Rigid Body Rotation Research Articles

Physics-informed neural network for nonlinear dynamics of self-trapped necklace beams

A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schrödinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution of necklace patterns with integer, half-integer, and fractional reduced orbital angular momenta by means of PINN. The patterns exhibit phenomena similar to the rotation of rigid bodies and centrifugal force. Even though the necklaces slowly expand (or shrink), they preserve their structure in the course of the quasi-stable propagation over several diffraction lengths, which is completely different from the ordinary fast diffraction-dominated dynamics. By comparing different ingredients, including the training time, loss value, and L2 error, PINN accurately predicts specific nonlinear dynamical properties of the evolving necklace patterns. Furthermore, we perform the data-driven discovery of parameters for both clean and perturbed training data, adding 1% random noise in the latter case. The results reveal that PINN not only effectively emulates the solution of partial differential equations but also offers applications for predicting the nonlinear dynamics of physically relevant types of patterns.

Scale dependence of local shearing motion in decaying turbulence generated by multiple-jet interaction

Scale dependence of local shearing motion is investigated experimentally in decaying homogeneous isotropic turbulence generated through multiple-jet interaction. The turbulent Reynolds number, based on the Taylor microscale, is between approximately 900 and 400. Velocity fields, measured using particle image velocimetry, are analysed through the triple decomposition of a low-pass filtered velocity gradient tensor, which quantifies the intensities of shear and rigid-body rotation at a given scale. These motions manifest predominantly as layer and tubular vortical structures, respectively. The scale dependence of the moments of velocity increments, associated with shear and rigid-body rotation, exhibits power-law behaviours. The scaling exponents for shear are in quantitative alignment with the anomalous scaling of the velocity structure functions, suggesting that velocity increments are influenced predominantly by shearing motion. In contrast, the exponents for rigid-body rotation are markedly smaller than those predicted by Kolmogorov scaling, reflecting the high intermittency of rigid-body rotation. The mean flow structure associated with shear at intermediate scales is investigated with conditional averages around locally intense shear regions in the filtered velocity field. The averaged flow field exhibits a shear layer structure with aspect ratio approximately 4.5, surrounded by rotating motion. The analysis at different scales reveals the existence of self-similar structures of shearing motion across various scales. The mean velocity jump across the shear layer increases with the layer thickness. This relationship is well predicted by Kolmogorov's second similarity hypothesis, which is useful in predicting the mean characteristics of shear layers across a wide range of scales.

Mechanism analysis of burn-up failure for needle roller bearing at high-speed gear in manual transmission

Adequate lubrication conditions of needle roller bearings are crucial for the normal operation of transmission. Addressing the burn-up and adhesion failures of needle roller bearings during transmission bench trials, two rigid body rotation physical models were developed to analyze and model the lubrication effect on the inner and outer surfaces of needle roller bearing. Through theoretical analysis and lubrication simulation, it was found that under the critical condition of d/D=0.553, the centrifugal force F on the outer ring surface of the needle bearing was related to the density of lubricant, rotational speed, as well as the angle and size of oil hole, rather than the position of the oil holes; Moreover, the centrifugal force F on the needle roller bearing at input shaft was related to the speed of transmission gear and was also associated with the clearance size between needle roller and cage. Theoretical analysis, simulation, and experimental results have demonstrated that the lubrication performance of needle roller bearings during operation at lower rotary speed gears was inferior to that at higher speed gears, and the lubrication was also less effective when the cage clearance was narrower. Employing angled oil inlets (holes), appropriately enlarging the diameter of oil inlets (holes), and increasing the clearance width between needle roller and cage will contribute to the improvement of lubrication effect.

Kyanite microstructural and microchemical characteristics reveal differences in growth, deformation and chemical modification: A case study from the Paleoproterozoic suture zone of South Harris, NW Scotland

Based on petrological association, cathodoluminescence (CL), trace element signatures and orientation relationships, two generations of kyanite are distinguished in a high temperature, high pressure garnet-biotite-aluminosilicate bearing migmatite of South Harris, NW Scotland. The migmatite shows a garnet and biotite rich domain (Grt-Bt domain) which is cut at a low angle by a dominantly coarse-grained plagioclase-quartz leucosome. In addition, a fine-grained plagioclase-quartz-kyanite domain (Plag-Qtz-Ky domain) is present intercalated with the Grt-Bt domain and subparallel to the plagioclase-quartz domain. Type 1 kyanite is coarse grained and associated with Bt clusters and garnet within the Grt-Bt domain. It grew relatively early, syn- to post-garnet growth, in a suprasolidus environment resulting in crystallographically determined oscillatory CL and trace element zoning. Grains record evidence of progressive deformation in the crystal plastic regime, where deformation is accommodated by dislocation glide, climb and deformation twinning. The dominant activated slip system is (100)<001> with minor component of <100>, while deformation twins show a ∼ 180° rotation around ∼<001> axis and a twin plane near (001). Grains appear to be impervious to deformation induced diffusion with all zoning remaining sharp despite crystal plastic deformation. Grains in direct contact with the Plag-Qtz-Ky domain show late modification of the CL and trace element signature suggesting melt-mediated interface-coupled dissolution-precipitation reaction. This modification resulted in crosscutting lobate high trace element regions and irregular rims with low Cr and V content. These rims show similar CL and trace element characteristics as Type 2 kyanite which are exclusively seen within the Plag-Qtz-Ky domain suggesting that Type 2 grains are cogenetic with Type 1 rims. Type 2 grains are finer grained than Type 1 grains and show near uniform CL and trace element distributions with rare oscillatory zoned and relatively higher Cr & V bright cores. Type 2 show either no or very localized internal deformation features. However, they exhibit a clear shape preferred orientation which coincides with a crystallographic preferred orientation where the longest shape axis is parallel to <001>. We propose that Type 2 kyanite grains underwent melt-present deformation by rigid body rotation in an externally derived melt with different trace element chemistry than the host rock. This melt thus interacted chemically by melt-mediated interface-coupled dissolution-precipitation reactions with the surrounding rocks forming the Type 1 rims.Our study shows detailed analysis of kyanite is an important tool for giving constraints on the deformation, P–T and melting history of high-grade metamorphic rocks and migmatites.

Dynamic Analysis of Rigid–Flexible Structures with Piezoelectric Actuation and Control

In this paper, the dynamic equation of a rigid body coupled with two flexible beams was established, considering the rotational motion of the rigid body and the elastic deflection of the flexible beams. The coupling effect between the rigid body rotation and flexible beam vibration was studied in detail. The dynamic response of the flexible beam with piezoelectric effect was established based on Hamilton’s principle. Under the premise of ignoring the nonlinear vibration coupling term of flexible beams, only the first two modes of transverse displacement and one directional rotation motion were studied in case studies. It was found that the coupling term caused by rigid body rotation can slightly alter the natural frequency and amplitude of flexible beams, mainly reflected in the first-order mode. With increasing the external excitation on the rigid body, the induced transverse displacement at the tip of the flexible beam increased significantly. Meanwhile, when the flexible beam was under external excitation, the vibration could also induce rigid body rotation. With the inverse piezoelectric effect, one may actively actuate the flexible beam vibration and rigid body rotation or control the undesired motion of the system. The control effect can be adjusted by varying the applied voltage excitation on the piezoelectric patches as well as patch positions. The conclusions drawn from this study can be applied to active precise control of space facilities such as satellites. Based on the dynamic modeling of rigid–flexible multi-body systems, this paper completed the study of the coupling effects of rigid body rotation and flexible body vibration, and proposed an application idea for completing small-angle maneuvers of rigid–flexible multi-body systems through piezoelectric control.

Left ventricular deformation in the presence of left ventricular 'rigid body rotation' in healthy adults-three-dimensional speckle-tracking echocardiographic insights from the MAGYAR-Healthy Study.

During the heart cycle, the left ventricle (LV) not only shows a contraction-relaxation pattern, but LV has a rotational mechanics, as well. It is a known fact that certain pathologies may be associated with an absence of LV twist, when LV basal and apical regions rotate in the same clockwise (cw) or counterclockwise (ccw) direction called LV 'rigid body rotation' (LV-RBR), but it can also occur in healthy subjects. The present cohort study aimed to examine LV strains in healthy subjects with LV-RBR versus with normally directed LV rotational mechanics by three-dimensional speckle-tracking echocardiography (3DSTE). The study consisted of 181 healthy individuals, from which 171 cases had normally directed LV rotational mechanics (mean age: 32.5±12.3 years, 79 males) and 10 healthy subject showed LV-RBR (mean age: 35.4±11.3 years, 3 males). Complete two-dimensional (2D) Doppler echocardiography and 3DSTE were performed in all healthy individuals. None of routine 2D Doppler echocardiographic parameters showed differences between the groups examined. There were no subjects with ≥ grade 1 regurgitation on any valves or with significant stenosis on any valves. 3DSTE-derived LV volumes, global and mean segmental strains did not differ between the groups examined. Apical anterior and lateral segments showed reduced segmental LV circumferential strain (CS) (-18.9%±8.5% vs. -26.7%±10.7%, P=0.02; -27.3%±12.6% vs. -34.8%±13.2%, P=0.08, respectively) and LV area strain (AS) (-26.8%±9.8% vs -36.8%±12.0%, P=0.01; -35.7%±13.2% vs. -45.0%±14.6%) in healthy subjects having LV-RBR as compared to cases with normally directed LV rotational mechanics. These abnormalities were present only in subjects having cwLV-RBR. Although global LV deformation is normal in the presence of LV-RBR in healthy adults, reduction of apical anterior and lateral LV-CS (and LV-AS) are present in cases with cwLV-RBR only suggesting segmental deformation abnormalities.

Left Ventricular Twist and the "Rigid Body Rotation" Pattern in Patients Treated with Anthracyclines or Anti-HER2.

Background: During the physiological cardiac cycle, the helix orientation of the muscle fibres induces the rotation of the apex relative to the base of the left ventricular (LV). In heart failure, LV torsion is impaired, and rotation at basal and apical levels occurs in the same direction, a phenomenon called rigid body rotation (RBR). We aimed to evaluate whether the RBR pattern and GLS together could improve the diagnosis of cardiotoxicity in patients treated with anthracyclines and/or anti-HER2. Methods: With an observational, retrospective study involving 175 patients (mean age 55 ± 12 years, 94% females), we evaluated the development of cancer therapeutic-related cardiac dysfunction (CTRCD) defined according to ESC guidelines. We characterised LV dysfunction by echocardiographic standard and speckle-tracking (GLS and RBR pattern) measurements. Patients with a previous diagnosis of structural heart disease or atrial fibrillation were excluded. Results: At the time of enrolment, the chemotherapy regimen included trastuzumab (96%), pertuzumab (21%), and anthracyclines (13%). Twenty-two patients (12.5%) developed cardiotoxicity, and thirteen patients developed an RBR within 6 months of follow-up. In all cases, the RBR pattern was associated with cardiotoxicity (p < 0.001), reporting an optimal specificity but poor sensitivity at three and six months. However, the addition of the RBR pattern to the global longitudinal strain (GLS) ≥ -16% increased the odds ratio (OR) from 25.6 to 32.6 at three months and from 32.5 to 49.6 at six months rather than GLS alone. Conclusions: The RBR pattern improves the diagnostic accuracy of GLS for the detection of cardiotoxicity secondary to anthracyclines and anti-HER2-based treatments.

In-cylinder flow evolution in the horizontal plane of a motoring compression ignition engine

This study used the two-dimensional particle image velocimetry technique to quantify the in-cylinder horizontal plane velocity field evolution in a swirl-supported light-duty single-cylinder diesel engine. The data were acquired at a constant engine speed of 1600 revolutions per minute. For each case, the distance of the laser sheet from the fire deck was varied (z = 5, 10, and 20 mm) to investigate the axial variations in the flow field during the flow evolution in the compression stroke. A vortex identification algorithm was used to detect the swirl center and its deviation from the rigid body rotation. A Bessel fit was obtained using the experimental data. The result revealed that the in-cylinder flow was not axisymmetric. The swirl center approached the geometrical center as the piston approached the top dead center. The flow evolved at the farthest plane from the fire deck. The axial diffusion of angular momentum resulted in the formation of the swirl flow structure in the plane closer to the fire deck. Angular momentum analysis of a simplified geometry has been presented to explain the swirl amplification. The estimated results were compared with the experimental results to show the momentum stratification in the engine cylinder later in the compression stroke.

A centroid measurement method of large components for active compliant assembly

In the active compliant assembly system of large components, the centroid parameter is an important factor affecting the dynamic model of the attitude adjustment mechanism. This paper proposes a novel automatic centroid measurement method. Firstly, the contact force calculation method between large components during active compliant assembly was described, and the impact of the centroid of large components on the accuracy of the contact force calculation was analyzed. Secondly, based on the principles of torque balance and rigid body rotation, a novel centroid calculation model considering lateral forces is established, and RANSAC is used to optimize the centroid solution. Then, numerical simulation methods were used to analyze the impact of random errors and weighing strategies on the centroid measurement accuracy, and suggestions were given to improve the centroid measurement accuracy. Finally, a compliant assembly system for large component was built in the laboratory, and centroid measurement and accuracy verification experiments were conducted. The experimental results show that the proposed method can significantly improve the accuracy of centroid measurement and can effectively reduce the contact force calculation error during the compliant assembly process of large components.

FINITE SHEAR STRAIN BASED ON IMAGE ANALYSIS FOR RECTANGULAR SECTION SHAFT WITH LARGE ASPECT RATIO

This paper describes the shearing strain distribution obtained by using image analysis proposed in this study when large torsion is applied to a rectangular cross-section shaft. As is well known, the shearing strain distribution for rectangular cross-section shaft have already been investigated by Saint-Venant. However, since this theory is based on the assumption that torsional angle is relatively small, it is not necessarily rational under large torsion. Therefore, in our previous study, using the image analysis based on the Natural Strain theory, where the commutative law of strain is applicable and the rigid body rotation can be removed accurately from shearing strain component, the shearing strain distributions have been investigated for the rubber shaft having square cross section. In the present paper, these distributions are investigated for a rectangular cross section with a large aspect ratio rather than a square shape. In particular, these distributions on the long side in rectangular cross-section are compared with those on the short sides. Consequently, the difference between the distribution of shearing strain obtained by the image analysis in this study and measurements based on Saint-Venant's theory increases as torsional deformation increases and this tendency is observed particularly on the short side.

FINITE SHEAR STRAIN BASED ON IMAGE ANALYSIS FOR RECTANGULAR SECTION SHAFT WITH LARGE ASPECT RATIO

This paper describes the shearing strain distribution obtained by using image analysis proposed in this study when large torsion is applied to a rectangular cross-section shaft. As is well known, the shearing strain distribution for rectangular cross-section shaft have already been investigated by Saint-Venant. However, since this theory is based on the assumption that torsional angle is relatively small, it is not necessarily rational under large torsion. Therefore, in our previous study, using the image analysis based on the Natural Strain theory, where the commutative law of strain is applicable and the rigid body rotation can be removed accurately from shearing strain component, the shearing strain distributions have been investigated for the rubber shaft having square cross section. In the present paper, these distributions are investigated for a rectangular cross section with a large aspect ratio rather than a square shape. In particular, these distributions on the long side in rectangular cross-section are compared with those on the short sides. Consequently, the difference between the distribution of shearing strain obtained by the image analysis in this study and measurements based on Saint-Venant's theory increases as torsional deformation increases and this tendency is observed particularly on the short side.

ANALYSIS OF ASYMMETRIC PLASTIC BENDING DEFORMATION OF WELDED TUBE SHEETS AND DERIVATION OF A DAMAGE LAW FOR J SHAPE-C SHAPE -O SHAPE FORMING

The J shape-C shape -O shape (JCO) forming method of sheets for large-diameter longitudinally welded pipes has been widely used to manufacture oil and gas pipelines. The quality of welded pipes formed through the JCO process is directly affected by the accurate control of asymmetric bending springback and damage during the procedure. A finite element model (FEM) for JCO asymmetric bending was constructed to investigate the characteristics of asymmetric plastic bending deformation and the distribution laws of damage in JCO forming. This model was based on a nonlinear mixed hardening Lemaitre damage model coupled with the Quasi-Plastic-Elastic (QPE) model. Then, residual stress, forming shape, and damage degree of crimping, first bending, second bending, and third bending were analyzed. Moreover, the accuracy of the model was experimentally verified. Results demonstrate that, the asymmetric bending deformation process can be divided into five stages, including rigid body rotation phase, full elastic deformation phase, elastic–plastic uncladded deformation phase, elastic–plastic cladded phase, and springback phase. In the first bending, the stress centerline significantly misaligns with the mold centerline. Asymmetry is not evident in the second and third bending stages. Furthermore, the peak residual stress and peak damage can be effectively reduced by a larger punch radius, while the peak damage can be reduced by a larger die span. This study lays a foundation for optimizing the technical parameters of JCO forming. Keywords: JCO forming, asymmetric bending, finite element, QPE model, deformation characteristics

Experimental study and modelling of flexural behaviour of continuous fibre-reinforced lightweight aggregate concrete one-way slab at ambient and elevated temperatures

An experimental study on the flexural behaviour of six fibre-reinforced lightweight aggregate concrete (FRLWAC) one-way slab strips under ambient and elevated temperatures is presented in this paper. Two slabs, one simply-supported and one continuous, were loaded to failure at ambient temperature as references for the fire tests, while another simply-supported and three continuous slabs with varying degrees of design moment redistribution were loaded and exposed to elevated temperatures until failure. The ambient tests showed that the steel fibre addition prevents premature flexural-compression failure commonly observed in lightweight aggregate concrete structures. The rotations of FRLWAC plastic hinges were concentrated in a single crack under ambient temperature and a few cracks under fire exposure. The fire tests revealed significant moment redistribution towards the hogging moment area in the continuous slabs due to restrained thermal-induced deflection. Furthermore, the reinforcement configuration that catered for moment redistribution towards the hogging area was found to enhance the fire resistance of continuous FRLWAC slabs. A fibre-reinforced concrete (FRC) plastic hinge model, based on the rigid-body rotation concept, was proposed and validated. This model predicts the moment-rotation behaviour of FRC hinges at ambient temperature and the fire resistance of FRLWAC one-way slabs with good accuracy.

Deformation microstructures of blueschists in Alpine Corsica, France, and implications for seismic anisotropy and the low-velocity layer in subducting oceanic crust

Understanding the deformation microstructures and seismic properties of blueschists is important for interpreting the seismic anisotropy at the top of subducting oceanic crust. The deformation microstructures and seismic properties of epidote blueschist, epidote-lawsonite blueschist, and lawsonite blueschist from Alpine Corsica, France, were studied using electron backscatter diffraction mapping and transmission electron microscopy. The crystal-preferred orientations (CPOs) of glaucophane show a strong maximum of the [001] axes aligned sub-parallel to the lineation. The maximum of the (010) poles of epidote is aligned sub-parallel to the lineation. The [001] axes of lawsonite are strongly aligned sub-normal to the foliation. Intracrystalline misorientation, dislocation, and occasional fragmentation of glaucophane indicate that glaucophane CPO was developed mainly by dislocation creep. The intracrystalline deformation features of epidote, such as subgrain boundaries and dislocations, indicate that the CPO of the epidote was formed by dislocation creep. In contrast, our data indicate that lawsonite CPO was developed by a combination of rigid-body rotation and dislocation creep with a minor effect of twinning. The P-wave anisotropy (AVp) and maximum S-wave anisotropy (max.AVs) of epidote blueschists (AVp = 12.3–16.9% and max.AVs = 6.53–11.75%) are higher than those of lawsonite blueschists. The seismic velocities of the blueschists are lower than those of mantle peridotites. The coexistence of epidote and lawsonite in the blueschist results in variations in seismic anisotropy and P-wave velocity in the whole rock, depending on the modal content of epidote and lawsonite. A high content ratio of epidote to lawsonite in blueschist produces strong P- and S-wave anisotropies of blueschist when the glaucophane content is more than ∼50%. The P-wave velocity of blueschist decreases proportionally with increasing epidote content. Our results indicate that the seismic properties of deformed blueschists contribute to the seismic anisotropy and the low-velocity layer in subducting oceanic crusts in subduction zones.

Investigating the dispersion characteristics of symmetric and asymmetric modes in rails: A theoretical and experimental study

The propagation law of ultrasonic guided waves in waveguide structures is determined by their dispersion characteristics, and the number of guided waves in symmetric and antisymmetric modes in rails is significant, so the dispersion characteristics are very complex. In order to study the dispersion characteristics of symmetric and antisymmetric modes in rails, this paper derives the wave equation based on the SAFE method with higher order elements, and the correctness of the wavestructure calculation in the SAFE model is verified using the FE method. This paper focuses on the wavestructure state at 0 kHz and the wavestructure changes during mode crossing through and repulsive deflections, and for the first time experimentally verifies the phenomenon of wave structure exchange in rails. The main conclusions are that the dispersion curves between modes with the same symmetry show repulsive deflection, and the dispersion curves between modes with opposite symmetry show crossover; the wavestructure of the rail is mainly rigid body translation and rigid body rotation at frequencies close to 0 kHz; the guided wave at the intersection of symmetric and antisymmetric modes transforms into a fading wave that cannot be continuously propagated in rails; when the dispersion curves are close, the wavestructures between the two modes are linearly superimposed, and when the dispersion curves are deflected by repulsion, the wavestructures of the two modes are exchanged.

Spectral energy transfer analysis of a forced homogeneous isotropic turbulence using triple decomposition of velocity gradient tensor

Triple decomposition of the velocity gradient tensor is exploited to investigate the role of the simple-shear, normal-strain, and rigid-body rotation, in the turbulent kinetic energy transfer of a forced, high-Reynolds-number homogeneous isotropic turbulent flow. Splitting the total energy flux into three elementary partial fluxes shows that the rigid-body rotation has a secondary contribution to turbulent kinetic energy transfer, while within 80% of the total energy flux is produced through the simple-shear and normal-strain processes. Energy is dominantly extracted through the shearing process from larger motion scales and injected into smaller scales by the normal-straining process. In addition, each partial energy flux contains a strong conservative part and a weak non-conservative part. Besides the total kinetic energy transfer, all partial energy fluxes also show scale-invariance behaviour over the inertial subrange. Statistically, total energy flux shows a strong correlation with the simple-shear and normal-strain processes. However, the relatively poor correlation between these two dominant processes, implies a fairly low efficiency for turbulent kinetic energy transfer. These results can provide new insights into sub-grid scale turbulence modelling based on the physical mechanism of simple-shear and normal-strain processes.

A Novel Enhanced Torsional Eddy Current Damper for Fixed-Axis Rotation Control of Rigid Bodies

The control of angular velocities in the fixed-axis rotation of rigid bodies is crucial for ensuring the safety and functionality of civil structures and mechanical systems. In this research, a novel enhanced torsional eddy current damper (ETECD) is proposed to effectively control the angular velocities of rigid bodies within confined installation spaces. At first, an estimation approach is developed to determine the damping coefficient of the eddy current damper (ECD) within limited installation space. Furthermore, we utilize a gearbox to enhance the damping performance of the ECD in confined spaces. To establish the framework for the design of the proposed ETECD, the motion equation and solution of the rotating body are derived. By analytically presenting the approximate solution for the responses of a rotating body with a torsional viscous damper, the required range of the torsional damping coefficient is derived. This range ensures compliance to velocity restrictions under linearly angle-related torques, guiding the design of the ETECD. The ETECD, comprising two cylindrical torsional eddy current dampers (ECDs) and a motion-amplified gearbox, is designed and tested for a rotating body. Numerical examples and experimental tests are carried out to validate the performance of the proposed ETECD. The calculated damping coefficients and predicted control performance in the numerical examples agree well with the experimental results. Notably, under the minimum and maximum torques, the terminal angular velocity (TAV) of the rotating body can be significantly reduced by 70.76% and 58.99%, respectively. The proposed work emphasizes the potential of the ETECD as an effective and economic method in reducing angular velocities for rotating bodies.

Investigation of neighboring grain effects on load shedding in titanium alloys under cold dwell fatigue

Load shedding under cold dwell fatigue in titanium alloys has been a threat to the safety of the aero-engine since it is responsible for crack formation. The strain incompatibility between the soft-hard grain pair arises from the significant creep in the soft grain during the dwell period, which is fundamentally related to the load shedding. Such deformational heterogeneity is not only affected by the soft-hard grain itself but also by its neighboring grains, but the effect of the latter is rarely reported. In this paper, the effect of neighboring grains, including location, crystal orientation, texture, etc., on load shedding is quantitatively investigated using a three-dimensional rate-dependent crystal plasticity model by controlling the microstructural morphology of the grains. In particular, the mechanism that the dwell fatigue cracks tend to nucleate from the sample's interior rather than the free surface is revealed. Restriction of rigid body rotation from neighboring grains can further enhance load shedding. The crystal orientation of individual and group neighboring grains sitting at different locations with respect to the soft-hard grain pair is evaluated. The grain directly attached to the hard grain has the strongest influence. The statistics of load shedding are analyzed by conducting hundreds of simulations with different textures. Stronger textures are found to be able to enhance load shedding and thus deteriorate the service lifetime. The change of locations showing the highest stress during the dwell period arising from plastic deformation in neighboring grain may lead to the phenomenon of reverse load shedding. Understanding the neighboring grain effects from both the mechanistic basis and the statistical point of view is important in integrity evaluations and service life assessments of titanium components in aero-engines.

A unified bond–based peridynamic model without limitation of Poisson's ratio

The issue of fixed Poisson's ratio is a critical problem plaguing bond–based peridynamic (BB–PD) models. The popular approach of introducing the bond's tangential stiffness cannot completely remove Poisson's ratio limitation, but instead leads to some additional troubles, such as negative tangential stiffness and bond force density misalignment in finite rigid body rotation problems. To address the issue of fixed Poisson's ratio thoroughly, a unified bond–based peridynamics (UPD) was originally proposed. In the proposed model, a novelty pairwise force density function has been developed, in which dilatation and distortion are distinguished, and the model assigns different stiffnesses to the two deformation components. Arbitrary and reasonable values of Poisson's ratio can be achieved by adjusting the PD parameters that control the bulk and shear moduli of the material. The theoretical range of Poisson's ratio in the proposed model is (-1, 0.5], which is consistent with those in continuum mechanics. In addition, the absence of tangential stiffness prevents the proposed model from misalignment of bond force density due to rigid body rotation. Several numerical examples, including four two–dimensional and three–dimensional deformation analyses and three quasi–static fracture analyses, were implemented to verify the accuracy and reliability of the proposed model. The results show that the proposed model can accurately simulate the elastic properties of the material and obtain the deformation with high accuracy. The numerical examples also demonstrate the fracture prediction capability of the proposed model.

Two circular incompressible liquid inclusions

AbstractWe apply Muskhelishvili's complex variable method to solve the plane strain problem associated with two circular incompressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to uniform remote in‐plane normal stresses. An analytical solution to the problem is derived primarily with the aid of conformal mapping and analytic continuation. To demonstrate our analytical solution, we present detailed numerical results characterizing the internal uniform hydrostatic stresses within the two liquid inclusions, the nonuniform hoop stresses along the two circular liquid‐solid interfaces on the matrix side and the nonuniform rigid body rotations within the two circular liquid inclusions.