Orthogonal basic deformation mode method for zero-energy mode suppression of hybrid stress elements

A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.

DEFORMATION RIGIDITY OF ASSUMED STRESS MODES IN HYBRID ELEMENTS

The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.

Influence factors on the seismic behavior and deformation modes of gravity retaining walls

This study investigated the influence factors on the seismic response and deformation modes of retaining walls using large-scale model shaking table tests. Experimental results showed that the distribution of peak seismic earth pressures along the height of a wall was a single peak value curve. The seismic earth pressures on a gravel soil retaining wall were larger than the pressures on the weathered granite and quartz retaining walls. Also, the peak seismic earth pressure increased with increases in the peak ground acceleration and the wall height. The measured seismic active earth pressures on a rock foundation retaining wall were larger than the calculated values, and the action position of resultant seismic pressure was higher than 0.33 H. In the soil foundation retaining wall, the measured seismic earth pressures were much smaller than the calculated values, while the action position was slightly higher than 0.33 H. The soil foundation retaining wall suffered base sliding and overturning under earthquake conditions, while overturning was the main failure mode for the rock foundation retaining walls.

Relationships between In SAR Seismic Deformation and Fault Motion Sense,Fault Strike,and Ascending/Descending Modes

Based on the working principle of satellite radars, the earthquake deformation field measured by interferometric synthetic aperture（InSAR） is the projection of ground displacement associated with the seismogenic fault in the line of sight（LOS） of the satellite. However, LOS projections are complex, and are not only related to the ascending/descending modes and incidence angles of SAR data, but also related to the strike and motion senses of the fault. Even for the same earthquake, the LOS deformation derived from different ascending/descending data can be almost identical in one case, but quite different in another case, which makes the interpretation of InSAR seismic deformation and its comparison with field observations difficult. In this study, we undertook a quantitative analysis of the relationships between LOS observation sensitivity of InSAR and fault strike, fault motion sense, and ascending/descending modes, as well as 3D deformation fields. We studied the features and differences of the LOS deformation fields in different types of earthquakes using ascending/descending modes, with a particularly detailed analysis of the relations for a strikeslip type of earthquake. We also summarized the characteristics of LOS deformation fields of faults with different strikes and optimal observational data modes. Taking the strike-slip Yushu earthquake and the normal Gaize event as examples, we used SAR data of the ascending/descending modes to verify the results of quantitative calculations. These analyses will not only provide a more reasonable interpretation of InSAR seismic deformation fields and but also help understand the differences of seismic deformation fields revealed by data with different observational modes, therefore promoting the application of InSAR technology in seismology.

Deformation and failure modes of composite foundation with sub-embankment plain concrete piles

With the development of high-speed railway in China, composite foundation with rigid piles has become a stamdard solution of meeting the high requirements of stability and post-construction settlement of embankment on soft subgrade. Among several im- provement pattems, plain concrete piles have been extensively used to treat soft ground supported embankment. To investigate the deformation and failure modes of unimproved soft ground and soft ground reinforced by sub-embankment plain concrete piles, and to learn the influences of track and vehicle load, the effect of pile spacing, as well as the compression moduli of soil layers and upper load condition on the failure modes, a series of centrifuge model tests were performed. Test results indicate that the dis- placement of unimproved soft ground under the embankment increases continuously as embankment, track and train loading, and slip circle failure takes place. The deformation law of soft ground reinforced by sub-embankment plain concrete piles depends on pile spacing, compression modulus of the soft ground, and loading conditions. It was also found that plain concrete piles show displacement and failure patterns depending on its location, compression modulus of soft soil around the pile, and loading condi- tions. Furthermore, the evaluation of improved ground stability as well as the model test procedure is also presented.

Comparison of large deformation failure control method in a deep gob-side roadway: A theoretical analysis and field investigation

Under the dual influence of the mining disturbance of the previous working face and the advanced mining of the working face,the roadway is prone to large deformation,failure,and rockburst.Roadway stabilization has always significantly influenced deep mining safety.In this article we used the research background of the large deformation failure roadway of Fa-er Coal Mine in Guizhou Province of China to propose two control methods:bolt-cable-mesh+concrete blocks+directional energy-gathering blasting(BCM-CBDE method)and 1st Generation-Negative Poisson’s Ratio(1G NPR)cable+directional energy-gathering blasting+dynamic pressure stage support(πgirder+single hydraulic prop+retractable U steel)(NPR-DEDP method).Meantime,we compared the validity of the large deformation failure control method in a deep gob-side roadway based on theoretical analysis,numerical simulations,and field experiments.The results show that directional energy-gathering blasting can weaken the pressure acting on the concrete blocks.However,the vertical stress of the surrounding rock of the roadway is still concentrated in the entity coal side and the concrete blocks,showing a’bimodal’distribution.BCM-CBDE method cannot effectively control the stability of the roadway.NPR-DEDP method removed the concrete blocks.It shows using the 1G NPR cable with periodic slipping-sticking characteristics can adapt to repeated mining disturbances.The peak value of the vertical stress of the roadway is reduced and transferred to the deep part of the surrounding rock mass,which promotes the collapse of the gangue in the goaf and fills the goaf.The pressure of the roadway roof is reduced,and the gob-side roadway is fundamentally protected.Meantime,the dynamic pressure stage support method withπgirder+single hydraulic prop+retractable U steel as the core effectively protects the roadway from dynamic pressure impact when the main roof is periodically broken.After the on-site implementation of NPR-DEDP method,the deformation of the roadway is reduced by more than 45%,and the deformation rate is reduced by more than 50%.

Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures

Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption(SEA)capacity.In this paper,square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption(EA)performance.Finite element(FE)simulations of in-plane compression are carried out,and the theoretical models from the energy balance principle are developed for calculating the EA of these lattice structures.Satisfactory agreement is achieved between the FE simulation results and the theoretical results.It indicates that the 30◦oriented lattice has the largest EA capacity.Furthermore,inspired by the polycrystal microstructure of metals,novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together.The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts.This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.

Effect of Vibrational Modes on Sand Pressure and Pattern Deformation in the EPC Process

During the EPC (expendable pattern casting) process, one of the essential requirements is to prevent pattern distortion duringsand filling and compaction. A new method which vibrates the system in a two-dimensional circular mode has been appliedto the EPC process. The molding properties of unbonded sand obtained by this new vibration mode are investigated andcompared with those in the one-dimensional vertical mode. For adequate compaction of sand. the circular vibration mode ismore effective than the vertical mode. Sand became more fluidized by the circular vibration and the particle pressure coefficientwas close to unity The particle pressure coefficient, which is defined as the ratio of horizontal to vertical sand pressure, isresponsible for the effectiveness of sand filling.

The Continuum Stored Energy for Constitutive Modeling Finite Deformations of Polymeric Materials

With symmetries measured by the Lie group and curvatures revealed by differential geometry, the continuum stored energy function possesses a translational deformation component, a rotational deformation component, and an ellipsoidal volumetric deformation component. The function, originally developed for elastomeric polymers, has been extended to model brittle and ductile polymers. The function fits uniaxial tension testing data for brittle, ductile, and elastomeric polymers, and elucidates deformation mechanisms. A clear distinction in damage modes between brittle and ductile deformations has been captured. The von Mises equivalent stress has been evaluated by the function and the newly discovered break-even stretch. Common practices of constitutive modeling, relevant features of existing models and testing methods, and a new perspective on the finite elasticity-plasticity theory have also been offered.

Rear-Surface Deformation of a Water Drop in Aero-Breakup of Shear Mode

Deformation of water drops in shock-induced high-speed flows is investigated with a focus to the influence of primitive flow parameters on the rear-surface deformation features. Two typical deformation patterns are discovered through high-speed photography. A simple equation to evaluate the radial acceleration of the drop surface is derived. The combined use of this equation and outer flow simulation makes it possible for us to reconstruct the profiles of the early deformed drops. The results agree well with the experiments. Further analysis shows that the duration of flow establishment with respect to the overall breakup time shapes the rear side profile of the drop. Thereby the ratio of the two times, expressed as the square root of the density ratio, appears to be an effective indicator of the deformation features.

Effect of strain rate on the compressive deformation behaviors of lotus-type porous copper

Lotus-type porous copper was fabricated by unidirectional solidification, and compressive experiments were subsequently conducted in the strain rate range of 10-3-2400 s-1 with the compressive direction parallel to the pores. A GLEEBLE-1500 thermal-mechanical simulation system and a split Hopkinson pressure bar （SHPB） were used to investigate the effect of strain rate on the compressive deforma-tion behaviors of lotus-type porous copper. The influence mechanism of strain rate was also analyzed by the strain-controlling method and by high-speed photography. The results indicated that the stress-strain curves of lotus-typed porous copper consist of a linear elastic stage, a plateau stage, and a densification stage at various strain rates. At low strain rate （〈1.0 s^-1）, the strain rate had little influence on the stress-strain curves; but when the strain rate exceeded 1.0 s^-1, it was observed to strongly affect the plateau stage, showing obvious strain-rate-hardening characteristics. Strain rate also influenced the densification initial strain. The densification initial strain at high strain rate was less than that at low strain rate. No visible inhomogeneous deformation caused by shockwaves was observed in lotus-type porous copper during high-strain-rate deformation. However, at high strain rate, the bending deformation characteristics of the pore walls obviously differed from those at low strain rate, which was the main mechanism by which the plateau stress exhibited strain-rate sensitivity when the strain rate exceeded a certain value and exhibited less densification initial strain at high strain rate.

Improved method for zero-energy mode suppression in peridynamic correspondence model

The peridynamic correspondence model provides a general formulation to incorporate the classical local model and,therefore,helps to solve mechanical problems with discontinuities easily.But it suffers from zero-energy mode instability in numerical implementation due to the approximation of deformation gradient tensor.To suppress zero-energy modes,previous stabilized methods were generally more based on adding a supplemental force state derived from bond-based peridynamic theory,which requires a bond-based peridynamic micro-modulus.In this work,we present an improved stabilized method where the stabilization force state is derived directly from the peridynamic correspondence model.Hence,the bond-based peridynamic micro-modulus is abandoned.This improved method needs no extra constant to control the magnitude of stabilization force state and it is suitable for either isotropic or anisotropic materials.Several examples are presented to demonstrate its performance in simulating crack propagation,and numerical results show its efficiency and effectiveness.

Experimental analysis of crack tip fields in rubber materials under large deformation

A three-nested-deformation model is proposed to describe crack-tip fields in rubber-like materials with large deformation. The model is inspired by the distribution of the measured in-plane and out-of-plane deformation. The in- plane displacement of crack-tip fields under both Mode 1 and mixed-mode （Mode I-II） fracture conditions is measured by using the digital Moir6 method. The deformation character- istics and experimental sector division mode are investigated by comparing the measured displacement fields under differ- ent fracture modes. The out-of-plane displacement field near the crack tip is measured using the three-dimensional digital speckle correlation method.

Anisotropic cyclic deformation behavior of an extruded Mg-3Y alloy sheet with rare earth texture

Mg-RE(magnesium-rare earth)alloys exhibit pronounced in-plane anisotropy of mechanical response under quasi-static monotonic loading resulting from the RE texture,as extensively reported.In this work,an obvious in-plane anisotropy of cyclic deformation behavior was observed in an extruded Mg-3Y alloy sheet during strain-controlled tension-compression low-cycle fatigue(LCF)at room temperature.The extrusion direction(ED)samples displayed better fatigue resistance with almost symmetrical hysteresis loops and longer fatigue life compared with the transverse direction(TD)samples.The influences of texture on the deformation modes,cracking modes,and mechanical behavior of Mg-Y alloy sheets under cyclic loading were studied quantitatively and statistically.The activation of various slip/twinning-detwinning systems was measured at desired fatigue stages via EBSD observations together with in-grain misorientation axes(IGMA)analysis.The results indicate that the activation of deformation modes in the TD sample was featured by the cyclic transition,i.e.,prismatic slip(at the tensile interval)→{10–12}tension twinning(at the compressive reversal)→detwinning+prismatic slip(at the re-tensile reversal).In the case of the ED sample,the cyclic deformation was dominated by the basal slip throughout the fatigue life.For cracking modes,intergranular cracking and persistent slip bands(PSB)cracking were the primary cracking modes in the ED sample while the TD sample showed a high tendency of{10–12}tension twinning cracking(TTW cracking).The underlying mechanisms influencing the activation of various slip/twinning-detwinning systems,as well as cracking modes and cyclic mechanical behavior,were discussed.

Influence of stress path change on the resistance to plastic deformation of cold rolled sheets

Flat workpieces have been tested in order to investigate the influence of stress path change （loading mode） while keeping strain path unchanged. These investigations are pertinent to the testing of cold rolled strips and to subsequent forming. The workpieces which first compressed by plane strain compression in thickness direction were then tested in perpendicular direction in order to measure the influence of strain and stress path. The tension workpieces came from flat die compression test at different deformation histories. Two different materials were investigated： 18/8 Ti stainless steel and AW-1050 aluminium. The results show that the plastic flow by tension in lengthwise direction after pre-strain by compression in thickness direction will begin at an appreciably lower stress than that of the workpieces unloaded after pre-compression. Comparing with two materials, it can be seen that both 18/8 Ti stainless steel and AW-1050 aluminium behave similarly. The drop in yield stress is lower for AW-1050 aluminium than that for 18/8 Ti stainless steel. However, reloading in different directions than in the precious step results in significantly higher strain hardening.

Zero-energy modes in serially coupled double quantum dots

We investigate symmetrically coupled double quantum dots via the hierarchical equations of motion method and propose a novel zero-energy mode(ZEM) at a temperature above the spin singlet–triplet transition temperature. Owing to the resonance of electron quasi-particle and hole quasi-particle, ZEM has a peak at ω = 0 in the spectral density function.We further examine the effect of the magnetic field on the ZEM, where an entanglement of spin and charge has been determined;therefore, the magnetic field can split the ZEM in the spectra.

Polarization Characteristics of the Deformed Low-Mode Fiber Waveguides with Polarization Conservation

In this work the results of polarization researches of low-optical fiber waveguides with conservation of polarization are presented. Obtained results quite convincingly testify regarding a high sensitivity low-mode regime of work of an optical fiber to anisotropic external influences, in comparison with one-mode regime of work of the same fibre. This result, can represent a big practical value at the realization of high-sensitivity fiber-optical devices of different physical values.

含Y型组合节理花岗岩单轴压缩破坏机理及声发射特征

利用劈裂法在花岗岩试件中预制不同倾角的Y型组合节理,进行单轴压缩实验,分析组合节理倾角对破坏模式、峰值强度、表面变形场、声发射能量释放特征的影响,探究不同破坏模式下的破坏机理.实验结果表明:1)含Y型组合节理岩石随节理倾角变化呈现整体破坏、楔形体弹射破坏和沿主节理面破坏三种主要模式;2)组合节理夹角、主节理倾角均与岩石强度具有负相关关系;3)破坏模式从整体破坏转变到弹射破坏、沿主节理破坏时,滑移变形集中区域由次节理向主节理转变,AE高能级事件诱发原因由主、次节理压密及滑移错动向主节理压密及滑移错动转变;4)随主节理倾角的不断增大,主节理面上释放的能量更高、能量的分布更加不均匀.

联肢弯剪型钢板剪力墙抗震性能试验研究

联肢钢板剪力墙结构是将2片钢板剪力墙通过钢连梁连接形成的抗侧力结构。通过对1榀1/3缩尺的4层联肢弯剪型钢板剪力墙试件进行低周往复加载试验,从滞回曲线、骨架曲线、延性、承载力及刚度退化、耗能能力等方面研究了该结构体系的抗震性能,并且对试件的屈服顺序和变形模式进行了分析。结果表明:联肢钢板剪力墙试件的延性系数达到5.03,承载力退化系数均大于0.96,承载力和刚度退化稳定,等效黏滞阻尼系数达到0.25以上,表明联肢弯剪型钢板剪力墙具有优越的抗震性能。加载过程中,连梁先于墙板发生屈服,墙板先屈曲后屈服,此后柱脚和横梁相继屈服。连梁的引入改变了结构的屈服机制,提高了整体的延性和耗能能力,能够组成多道抗震防线,且试件整体最终也体现出合理的破坏机制。整体侧移曲线呈弯剪变形模式。该试验研究更加贴合实际工程中联肢钢板剪力墙结构的应用情况,为联肢钢板剪力墙结构的进一步研究和应用提供了试验基础。