Fracture behavior of sandstone with partial filling flaw under mixed-mode loading: Three-point bending tests and discrete element method

The fracture behavior of natural fracture in the geological reservoir subjected to filling property,affects the crack initiation and propagation under stress perturbation.Partial filling flaws were intermediate between open fractures and filled fractures,the fracture response may be worth exploring.In this work,the effect of the filling property of sandstone with partial filling flaws on the fracture behavior was systematically investigated based on three-point bending tests and the numerical approach of discrete element method(DEM).In the laboratory,semi-circular three-point bending tests were carried out with partial filling flaws of various filling strengths.Based on this,numerical simulations were used to further investigate the effect of the filling ratio and the inclination of the partial filling flaw on the mechanical and fracture responses,and the effect of the partial filling flaw under mixed-mode loading on the fracture mechanism was elucidated coupled with acoustic emission(AE)characteristics.The obtained results showed that the increase in filling strength and filling ratio of partial filling flaw led to an increase in peak strength,with a decreasing trend in peak strength with the inclination of partial filling flaw.In terms of crack propagation pattern,the increasing filling strength of the partial filling flaw induced the transformation of the fracture mechanism toward deflection,with a tortuosity path,while the filling ratio and inclination of partial filling flaw led to fracture mechanism change from deflection to penetration and attraction,accompanied with a larger AE event source in filler.Accordingly,the b-value based on the Gutenberg-Richter equation fluctuated between 5 and 4 at low filling ratio and inclination and remained around 5 at high filling ratio and inclination of partial filling flaw.Related results may provide an application prospective for reservoir stimulation using the natural fracture system.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

Mixed-mode fast-slow oscillations in the frequency switching Duffing system with a 1:n frequency ratio

Sliding fast-slow oscillations are interesting oscillation patterns discovered recently in the Duffing system with frequency switching.Such oscillations have been obtained with a fixed 1:2 low frequency ratio in the previous work.The present paper aims to explore composite fast-slow dynamics when the frequency ratio is variable.As a result,a novel route to composite fast-slow dynamics is obtained.We find that,when presented with variable frequency ratios in a 1:n fashion,the sliding fast-slow oscillations may turn into the ones characterized by the fact that the clusters of large-amplitude oscillations of relaxational type are exhibited in each period of the oscillations,and hence the mixedmode fast-slow oscillations.Depending on whether the transition of the trajectory is from the upper subsystem via the fold bifurcation or not,these interesting oscillations are divided into two classes,both of which are investigated numerically.Our study shows that,when the frequency ratio n is increased from n=3,newly created boundary equilibrium bifurcation points may appear on the original sliding boundary line,which is divided into smaller parts,showing sliding and downward crossing dynamical characteristics.This is the root cause of the clusters,showing large-amplitude oscillations of relaxational type,resulting in the formation of mixed-mode fast-slow oscillations.Thus,a novel route to composite fast-slow dynamics by frequency switching is explained.Besides,the effects of the forcing on the mixed-mode fast-slow oscillations are explored.The magnitude of the forcing frequency may have some effects on the number of large-amplitude oscillations in the clusters.The magnitude of the forcing amplitude determines whether the fast-slow characteristics can be produced.

A modified 3D mean strain energy density criterion for predicting shale mixed-mode Ⅰ/Ⅲ fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing.The edge-notched disk bending(ENDB)specimens are employed to measure the entire range of mixed-modeⅠ/Ⅲfracture toughness of Longmaxi shale.To theoretically interpret the fracture mechanisms,this research first introduces the detailed derivations of three established fracture criteria.By distinguishing the volumetric and distortional strain energy densities,an improved three-dimensional mean strain energy density(MSED)criterion is proposed.As the critical volumetric to distortional MSED ratio decreases,the transition from tensiondominated fracture to shear-dominated fracture is observed.Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I(i.e.,tension)to pure modeⅢ(i.e.,torsion or tearing)since mode-Ⅲcracking happens in a twisted manner and mode-Ⅰcracking occurs in a coplanar manner.The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing.The average ratio of pure mode-Ⅲfracture toughness to pure mode-Ⅰfracture toughness is 0.68,indicating that the obtained mode-Ⅲfracture resistance for a tensionbased loading system is apparent rather than true.Compared to the three mainstream fracture criteria,the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-modeⅠ/Ⅲfracture toughness of distinct materials and loading methods.

A New Clustering-Based Partitioning Method for VLSI Mixed-Mode Placement

An efficient partitioning algorithm for mixed-mode placement,extended-MFFC-based partitioning,is presented.It combines the bottom-up clustering and the top-down partitioning together.To do this,designers can not only cluster cells considering logic dependency but also partition them aiming at min-cut.Experimental results show that extended-MFFC-based partitioning performs well in mixed-mode placement with big pre-designed blocks.By comparison with the famous partitioning package HMETIS,this partitioning proves its remarkable function in mixed-mode placement.

Adsorption behaviors of avian immunoglobulins and purification of immunoglobulin Y from chicken serum with mixed-mode resins

The importance of immunoglobulin Y(IgY) as a specific antibody equivalent to mammalian immunoglobulin G(IgG) is well recognized. However, production of highly purified IgY is still difficult due to the lack of specific purification methods. In this study, adsorption behaviors of Ig Y on four mixed-mode resins with functional ligands of 4-mercatoethyl-pyridine(MEP), 2-mercapto-1-methyli-midazole(MMI), 5-aminobenzi-midazole(ABI) and tryptophan-5-aminobenzi-midazole(W-ABI) were evaluated. The results showed that high adsorption ratio were found at p H 6.0–7.0 with little adsorption under acidic conditions. The resin with ABI ligand was then used to separate IgY from immunized chicken serum. An efficient process with Ig Y purity of 95% and recovery of 90% was developed after optimization of loading and elution p H and injection volume. The biological activity of the purified Ig Y was fully maintained. These results indicated that mixed-mode chromatography with specially-designed ligands has great potential for the separation of Ig Y from crude feedstock.

Preparation and evaluation of mixed-mode resins with tryptophan analogues as functional ligands for human serum albumin separation

Five tryptophan analogues with a hydrophobic indole ring and an amino group on each molecule were used as functional ligands of mixed-mode resins for human serum albumin(HSA) purification. Their adsorption performance was evaluated and the effects of p H and salt addition on HSA adsorption were studied. The resins prepared showed typical p H-dependent adsorption and the highest adsorption capacity and affinity were found at pH 5.0for all the resins tested. The saturated adsorption capacity was 138.02 mg·g^(-1)with the tryptaminefunctionalized resin, which significantly decreased at p H below 4.0 due to electrostatic repulsion between ligands and HSA. Moreover, the addition of Na Cl or(NH_4)_2SO_4in media reduced HSA adsorption capacity, although the two salts showed different affecting profiles. The tryptamine-functionalized resin showed the best salt-tolerant performance, and its high adsorption capacity was maintained under high salt concentrations. In addition, the five resins prepared showed good adsorption selectivity for recombinant HSA from Pichia pastoris broth. Molecular docking results between tryptamine and HSA indicated that tryptamine was favorable to bind on Site II(indole-binding site) of HSA.

Development of X-FEM methodology and study on mixed-mode crack propagation

The extended finite element method（X-FEM） is a novel numerical methodology with a great potential for using in multi-scale computation and multi-phase coupling problems. The algorithm is discussed and a program is developed based on X-FEM for simulating mixed-mode crack propagation. The maximum circumferential stress criterion and interaction integral are deduced. Some numerical results are compared with the experimental data to prove the capability and efficiency of the algorithm and the program. Numerical analyses of sub-interfacial crack growth in bi-materials give a clear description of the effiect on fracture made by interface and loading condition.

Mixed-mode fracture behavior in deep shale reservoirs under different loading rates and temperatures

In the last years,shale gas has gradually substituted oil and coal as the main sources of energy in the world.Compared with shallow shale gas reservoirs,deep shale is characterized by low permeability,low porosity,strong heterogeneity,and strong anisotropy.In the process of multi-cluster fracturing of horizontal wells,the whole deformation process and destruction modes are significantly influenced by loading rates.In this investigation,the servo press was used to carry out semi-circular bend(SCB)mixedmode fracture experiments in deep shales(130,160,190℃)with prefabricated fractures under different loading rates(0.02,0.05,0.1,0.2 mm/min).The fracture propagation process was monitored using acoustic emission.The deformation characteristics,displacementeload curve,and acoustic emission parameters of shale under different loading rates were studied during the mixed-mode fracture propagation.Our results showed that during the deformation and fracture of the specimen,the acoustic emission energy and charge significantly increased near the stress peak,showing at this point the most intense acoustic emission activity.With the increase in loading rate,the fracture peak load of the deep shale specimen also increased.However,the maximum displacement decreased to different extents.With the increase in temperature,the effective fracture toughness of the deep shale gradually decreased.Also,the maximum displacement decreased.Under different loading rates,the deformation of the prefabricated cracks showed a nonlinear slow growthelinear growth trend.The slope of the linear growth stage increased with the increase in loading rate.In addition,as the loading rate increased,an increase in tension failure and a decrease in shear failure were observed.Moreover,the control chart showing the relationship between tension and the shear failure under different temperatures and loading rates was determined.

Stabilization of Networked Control Systems Using a Mixed-Mode Based Switched Delay System Method

The phenomenon of mixed-mode is one of the most important characteristics of switched delay systems. If a networked control system(NCS) with network induced delays and packet dropouts(NIDs & PDs) is recast as a switched delay system, it is imperative to consider the effects of mixed-modes in the stability analysis for an NCS. In this paper, with the help of the interpolatory quadrature formula and the average dwell time method, stabilization of NCSs using a mixed-mode based switched delay system method is investigated based on a novel constructed Lyapunov-Krasovskii functional. With the Finsler's lemma, new exponential stabilizability conditions with less conservativeness are given for the NCS. Finally, an illustrative example is provided to verify the effectiveness of the developed results.

MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL

A meshless method integrated with linear elastic fracture mechanics(LEFM)is presented for 2D mixed-mode crack propagation analysis.The domain is divided automatically into sub-domains based on Voronoi cells,which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path.For each increment of the crack extension,the meshless method is applied to carry out a stress analysis of the cracked structure.The J-integral,which can be decomposed into mode Ⅰ and mode Ⅱ for mixed-mode crack,is used for the evaluation of the stress intensity factors(SIFs).The crack-propagation direction,predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method.The meshless results agree well with the experimental ones,which validates the accuracy and efficiency of the method.

FATIGUE GROWTH MODELING OF MIXED-MODE CRACK IN PLANE ELASTIC MEDIA

This paper presents an extension of a displacement discontinuity method with cracktip elements （a boundary element method） proposed by the author for fatigue crack growth analysis in plane elastic media under mixed-mode conditions. The boundary element method consists of the non-singular displacement discontinuity elements presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or right crack-tip element is placed locally at the corresponding left or right crack tip on top of the non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the maximum circumferential stress criterion. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the numerical approach. Crack growth is modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characteristics of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the fatigue growth process of cracks emanating from a circular hole in a plane elastic plate is simulated using the numerical simulation approach.

A 90° mixed-mode twisted nematic liquid-crystal-on-silicon with an insulating protrusion structure

A 90°mixed-mode twisted nematic liquid-crystal-on-silicon(90°-MTN LCoS) with protrusion located between the adjacent pixels is proposed to reduce the effect of fringing field. The influence of the protrusion with different widths from0.5 μm to 0.9 μm and different heights from 0.3 μm to 0.7 μm is investigated. The results demonstrate that the invalid pixel region width can be reduced by 31.5% via using the protrusion with the suitable width and height compared with no protrusion case, which provides a higher display quality, such as the higher reflectance and contrast ratio.

Characteristic Tensor for Evaluation of Singular Stress Field Under Mixed-Mode Loadings

A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain radius.It possesses the original stress tensor characteristics and has a simple relationship with conventional fracture-mechanics parameters.Therefore,it can be used to estimate stress intensity factors(SIFs)for cracks of arbitrary shape subjected to multiaxial stress loads.A characteristic tensor can also be used to estimate SIFs for kinked cracks.This study examines the relation between a characteristic tensor and SIFs to demonstrate the correlation between the characteristic tensor and fracture-mechanics parameters.Consequently,a single straight crack and a kinked crack of finite length existing in a twodimensional,infinite isotropic elastic body in a plane stress state,were considered to investigate the properties of the characteristic tensor under mixed-mode loadings.To demonstrate the practical utility of the characteristic tensor,the stress distribution obtained through finite element analysis(FEA)was used to estimate mixed-mode SIFs,and the values of estimated SIFs were compared with those obtained using an analytical solution.Results demonstrate that SIFs estimated under mixed-mode loadings exhibit a good agreement with the analytical values.This indicates that the proposed characteristictensor-based approach is effective in extracting features of singular stress fields at crack tips,and can be employed to estimate values of fracture-mechanics parameters,such as SIFs.Owing to its simplicity,the proposed approach can be easily incorporated in commercial FE codes for practical applications to simulate the crack-growth problem under both static and dynamic loading scenarios.The excellent applicability of the characteristic tensor greatly contributes to efficiency of the design process in industries.

Autonomous Development Strategies for College English Teachers in a Mixed-mode Learning Community

At present,the improvement of the quality of higher education and the improvement of the professional ability and comprehensive quality of college students all depend on the education level and discipline professional ability of teachers in colleges and universities.In the new era of educational reform and development,university teachers also need to continuously learn and progress in order to adapt to changes in the educational environment and the update of the knowledge system.Nowadays,the construction and development of the mixed-mode learning community environment is becoming one of the effective ways for college teachers to improve their learning.From the perspective of the significance of autonomous development of college English teachers in the context of mixed-mode learning community,the current situation and other issues,this article expounds the strategies that promote the autonomous development of college English teachers in the context of mixed-mode learning community to improve the professional quality of college English teachers.

A new mixed-mode phase-field model for crack propagation of brittle rock

Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.

A Mixed-Mode Biquad Employing OTAs and Grounded Capacitors

This paper introduces a mixed-mode biquad employing OTAs （operational trans-conductance amplifiers） and grounded capacitors. The circuit can perform mixed-mode operation by selecting the input and output terminals. Additionally, the circuit enables low-pass, band-pass, high-pass, band-stop and all-pass transfer functions suitably choosing the input terminals. The circuit parameters ω0 and Q can be tuned orthogonally through adjusting the trans-conductance gains of the OTAs. The biquad enjoys very low sensitivities with respect to the circuit active and passive components. The achievement examples are given together with simulation results by PSPICE.

A DVCC-Based Mixed-Mode Biquadratic Circuit

This paper introduces a mixed-mode biquadratic circuit employing DVCCs （differential voltage current conveyors） and grounded passive components. The biquadratic circuit can perform mixed-mode operation selecting the input and output terminals. And the circuit enables LP （low-pass）, BP （band-pass）, HP （high-pass）, BS （band-stop） and AP （all-pass） transfer functions by suitably choosing the input terminals. The circuit parameters o30 and Q can be tuned orthogonally through adjusting the passive components. The biquadratic circuit enjoys very low sensitivities with respect to the circuit components. The achievement example is given together with simulation results by PSPICE.

The Al_(2)O_(3)and Mn/Al_(2)O_(3)sorbents highly utilized in destructive sorption of NF_(3)

NF_(3)is commonly used as an etching and cleaning gas in semiconductor industry,however it is a strongly greenhouse gas.Therefore,the destruction of disposal NF_(3)is an urgent task to migrate the greenhouse effect.Among the technologies for NF_(3)abatement,the destructive sorption of NF_(3)over metal oxides sorbents is an effective way.Thus,the search for a highly reactive and utilized sorbent for NF_(3)destruction is in great demand.In this work,AlOOH supported on carbon-sphere(AlOOH/CS)as precursors were synthesized hydrothermally and heat-treated to prepare the Al_(2)O_(3)sorbents.The influence of AlOOH/CS hydrothermal temperatures on the reactivity of derived Al_(2)O_(3)sorbents for NF_(3)destruction was investigated,and it is shown that the Al2O3 from AlOOH/CS hydro-thermalized at 120℃is superior to others.Subsequently,the optimized Al_(2)O_(3)was covered by Mn(OH)x to prepare Mn/Al_(2)O_(3)sorbents via changing hydrothermal temperatures and Mn loadings.The results show that the Mn/Al_(2)O_(3)sorbents are more utilized than bare Al_(2)O_(3)in NF_(3)destructive sorption due to the promotional effect of Mn_(2)O_(3)as surface layer on the fluorination of Al_(2)O_(3)as substrate,especially the optimal 5%Mn/Al2O3(160℃)exhibits a utilization percentage as high as 90.4%,and remarkably exceeds all the sorbents reported so far.These findings are beneficial to develop more efficient sorbents for the destruction of NF_(3).

Synthesis of highly reactive sorbent from industrial wastes and its CO_2 capture capacity

A kind of industrial solid waste, i.e., carbide slag, was used as CaO precursor to synthesize CO2 sorbent. The highly reactive synthetic sorbent was prepared from carbide slag, aluminum nitrate hydrate and glycerol water solution by the combustion synthesis method. The results show that the synthetic sorbent exhibits a much higher CO2 capture capacity compared with carbide slag. The CO2 capture capacity and the carbonation conversion of the synthetic sorbent are 0. 38 g/g and 0. 70 after 50 cycles, which are 1.8 and 2. 1 times those of carbide slag. The average carbonation conversion and the CO2 capture efficiency of the synthetic sorbent are higher than those of carbide slag with the same sorbent flow ratios. The required sorbent flow ratios are lower for synthetic sorbent to achieve the same CO2 capture efficiency compared with carbide slag. With the same sorbent flow ratio and CO2 capture efficiency, the energy requirement in calciner for the synthetic sorbent is less than that for carbide slag.