properties of the model on the resulting fracture patterns. It was found that complex crack networks always develop in heterogeneous GBMs, and crack network complexity increases with increasing heterogeneity. While each of the particles, parallel bond, and smooth joint properties govern the development of a specific crack type, no obvious relations between these properties and the total number of cracks and the resulting crack network complexity were found.

A calibration procedure for two-dimensional laboratory-scale hybrid finite–discrete element simulations

In recent years, Bonded-Discrete element methods (Bonded-DEM) and hybrid finite–discrete element methods (FDEM) have become widely employed to model brittle fracturing processing in geomaterials. These approaches possess the ability to explicitly simulate fracture and fragmentation, but necessitate a large number of input parameters to be specified. Many of these parameters cannot be directly measured or characterized via laboratory tests and therefore must be estimated via calibration procedures to attain reliable results. In this work, a prescriptive procedure to arrive at a combination of input parameters for the newly developed Y-Geo FDEM code is developed. The proposed procedure is applicable for laboratory-scale simulations where some laboratory testing data for the material to be simulated is available. It uses a combination of the known elastic parameters, uniaxial compressive strength, and Brazilian disc strength of a material as calibration targets and limits the over-determined nature of the calibration problem by considering the similitude of the resulting fracture patterns. The development of this procedure represents a major step forward in obtaining reliable and consistent results using an FDEM approach.

Mechanical stability model of progradational carbonate platform margins under tectonic loads: Deformation of Cretaceous carbonate platforms in the Sierra Madre Oriental fold‐thrust belt (east central Mexico)

AbstractShortening in the Sierra Madre Oriental fold‐thrust belt (east central Mexico) is localized along the margins of Cretaceous carbonate platforms and controlled by mechanical stratigraphy. The platform margins are deformed by imbricate series of thrust ramps, whereas the coeval basins and platform interiors are deformed by map‐scale detachment folds. Here we present a finite element model to evaluate the influence of the boundary geometry and boundary conditions on the style of deformation observed at these basinward progradational platform margins. We calculate the stress distribution in a linearly elastic platform‐basin transition zone under the action of horizontal tectonic stress, taking into account changes of rock mechanical properties across the platform margin, as well as their dependence on direction, and infer the resulting fracture patterns based on the Mohr‐Coulomb failure criterion. Stress concentrations are predicted at the contacts between the massive rocks of the platform margin and the well‐layered rocks of both, the platform interior and the adjacent basin. Brittle failure of the platform border can be mostly attributed to three effects: mechanical coupling between the carbonate platform and a substratum of moderate to low viscosity, variations in layering and texture that governed the mechanical properties of the involved carbonates as well as their dependence on direction, and the development of sharp domain boundary corners associated with progradational facies changes. In contrast, the dip of the basement and a possible taper of the overlying Upper Cretaceous shale toward the basin appear to have little influence on the mechanical failure of the platform margin.