Dynamic Stress Field Research Articles

Dynamic Ruptures on Bending Fault: Insights from Numerical Simulations of Transient Stress Field

ABSTRACT We delve into the spontaneous rupture propagation on bending faults by numerical simulations based on the boundary integral equation method with unstructured meshes. To study the effect of fault geometry on dynamic rupture propagation, special attention is paid to the role of the dynamic stress field. The numerical results demonstrate that the bending angle is a key geometrical factor influencing the rupture propagation because it affects both the initial stress distribution and the dynamic stress field on the bending branch. The rupture propagation on the bending branch can be separated into two distinct stages: first, the propagation from the main branch to the bending branch, which largely depends on the dynamic stress field near the bend; and second, a subsequent propagation stage primarily influenced by the initial stress state on the bending branch, with the influence of the dynamic stress field decreasing rapidly with distance from the bend. Geometrical smoothing of the bend can be regarded as a modification of the bending angle, which may significantly alter the behavior of rupture propagation near the bend. In theory, if the bending angle ranges between −120° and 60°, there is a potential for rupture to propagate onto the bending branch through the bend.

Surrogate Model of Shale Stress Based on Plackett-Burman and Central Composite Design

Summary Multifactor analysis and accurate prediction of dynamic stress in shale reservoirs are of great practical significance for designing hydraulic fracturing. In this paper, a surrogate model for the rapid prediction of shale stress is proposed by considering the geomechanical heterogeneity and multiscale seepage mechanism of shale gas. The Plackett-Burman method is used to compare the influence of different parameters on shale stress, and significant parameters are selected as decision variables for establishing a surrogate model. The surrogate model for predicting stress is obtained by central composite design fitting, and the interaction of significant factors on shale stress is studied. The results show that after considering the heterogeneity, the minimum horizontal stress fluctuation range is 20.25 to 44.03 MPa and the maximum horizontal stress fluctuation range is 26.46 to 49.77 MPa in the area controlling hydraulic fracture. The initial reservoir pressure, as well as the length and width of hydraulic fractures, are the key factors influencing reservoir stress. The analysis of variance demonstrates that the proposed method is effective for predicting shale stress. The research results are helpful for gaining a deeper understanding of the evolution mechanism of dynamic stress fields in shale reservoirs and provide guidance for treatment design and dynamic optimization of gas wells.

High-Speed Stress Field Measurement In A Soft Substrate During Droplet Impact

In this study, we utilized high-speed photoelastic tomography to quantify dynamic stress fields within a soft substrate during droplet impact. This manuscript details the measurement technique, which employs a high-speed polarization camera and the principles of photoelastic tomography. Our method successfully enabled the quantitative measurement of dynamic stress fields in a soft substrate during droplet impact. Additionally, we conducted an analysis of the impact force derived through the spatial integration of the measured stress field. The discussion explored the interplay between the maximum impact force, droplet viscosity, and substrate elasticity. Our findings indicate that the maximum impact force 𝐹max can be expressed as a function with a self-similar variable of 𝑅𝑒 / 𝐶𝑎^2 , where 𝑅𝑒 is Reynolds number representing the droplet inertial force and droplet viscous force and 𝐶𝑎 is Cauchy number representing the ratio of the droplet inertial force and substrate elastic force. This combination, 𝑅𝑒 / 𝐶𝑎^2 , represents the relationship between the relaxation time of droplet and substrate deformation ( 𝜂/ 𝐸), the contact time of the droplet (𝑅 / 𝑉), and the ratio of substrate elastic force to droplet inertial force. Consequently, the maximum impact force 𝑅𝑒 / 𝐶𝑎^2 is determined by the balance between the relaxation and contact times. We believe that our developed method will significantly enhance the understanding of droplet impact phenomena. Furthermore, it holds potential for broader applications in various engineering processes, such as analyzing stress distribution in materials caused by liquid jet impact and studying cavitation bubbles in viscoelastic materials. This method's ability to provide detailed quantitative measurements of dynamic stress fields offers a valuable tool for future research and technological advancements in related fields.

Analysis of Mode I Dynamic Crack Tip Singular Stress Fields for MEMS Structural Design

Analysis of Mode I Dynamic Crack Tip Singular Stress Fields for MEMS Structural Design

High-speed photoelastic tomography for axisymmetric stress fields in a soft material: Temporal evolution of all stress components

This study presents a novel approach for reconstructing all stress components of the dynamic axisymmetric fields of a soft material using photoelastic tomography (PT) and a high-speed polarization camera. This study focuses on static and dynamic Hertzian contact as an example of transient stress field reconstructions. For the static Hertzian contact (a solid sphere pressed against a gel block), all stress components in the urethane gel, which has an elastic modulus of 47.4 kPa, were reconstructed by PT using the measured photoelastic parameters. The results were compared with theoretical solutions and showed good agreement. For the dynamic Hertzian contact (a sphere impacting gel), a high-speed polarization camera was used to reconstruct the transient stress field within the gel. PT was used to quantitatively measure the shear and axial stress waves and showed different propagation speeds on the substrate. The technique allowed the simultaneous measurement of stress fields ranging from O(10−1) to O(101) kPa during large deformations, demonstrating its accuracy in capturing rapidly changing stress tensor components in dynamic scenarios. The scaling laws of the calculated impact force agreed with theoretical predictions, validating the accuracy of PT for measuring dynamic axisymmetric stress fields in soft materials.

Refining the final phase of the seafloor spreading process in the West Philippine Basin through the recalibration of magnetic isochrones

The evolution of the West Philippine Basin (WPB), the largest back-arc basin in the northwestern Pacific margin, remains unclear, mainly due to the lack of accurate magnetic chronological constraints. We integrate a newly acquired shipborne magnetic grid and EMAG2 data to investigate the final phase of seafloor spreading and post-spreading magma-poor extension in the WPB during the Eocene and Oligocene. An ∼800 km-long transect located in the eastern part of the WPB was modeled to recalibrate the magnetic isochrones. The results show that the seafloor spreading direction of the WPB rotated counterclockwise from ∼NE–SW to ∼NNE–SSW at ∼44 Ma (Isochrone C20r) and from ∼NNE–SSW to ∼N–S at ∼39 Ma (Isochrone C18n.1n). After the latter rotation, the spreading became unstable, decreased significantly, fluctuated, and finally ceased at ∼33 Ma (Isochrone C13n). The post-spreading magma-poor extension along the Central Basin Rift (CBR) driven by the initial opening of the Parece Vela Basin (PVB) began ∼4 Myr after the cessation of spreading. In the area east of ∼132°E, the CBR inherited the fossil spreading center, but to the west, it manifests a newly formed rift valley intersecting the segmented fossil spreading center. The destabilization of the spreading process in the marginal basin during its extinction phase was predominantly controlled by the dynamic process and stress field imposed by the adjacent plate boundaries.

The effect of ballast moisture content and fouling index on railway track settlement

A primary function of railway ballast is to maintain vertical track geometry, however over time it becomes contaminated with fines which reduce its ability to free-drain. Then, in the presence of moisture, the individual particles have greater scope for rearrangement thus leading to increased track settlement. This behaviour has received limited studied from a differential settlement viewpoint despite track geometry being the dominant metric used for scheduling railway maintenance. Therefore this paper presents a novel numerical modelling approach capable of simulating the effect of ballast fouling and moisture content on the evolution of track geometry. First the model is presented, which uses a 2.5D finite element approach with perfectly matched layers to simulate static and dynamic stress fields from trains. Non-linear track-soil effects are considered and loading is applied using a multi-body vehicle with train-track coupling. Differential track settlement is calculated in an iterative manner, being updated after every train passage. It is used to perform four analyses, the first of which is to investigate the effect of ballast fouling considering dry conditions. Next the effect of moisture of fines is studied. Then, the effect of earthwork stiffness and train speed is analysed. It is shown that elevated levels of ballast fouling lead to faster deterioration in track geometry, particularly in the presence of moisture. When the ballast is heavily fouled and the moisture of fines is high, rapid deterioration occurs. In contrast, when the ballast is kept dry, the increase in degradation rate for fouled ballast is limited. Higher train speeds and lower earthwork stiffness’s make this effect more pronounced.

Advancing instantaneous photoelastic method with color polarization camera

Digital photoelasticity is an essential experimental method. For dynamic objects and transient stress fields, the utilization of the instantaneous photoelastic method becomes necessary. Existing instantaneous photoelastic methods, represented by the conventional RGB method and instantaneous phase shifting techniques, encounter a significant challenge in simultaneously obtaining both the isochromatic and isoclinic parameters while ensuring a considerable measurement range for the isochromatic fringe order (retardation). This severely limits the application scope of instantaneous photoelasticity. In this paper, a novel approach is proposed by introducing a color polarization camera into the field of photoelasticity. The proposed method enables simultaneous determination of the full-field continuous isochromatic fringe order and the isoclinic parameter, ensuring a considerable measurement range for the isochromatic fringe order. Additionally, the obtained isoclinic parameter is consistent, eliminating the need for tedious and time-consuming phase unwrapping procedures. To validate the accuracy and effectiveness of the method, it was applied to standard problems involving a disc and a ring under diametral compression and an instantaneous problem concerning a rotating blade. The proposed method expands the application potential of instantaneous photoelasticity, enabling the resolution of a broader range of problems.

The relation of regional earthquakes to an intraplate volcano in the northern Hainan Island, China from magnetotelluric imaging

Volcanic activity can cause regional earthquakes before or during an eruption, while violent earthquakes are capable of changing static and dynamic stress-fields that may consequently accelerate or trigger volcanic eruption. It is thus important to consider the volcano and regional earthquake as an integrated system, which has implications for disaster prevention and may enable early warning. In this work, two magnetotelluric (MT) profiles were deployed across the active volcanic and seismic region in the northern Hainan Island, China. Data were inverted to generate a three-dimensional resistivity structure beneath the two profiles. The resistivity model shows a shallow (< 5 km) low-resistivity (< 10 Ωm) zone corresponding to Paleogene and Neogene sediments, and two conductors (10–30 Ωm) at depths of 5–12 km. The conductors in the middle-upper crust are attributed to the accumulation of high-salinity fluids supplied by deeper magmas. The north-south trending small earthquakes (< M3) are mainly distributed in high-resistivity basement, independent of the volcanic plumbing system, which are attributed to small-scale rupture in higher tensile rocks. The volcanic plumbing system appears to extend below the Qiongzhou Earthquake (M7.5 in 1605), indicating the possibility of distal volcano-tectonic earthquake.

A semi-analytical solution to the stress intensity factors of branched cracks

Crack branching is ubiquitous in engineering practice, and it often takes place when a crack is subjected to dynamic stress fields, or runs into heterogeneous regions. The mechanical analysis of branched cracks is of great significance in safety analysis and crack-path engineering. In this work we developed a theoretical method to calculate the stress intensity factors (SIFs) of branched cracks. By employing both Schwarz–Christoffel mapping and Muskhelishvili approach, we present an asymptotic approximation for the conformal mapping and SIFs of arbitrary branched cracks are then readily derived. We further demonstrate the convenience of this analytical approach to obtain the SIFs of forked crack as well as four-branched cracks. The theoretical solutions are validated by using finite-element simulations. It is shown that the semi-analytical approach agrees well with the FEM calculations on SIFs. The analytical methods supply a general way to solve the SIFs and therefore the energy release rate of branched cracks. It can then be adopted to understand crack splitting and crack network engineering.

Ultrasonic guided waves through Coalesence of matrix cracks and delaminations in laminated composites

Composite fabric-matrix interface mismatch during manufacturing and applied loads cause matrix micro-cracks and their evolution toward interface delamination and stiffness reduction. Fatigue and impact loads can grow these matrix cracks further as early damage precursors, which are not easily detectable. We simulate ultrasonic guided wave propagation in laminated composite with matrix crack mixed delamination site to understand better detection possibilities for these damage precursors using the ultrasonic inspection method. Since extremely small wavelength ultrasonic waves attenuate rapidly in composites, whereas long wavelength guided waves may not produce high sensitivity to small-scale defects, therefore we attempt to analyze super-resolution quantitative scheme with suitable frequencies to correlate defect parameters. We employ a time-domain spectral finite element method for fast computation of high-frequency wavefield while accurately resolving the matrix crack-delamination geometric features. Its high-order field interpolation enables us to model the nearfield interactions of the waves with the transverse micro-cracks and further with an evolved macro-scale delamination. The computational scheme is aimed to scale to complex defect local field simulations and cover larger size composite structures. This is achieved due to a mathematically consistent diagonalized mass matrix property which makes the implicit time marching-based computation highly efficient for highly resolved and large-size finite element systems. The transient dynamic stress field around the cracks modulates the guided wave mode packets. We analyze the characteristics of the signal sensitivities due to the defect features, most notably, an interesting correlation between matrix crack density and frequency modulation or sub-band contribution. Wave interaction with the defect region creates weak but distinct reflection patterns while transmitting through the region. The study provides useful and new understanding towards defect size estimation and indicative measure of thickness wise layers of matrix cracks and its coalescence into delamination in terms of energy spectral density of the sub-bands.

Dynamic surface stress field of the pure liquid-vapor interface subjected to the cyclic loads.

We demonstrate a methodology for computationally investigating the mechanical response of a pure molten lead surface system to the lateral mechanical cyclic loads and try to answer the following question: how does the dynamically driven liquid surface system follow the classical physics of the elastic-driven oscillation? The steady-state oscillation of the dynamic surface tension (or excess stress) under cyclic load, including the excitation of high-frequency vibration mode at different driving frequencies and amplitudes, was compared with the classical theory of a single-body driven damped oscillator. Under the highest studied frequency (50GHz) and amplitude (5%) of the load, the increase of in (mean value) dynamic surface tension could reach ∼5%. The peak and trough values of the instantaneous dynamic surface tension could reach (up to) 40% increase and (up to) 20% decrease compared to the equilibrium surface tension, respectively. The extracted generalized natural frequencies seem to be intimately related to the intrinsic timescales of the atomic temporal-spatial correlation functions of the liquids both in the bulk region and in the outermost surface layers. These insights uncovered could be helpful for quantitative manipulation of the liquid surface using ultrafast shockwaves or laser pulses.

Can the geometry of an injection clastic dike swarm indicate a short-term process? Examining the Dead Sea Basin in Israel

Despite the importance of identifying dynamic stress fields, doing so is not straightforward. This is because most geological processes occur slowly and the formation of fractures is generally attributed to long-term processes.Within the seismically active Dead Sea Basin (DSB), radial and concentric injection clastic dikes were emplaced during earthquake events, but a satisfactory explanation for their geometric configuration is lacking. In this study, field observations were used to explore whether the geometry of the injection clastic dike swarm reflects a quasistatic state of stress, such as with a salt diapir, or if it reflects a dynamic short-term stress state associated with the passage of seismic waves. The results show that the radial clastic dikes are not concentrated toward one central point located approximately 3 km east of the Ami'az Plain, that the concentric clastic dikes are arranged by three subsets, and that the spatial density and strain of both fracture sets are focused mainly toward the center of the Ami'az Plain. This evidence does not fit with a quasistatic state-of-stress interpretation of the region that would be associated with a local stress state around a salt diapir. A more plausible explanation is that the geometry of the radial and concentric clastic dike sets was controlled by short-term seismic waves that were probably generated by earthquake events located along an adjacent fault and that were trapped by the sedimentary basin located below the Ami'az Plain itself.The reconstruction of the injection clastic dike pattern may provide an opportunity to more deeply understand the short-term process induced by paleoearthquakes occurring adjacent to sedimentary basins close to the surface.

Abutment Pressure Distribution Law and Support Analysis of Super Large Mining Height Face.

Under the condition of the shallow coal seam, the laws of roof activity after large mining height longwall face mining and prevention measures for large-area roof weighting are problems that need to be solved urgently. In the background of the super large mining height working face in the upper 108 working face of Jinjitan Coal Mine 12-2, the spatial distribution characteristics of the development and change of the mining-induced abutment pressure and the related support design in the 8.2 m super large mining height and fully mechanized mining face were conducted. It reveals the distribution characteristics of the dynamic stress field and internal and external stress fields. The influence range of the abutment pressure of the super high mining height working face was measured on site. The numerical simulation is carried out, the roadway support structure is analyzed, and the improvement measures are proposed. The research results demonstrate that: The influence range of abutment pressure is 234 m, the obvious influence range of the leading pressure is 47-60 m, and the peak position of the influence of the leading pressure is 15-20 m. The 5 m range is the lateral inward stress field of the coal pillar, the 10-15 m range is the outward stress field of the coal pillar, and the 20 m range is the original rock stress field of the coal pillar. Therefore, it is proposed that the reasonable size of the coal pillar for roadway protection is 20-22 m. Adjusting the distance between screw steel and FRP bolts from 1000 mm to 1200 mm, the length of the roof prestressed anchor cable should be appropriately reduced to 5.5-6 m according to the lithology of the roof.

Finite Fracture Mechanics extension to dynamic loading scenarios

The coupled criterion of Finite Fracture Mechanics (FFM) has already been successfully applied to assess the brittle failure initiation in cracked and notched structures subjected to quasi-static loading conditions. The FFM originality lies in addressing failure onset through the simultaneous fulfilment of a stress requirement and the energy balance, both computed over a finite distance ahead of the stress raiser. Accordingly, this length results to be a structural parameter, thus able to interact with the geometry under investigation. This work aims at extending the FFM failure criterion to dynamic loadings. To this end, the general requisites of a proper dynamic failure criterion are first shortlisted. The novel Dynamic extension of FFM (DFFM) is then put forward assuming the existence of a material time interval that is related to the coalescence period of microcracks upon macroscopic failure. On this basis, the DFFM model is investigated in case a one-to-one relation between the external solicitation and both the dynamic stress field and energy release rate holds true. Under such a condition, the DFFM is also validated against suitable experimental data on rock materials from the literature and proven to properly catch the increase of the failure load as the loading rate rises, thus proving to be a novel technique suitable for modelling the rate dependence of failure initiation in brittle and quasi-brittle materials.

Partially-drained deformation properties of anisotropically overconsolidated clay by triaxial tests with cyclic confining pressure

The subgrade clay in situ may be anisotropically overconsolidated, the traffic-induced dynamic stress field on the subgrade clay can be simulated more accurately by the simultaneous application of cyclic axial stress and cyclic confining pressure by the VCP test, and the partially drained condition represents a more appropriate field scenario for the cyclic response of subgrade clays under long-term traffic loading. To mimic the coupling of the above factors, this study performed a large number of cyclic triaxial tests on a overconsolidated clay in partially drained condition. The ratio of the radial consolidation stress to vertical consolidation stress (K), cyclic stress ratio (CSR) and the ratio of cyclic deviatoric stress amplitude to cyclic mean principal stress amplitude (ηampl) are proposed, and their effects on the partially-drained permanent and resilient deformation behaviors of saturated clay are investigated. Test results show that the increase of consolidation-induced anisotropy (i.e., the decrease of K) leads to a remarkable increase of permanent axial strain, while it induces a first slight growth and then a decrease of permanent volumetric strain. Based on the shakedown theory, the allowable cyclic stress ratio separating the shakedown ranges of metastable and stable is determined, and it is unrelated to either K or ηampl. The effects of ηampl on the permanent axial strain are related to the shakedown range, and a uniform linear relationship is established between the permanent volumetric strain and cyclic mean principal stress amplitude. The anisotropically overconsolidated clay produces stiffness hardening in partially drained condition, in which the increase of both CSR and ηampl promote the hardening. It is suggested the prediction and control of subgrade clay settlement in engineering practice should consider all the factors involved in this study.

Startup Process Optimization of Hydropower Unit Based on Stress Measurement of Francis Turbine Runner

The energy efficiency characteristics of the turbine, cavitation performance of the runner, and operation stability of the unit are the three major concerns of a hydropower field, the latter two factors leading to the units’ cavitation and stability problems under some operation conditions and fatigue failure of the runner blades, which are the main causes of structural and mechanical failure for the hydropower units. In this article, three conventional unit startup processes are introduced, and combined with the optimal impulse control strategy, an optimized unit startup method is proposed. As the optimal guide vane opening adjustment setting value is obtained by solving the planned startup control strategy, 3D modeling and CFD simulation are carried out, then the equivalent stress characteristics are obtained by finite element calculation when the unit is running from startup to no load at a rated speed on three different startup modes. At last, the dynamic stress tests of the runner blade are performed at the hydropower station by using wireless acquisition and transmission technology, and the peak value and characteristics of the dynamic and static stresses of the blade under different startup processes are obtained. In this, the validity of the model analysis is proved by the comparison between the simulation calculation and the measured results, and the effectiveness of the startup control strategy is proved by combining the runner blade dynamic stress simulation, calculation, and the field dynamic stress test results. The optimization method of the startup process proposed in the article can alleviate the abnormal vibration of the unit and provide a basis for long-term stable operation of the hydropower unit.

Oscillating membranes: autonomous shape-transforming sheets via chemo-mechanical “metabolism”

Living organisms have mastered the dynamic control of residual stresses within sheets to induce shape transformation and locomotion. For instance, the spatiotemporal pattern of action-potential in a heart induces a dynamical stress field that leads to shape changes and biological function. Such out-of-equilibrium structures inspired the emerging field of soft robotics. However, state-of-the-art attempts to replicate this ability in synthetic materials are still lacking.

Dynamic contact stress and frictional heat analysis of femoral head-on-acetabular cup interface based on calculation and simulation methods

Purpose The purpose of this paper is to systematically study the dynamic contact stress, frictional heat and temperature field of femoral head-on-acetabular cup contact pairs in a gait cycle. Design/methodology/approach In this paper, four common femoral head-on-acetabular cup contact pairs are used as the research objects, mathematical calculations and finite element simulations are adopted. The contact model of hip joint head and acetabular cup was established by finite element simulation to analyze the stress and temperature distribution of the contact interface. Findings The results show that the contact stress of the head-on-cup interface is inversely proportional to the contact area; high contact stress directly leads to greater frictional heat. However, hip joints with metal-on-polyethylene or ceramic-on-polyethylene paired interfaces have lower frictional heat and show a significant temperature rise in one gait cycle, which may be related to the material properties of the acetabular cup. Originality/value Previous studies about calculating the interface frictional heat always ignore the dynamic change process in the contact load and the contact area. This study considered the dynamic changes of the contact stress and area of the femoral head-on-acetabular cup interface, and four common contact pairs were systematically analyzed.

Three-dimensional cyclic behavior of saturated clays: comparison between undrained and partly drained conditions

The cyclic response of subgrade clays under traffic loadings is likely to be partly drained rather than undrained, and the traffic-induced dynamic stress field is three-dimensional rather than axisymmetric. To compare the three-dimensional deformation behaviors of saturated clays between partly drained and undrained conditions, a large number of cyclic true triaxial tests were conducted. Experimental results show that a partly drained condition leads to a remarkable increase of permanent major principal strain ([Formula: see text]) compared to an undrained condition, and the differences of [Formula: see text] between the two drainage conditions are affected greatly by the factors of cyclic stress ratio (CSR), overconsolidation ratio (OCR), and coefficient of cyclic intermediate principal stress (bcyc). The increase of bcyc induces a linear reduction of [Formula: see text] in an undrained condition, while it causes an increase first followed by a decrease of [Formula: see text] in a partly drained condition. The clays undergo stiffness softening and hardening in partly drained and undrained conditions, respectively, and the effects of bcyc and CSR on the stiffness evolution are very different between the two drainage conditions. The mechanism of the complex [Formula: see text] and resilient modulus behaviors in a three-dimensional state and partly drained condition is further discussed. In addition, two different empirical models are employed to predict [Formula: see text] in partly drained and undrained conditions.