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 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.

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.

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.

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.

Prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum

This study focuses on the analytical prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum considering the volumetric deformation modes of the soil above the tunnel crown.A series of numerical analyses is performed to examine the effects of cover depth ratio(C/D),tunnel volume loss rate(h t)and volumetric block proportion(VBP)on the characteristics of subsurface settle-ment trough and soil volume loss.Considering the ground loss variation with depth,three modes are deduced from the volumetric deformation responses of the soil above the tunnel crown.Then,analytical solutions to predict subsurface settlement for each mode are presented using stochastic medium theory.The influences of C/D,h t and VBP on the key parameters(i.e.B and N)in the analytical expressions are discussed to determine the fitting formulae of B and N.Finally,the proposed analytical solutions are validated by the comparisons with the results of model test and numerical simulation.Results show that the fitting formulae provide a convenient and reliable way to evaluate the key parameters.Besides,the analytical solutions are reasonable and available in predicting the subsurface settlement induced by shield tunnelling in sandy cobble stratum.

Analysis of granular assembly deformation using discrete element method

The discrete element method is used to simulate specimens under three different loading conditions（conventional triaxial compression,plane strain,and direct shear）with different initial conditions to explore the underlying mechanics of the specimen deformation from a microscale perspective.Deformations of specimens with different initial void ratios at different confining stresses under different loading conditions are studied.Results show that the discrete element models successfully capture the specimen deformation and the strain localization.Particle behaviors including particle rotation and displacement and the mesoscale void ratio distributions are used to explain the strain localization and specimen deformation.It is found that the loading condition is one of the most important factors controlling the specimen deformation mode.Microscale behavior of the granular soil is the driving mechanics of the macroscale deformation of the granular assembly.

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.

Assessment of the ballistic response of honeycomb sandwich structures subjected to offset and normal impact

In the present study,experimental and numerical investigations were carried out to examine the behavior of sandwich panels with honeycomb cores.The high velocity impact tests were carried out using a compressed air gun.A sharp conical nosed projectile was impacted normally and with some offset distance(20 mm and 40 mm).The deformation,failure mode and energy dissipation characteristics were obtained for both kinds of loading.Moreover,the explicit solver was run in Abaqus to create the finite element model.The numerically obtained test results were compared with the experimental to check the accuracy of the modelling.The numerical result was further employed to obtain strain energy dissipation in each element by externally running user-defined code in Abaqus.Furthermore,the influence of inscribe circle diameter and cell wall and face sheet thickness on the energy dissipation,deformation and failure mode was examined.The result found that ballistic resistance and deformation were higher against offset impact compared to the normal impact loading.Sandwich panel impacted at 40 mm offset distance required 3 m/s and 1.9 m/s more velocity than 0 and 20 mm offset distance.Also,increasing the face sheet and wall thickness had a positive impact on the ballistic resistance in terms of a higher ballistic limit and energy absorption.However,inscribe circle diameter had a negative influence on the ballistic resistance.Also,the geometrical parameters of the sandwich structure had a significant influence on the energy dissipation in the different deformation directions.The energy dissipation in plastic work was highest for circumferential direction,regardless of impact condition followed by tangential,radial and axial directions.

Quasi-static and dynamic plastic deformation behavior in titanium with vanadium addition

Compressive properties,microstructure features and deformation modes were investigated in binary Ti-(2,4,8)wt%V alloys during quasi-static(1×10^(-3)s^(-1))and dynamic(3×10^(3)s^(-1))compressions.The compressive behavior shows a strong dependence on the loading strain rate and vanadium content contained in pure Ti,such that the flow stress increases with the increase in strain rate and vanadium content ranging from 2 wt%to 8 wt%.The microstructure features are clearly different from each other for alloys with different vanadium contents or under quasi-static and dynamic loading conditions.An examination of deformation microstructures by optical microscopy and electron backscattered diffraction indicates that twinning behavior occurs during quasi-static and dynamic compressions and the twinning density increases with strain rate increasing but decreases with vanadium addition.The existence of{1012},{1121}and{1122}type twinning was further identified.With the help of the calculated Schmid factor map,the values of critical resolved shear stress of twinning types mentioned above have been obtained and verified to be rarely affected by the loading strain rate but sensitive to the vanadium content.In vanadium-rich alloys(Ti-8V),twins are rarely observed but dislocation slip mechanism is active by transmission electron microscopy investigations.With vanadium content increasing,both the critical resolved shear stress of twinning types and the content ofβphase with abundant slip systems increase,reflecting a suppression of twinning but an active dislocation slip mechanism.

Classification of inelastic deformation and material-intrinsic indices about mechanical performance of general solid matter

The present article is aimed to detect material-intrinsic indices that can be used to supervise the mechanical performance of general solid matter.The novelty carried in this article can be summarised as follows.Firstly,an inelastic deformation state of almost any solid matter can be treated as the combination of two fundamental modes due to different microscopic causation:Mode I inelastic distortion due to the movement of sliding types of defects and Mode II inelastic dilation due to the evolution of voids/bubbles.Secondly,each inelastic deformation mode is characterised by a single principal inelastic deformation descriptor(PIDD):Mode I by a newly introduced quantity of maximum distortional angle changeαand Mode II by the logarithm of dilating magnificationω.In particular,the concept of maximum distortional angle change gives rise to a geometrically intuitive yield criterion ofα>α_(c),which in situations of small deformation,is shown to asymptote von Mise's,and to become Tresca's in cases of plane stress.Thirdly,the deformation process of a solid matter under monotonic and ambient loads is formulated by means of trajectories of thermodynamic equilibria with respect to the PIDD pair.Then a pair of physical quantities which measure the stresses needed to change the local PIDD state are singled out.Being termed as inelastic deformation resistances(IDRs),these two quantities are shown to depend only on the onsite atomic configurations.It is also shown that key descriptive properties about the mechanical behaviours of materials,such as ductility,are encoded in IDRs as functions of PIDDs.Hence the IDR pair may serve as material performance indices that may be more intrinsic than conventional stress-strain relationships.

正/负泊松比的排斥效应诱导的复合水凝胶在低应变下的刚性响应

水凝胶作为承载组织的替代产品引起了广泛关注.然而,与能够通过有限的变形来承受复杂载荷的承载组织不同,传统的水凝胶由于其柔软的特性,无法在低应变状态下表现出刚性响应.基于承载组织的软硬组分之间的协同作用,我们设计了采用软基质(正泊松比)和硬框架(负泊松比)的复合水凝胶,其刚度分别比基质和框架高18.9和4.2倍.相反,结合软基质(正泊松比)和框架(正泊松比)的设计对刚度增强有限.通过有限元分析,揭示了软基质与框架之间正、负泊松比斥力作用的内在机理.本研究为今后设计基于软硬组分协同效应的复合水凝胶提供了思路.

Tailoring Texture to Highly Strengthen AZ31 Alloy Plate in the Thickness Direction via Pre-tension and Rolling-Annealing

Conventional wrought Mg alloys,such as AZ31 and ZK60 rolled plates,usually exhibit significantly low tensile yield strength in the thickness direction.This can be attributed to the high activity of{10-12}tension twinning due to the strong basal texture(<0001>//ND,normal direction).In this work,the tensile yield strength in the ND of the as-rolled(AR)AZ31 plate increased from 50 to 150 MPa(increased by 200%)via simple processing,i.e.,pre-tension and rolling-annealing(PTRA)treatment.The strong basal texture(<0001>//ND)of the AR plate was changed into a weakened fiber texture(<0001>⊥ND).The evolution of microstructures during PTRA treatment and the activated deformation modes during uniaxial tension were studied quantitatively and statistically by the means of intergranular misorientation(IM)and in-grain misorientation axes(IGMA)analysis.The results indicate that various twin variants,as well as{10-12}-{10-12}secondary twins,were activated during pre-tension and rolling,and most residual matrix was consumed by twins after annealing.The dominated deformation modes in tension changed from{10-12}tension twinning(the AR sample)to prismatic slip(the PTRA sample)in the early tensile deformation.The underlying formation mechanism of the fiber texture and corresponding strengthening mechanism were discussed.

Numerical Simulations of the Richtmyer-Meshkov Instability of Solid-Vacuum Interface

The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum is investigated by numerical simulation using a multi-material solid mechanics algorithm based on an Eulerian framework.The research efforts are directed to reveal the influence of the initial perturbation and material strength on the deformation of the perturbed interface impacted by an initial shock.By varying the initial amplitude(kx0)of the perturbed interface and the yield stress(sY),three typical modes of interface deformation have been identified as the broken mode,the stable mode and the oscillating mode.For the broken mode,the interface width(i.e.,the bubble position with respect to that of the spike)increases continuously resulting in a final separation of the spike from the perturbed interface.For the stable mode,the interface width grows to saturation and then maintains a nearly constant value in the long term.For the oscillating mode,the wavy-like interface moving forward obtains an aperiodic oscillation of small amplitude,namely,the interface width varies in time slightly around zero.The intriguing difference of the typical modes is interpreted qualitatively by comparing the early-stage wave motion and the commensurate pressure and effective stress.Further,the subsequent interface deformation is illustrated quantitatively via the time series of the interface positions and velocities of these three typical modes.

A simultaneous improvement of both strength and ductility by Sn addition in as-extruded Mg-6Al-4Zn alloy

Commercial wrought Mg alloys normally contain low alloying contents to ensure good formability.In the present work,high-alloyed Mg-6 Al-4 Zn-x Sn(x=1,2 and 3 wt.%,respectively)alloys were fabricated by extrusion.Hereinto,Sn was proven to play an effective contribution to simultaneous improvement in strength and ductility that are traditional trade-off features of synthetic materials.It was found that the average grain size of those alloys decreases significantly from^11 to^4μm as a function of Sn contents increasing from 0 to 3 wt.%,while the amounts of Mg2 Sn and Mg17 Al12 particles continuously increase.More importantly,the addition of Sn leads to the transformation of dominated deformation modes from{1012}extension twinning(1 wt.%)to pyramidal slip(3 wt.%)during tensile tests along the extrusion direction at room temperature.The advantageous combination of ultimate tensile strength(~366 MPa)and elongation(~19%)in Mg-6Al-4Zn-3 Sn alloy is mainly attributed to the strong strain hardening ability induced by the enhanced activity of non-basal slip.This work could provide new opportunities for the development of high-alloyed wrought Mg alloys with promising mechanical properties.

Improving Mechanical Properties and Energy Absorption of Additive Manufacturing Lattice Structure by Struts’Node Strengthening

The lattice structure has unique performance and superior deformation behavior,which effectively stimulates the design and application of new lattice structures.The development of additive manufacturing technology makes it easy and efficient to manufacture complex lattice structures.However,it has been found that excessively high stress concentration exists at the struts’nodes during the compression of lattice structure.Therefore,three node strengthening strategies were proposed to reduce stress concentration,which were adding fillet at nodes,using circular arc transition and changing the angle of nodes.Firstly,lattice structures were manufactured by selective laser melting technique.The surface morphology of the lattice structures was observed by scanning electron microscopy.Then,the stress distribution and deformation mechanism of different lattice structures were investigated by quasi-static compression experiments and numerical simulation.Finally,the Gibson–Ashby model was adopted to predict lattice structures’modulus and strength.And the energy absorptions of different structures were compared.The results revealed that the deformation mode of the optimized structures changed from shear failure to layer-by-layer collapse.Compared with the hourglass lattice structure and gradient lattice structure,the mechanical properties of curve lattice structure were improved the most.

Correlation of the anisotropic hardening behavior and texture features of cold rolled Zr-4 sheet under uniaxial tension

The strongly anisotropic mechanical behaviors commonly observed in Zr-4 sheets typically lead to inferior formability.In this study,the mechanical behavior and texture evolution of a cold-rolled Zr-4 sheet under uniaxial tension in various directions were systematically investigated,and the results showed both anisotropic yielding and hardening behavior in the Zr-4 sheet.The microstructure and texture features revealed by electron backscattered diffraction(EBSD)method indicate that this anisotropic mechanical behavior is closely related to the initial texture and its evolution during plastic deformation.In conjunction with experimental observations,a visco-plastic self-consistent(VPSC)model was employed to quantitatively analyze the relationship between the mechanical anisotropy and the texture features and activation of deformation modes.It was found that the yield anisotropy is affected by the distinct activity of prismaticslip,while the different activities of basalslip and extension twinning(ETW)result in anisotropic hardening.The distinct activation of deformation modes is mainly caused by differences in the evolution of the Schmid factor(SF)and critical resolved shear stress(CRSS)with increasing strain.Additionally,the results prove that the limited twinning activation with a fraction of less than 3%plays a non-negligible role in the hardening behavior during tension along the transverse direction.The latent hardening effect caused by the interaction between prismatic slip and tensile twinning is considered to successfully capture the anisotropic hardening behavior of the Zr-4 sheet.The implementation and insights from the predictions are presented and discussed in this work.

Studies on the Compressive Mechanical Properties of Antitetrachiral Honeycombs with Different Thickness Ratios of Ligament to Cylinder

This paper investigated the compressive mechanical properties of antitetrachiral honeycombs with different thickness ratios of ligament to cylinder.The deformation and energy absorption performance of the structures were characterized by the cooperation of experimental and numerical methods.First,two types(small and large thickness ratios)of antitetrachiral honeycombs were manufactured by 3D printing.Then,the deformation mode,negative Poisson’s ratio(NPR)and crushing stress of the honeycombs were obtained experimentally.After that,a finite element(FE)model was established by using ABAQUS/Explicit,and the numerical model and method were validated.Based on experimental and numerical results,the X mode,double-parallel line mode and cylinder mode were obtained in the compressive deformation of the honeycomb with a small thickness ratio.The Bi-V mode,“e”mode and Z mode were obtained in the compressive deformation of the honeycomb with a large thickness ratio.The influence of the thickness ratio of ligament to cylinder was studied,and a thickness ratio of 1.625 was the critical value for the transformation of the antitetrachiral honeycomb deformation modes.