Shear Stress-strain Relationship Research Articles

Research on the State-Dependent Hyperbolic Model of the Interface between Spoil Mixture and Concrete

Abstract A series of large-scale direct shear tests were carried out to study the stress-strain relationship of the interface between the spoil mixture and concrete under different roughness conditions. The results showed that roughness significantly affects the shear strength properties and dilatancy characteristics of the interface. Under different roughness conditions, the shear stress ratio and the normal deformation of the interface tend to be stable after larger shear strain, and the interface presents the characteristics of a critical state. With the increase of shear strain, the void ratio of the interface shows the law of transformation from the initial void ratio to a certain stable void ratio. Based on the void ratio prediction formula of the interface, the relationship between roughness and critical state parameters was established, and the interface state parameters were introduced into the hyperbolic model. Finally, a state-dependent hyperbolic model of the interface considering the roughness was established. Importantly, the model can well reflect the shear stress-strain relationship of the interface under different roughness conditions.

Undrained cyclic behavior of underconsolidated marine clay in multidirectional simple shear tests

In the field of marine reclamation engineering, underconsolidated marine clay often presents challenges owing to its susceptibility to multidirectional cyclic stresses and potential for excessive deformation. This research examined the undrained cyclic behavior of underconsolidated marine clay through multidirectional cyclic simple shear tests. It explored shear strain evolution, the cyclic shear stress–strain relationship, and stiffness degradation by analyzing the impacts of clay consolidation levels and phase differences in the cyclic stress. The findings indicated that as the degree of consolidation increased, the rate of cyclic shear strain development in marine clay gradually diminished. Conversely, an enhanced phase difference led to a quicker evolution of shear strain. Additionally, as loading continued, the tested clay exhibited notable softening behavior, leading to stiffness degradation. A larger phase difference resulted in more pronounced stiffness degradation, although a higher degree of consolidation effectively delayed this degradation. These findings provide new insights on the cyclic behavior of underconsolidated marine clay under multidirectional loading, offering crucial information for marine reclamation engineering.

Experimental and numerical investigation of the intra-ply shear behaviour of unidirectional prepreg forming through picture-frame test

Intra-ply shear behaviour of uncured composite plies strongly influences component quality in advanced manufacturing processes such as prepreg compression moulding (PCM) and double diaphragm forming (DDF). This study investigates a straightforward method to characterise the intra-ply shear behaviour of a carbon fibre/epoxy UD prepreg using a specially designed picture-frame rig, by which specimens can be tested without involving inter-ply shear as would normally be observed in cross-plied UD prepreg stacks. Applying the proposed method, it is seen that specimens tend to suffer transverse buckling/wrinkling and local fibre-splitting at large shear strains. 3D digital image correlation (DIC) and a non-contacting video extensometer were utilised to determine the shear strain distribution throughout the test and particularly to determine the onset of out-of-plane deformations such that the trellis shear deformation portion of the test can be identified. The obtained shear stress-strain results show a temperature- and rate-dependent viscoelastic response, with the greatest influence from the temperature. The obtained in-plane shear properties were applied in the numerical simulation of the picture frame test based on a hypoelastic law. Although the predicted reaction forces are greater than experimental results at high strains due several factors including local fibre-splitting, a good agreement overall between physical test data and simulation results is seen for all test conditions. Finally, it is demonstrated that major advantages of the proposed test with respect to the conventional picture-frame test are that only load-extension data are required from the trellis shear experiment to calculate accurately the intra-ply shear stress-strain relationship and that the deformation rate can be easily controlled.

Influence of frozen soil site conditions on ground motion characteristics in cold regions

It is necessary to understand the site seismic response for seismic design and post-earthquake damage assessment of structures in seismically active regions. In cold regions, the presence of layered frozen soil not only affects the ground motion characteristics but also influences the seismic response of structures on these sites. This study aims to investigate the effect of frozen soil site conditions on ground motion characteristics in cold regions through shaking table tests using a laminar shear box equipped with a soil freezing system. The seismic acceleration response, displacement response, and dynamic shear stress-strain relation were analyzed for both unfrozen and frozen soil sites under various seismic waves with different intensities. The existence of the frozen soil layer has been observed to mitigate ground motion during earthquakes, resulting in a reduced peak ground acceleration compared with the unfrozen soil site. If an earthquake occurs, the high-frequency waves will be attenuated by the frozen soil layer, which possesses a dominant frequency lower than that of the unfrozen soil site. Moreover, the energy dissipation capacity of the frozen soil site is larger than that of the unfrozen soil site during earthquakes. By combining the Fourier spectral ratio curves, it can be inferred that different input ground motions have varying effects on the seismic response of both unfrozen and frozen sites. These findings serve as valuable references for seismic design of structures in cold regions.

A Micromechanical Analysis to the Viscoplastic Behavior of Sintered Silver Joints under Shear Loading.

Ag paste has been recognized as a promising substitute for Sn/Pb solder in SiC or GaN power electronic devices, owing to its ability to withstand high temperatures and facilitate low-temperature packing. The reliability of these high-power circuits is greatly influenced by the mechanical properties of sintered Ag paste. However, there exist substantial voids inside the sintered silver layer after sintering, and the conventional macroscopic constitutive models have certain limitation to describe the shear stress-strain relationship of sintered silver materials. To analyze the void evolution and microstructure of sintered silver, Ag composite pastes composed of micron flake silver and nano-silver particles were prepared. The mechanical behaviors were studied at different temperatures (0-125 °C) and strain rates (1 × 10-4-1 × 10-2) for Ag composite pastes. The crystal plastic finite element method (CPFEM) was developed to describe the microstructure evolution and shear behaviors of sintered silver at varied strain rates and ambient temperatures. The model parameters were obtained by fitting experimental shear test data to a representative volume element (RVE) model built on representative volume elements, also known as Voronoi tessellations. The numerical predictions were compared with the experimental data, which showed that the introduced crystal plasticity constitutive model can describe the shear constitutive behavior of a sintered silver specimen with reasonable accuracy.

Nano and micro-indentation driven characterisation of asperity and bulk plasticity at the surface of modern premium rail steels

The plastic deformation behaviour of rail steels due to cyclic rail-wheel contacts is important to understand due to its connection to wear and rolling contact fatigue (RCF) damage initiation in service. Simulation models such as the ‘Layer’ and ‘Brick’ model have previously been developed to estimate the accumulation of plastic damage in a rail steel; however, the data available to drive these models is currently sparse, with limited applicability to modern rail steel grades. This paper presents the research examining the shear stress-strain curve relationships of rail steels derived from plastic shear strain and shear yield stress data collected from twin-disc test samples. A combination of microhardness and nanohardness testing was used to derive the shear yield stress data, whereas the plastic shear strain was acquired from optical microscopy. Six different conditions were investigated for this research for the purpose of examining how shear stress-strain curve relationships compared between the standard R260 and the premium HP335 and R350HT rail steels and how this compares to wear damage data. The influence of the maximum Hertzian contact pressure on the shear stress-strain curve relationships of R260 between 600 and 1500 MPa contact pressure was also investigated. The wear rate results derived from the mass loss in interrupted twin-disc tests showed HP335 wearing the least, followed by R350HT and then R260 for 1500 MPa, dry contact conditions. However, the highest shear yield stress achieved was for R350HT, then HP335, and R260. The results show that the shear stress-strain curve relationships by themselves are insufficient to determine rail steel wear performance in a laboratory environment. The shear stress-strain curve relationships for R260 collected under different contact pressures showed the results are near independent of the contact pressure within the range explored.

A Study on Torsional Behavior of Glued Laminated Bamboo Glubam

Glubam is a type of engineered bamboo increasingly attracting research and application interest. This study focused on the torsional shear properties of glubam. Prismatic specimens with square sections were tested using a torsional loading device along with both conventional strain gauge–based instrumentation and a digital image correlation (DIC) system. Testing parameters included thick- and thin-strip glubams, the influence of carbonization of thick-strip glubam, as well as comparative spruce-pine-fir (SPF). Mechanical behavior and properties, including failure process, shear stress-strain relationships, modulus, and strength, were examined. The testing results indicated that carbonization of thick-strip glubam increased its strength slightly; however, specimens failed with more brittleness. The existence of bi-directional bamboo fibers in the thin-strip glubam apparently contributed to the larger deformability compared with the unidirectional thick-strip glubam.

Impact of Isothermal Aging on Mechanical Properties of 92.8%Sn-3%Ag-0.5%Cu-3.3%Bi (Cyclomax) Solder Joints

During operation, electronic components are exposed to high temperatures that may last for long periods, depending on the operating duration. Solder joints are one of the components most affected by thermal aging while in service. In this research, the effect of thermal aging duration and temperature on the mechanical properties of 92.8%Sn-3%Ag-0.5%Cu-3.3%Bi (Cyclomax) was investigated. The novelty of this work lies in the study of the important properties of a new generation of Sn-Ag-Cu (SAC) materials (i.e., Cyclomax). Cyclomax is rare in industry and immature in research. To understand the effect of thermal aging, the microstructure was investigated, and changes in it and its mechanical properties were observed. To simulate solder joints in electronic devices, samples of solder balls were prepared and attached to copper pads on electronic boards. Most samples were then treated at 150 °C or 100 °C for up to 1000 h and some samples were left untreated for comparison. A scanning electron microscope (SEM) was used to obtain images of the microstructure. The shear stress–shear strain relationships, including the ultimate shear strength (USS), the modulus of elasticity and the ultimate energy (UE), were investigated. The microstructure images indicated the presence of a layer of Cu6Sn5 on top of the copper pad before thermal aging was applied. The thickness of this layer increased with the application of thermal aging over time. The results for the shear stress–shear strain relationship indicate that all of the USS, the total energy (TE) to shear off the solder balls and the UE decreased at the beginning of the thermal aging and then reversed to increase later. In general, isothermal aging reduces the performance of Cyclomax solder joints in terms of the minimum force and energy required to separate and subsequently damage electronic components.

Effect of the seasonal freeze–thaw cycle of the active layer on the seismic response of the free field in the permafrost region

Seasonal freezing and thawing of the active layer in permafrost can significantly alter the seismic response of the free field. In this study, a specific laminar shear model box with a soil-freezing system was designed, and shaking table tests of free fields under different soil-freezing conditions were conducted for ground motions with different intensities. The lateral displacement and acceleration responses of the free field were collected. Based on these results, the acceleration spectrum, shear stress–strain relationship, and frequency component of the ground motions of the free field were analysed. During the tests, the lateral displacement of the free field during both warm (thawed active layer) and cold (frozen active layer) seasons transitioned from linear to nonlinear relationships. The permafrost layer suppressed the amplification effect under ground motion with low intensity, and the frozen active layer enhanced the global stiffness of the free field during the cold season. As the seismic intensity increased, the restraining effect of the permafrost layer on ground motion decreased to a certain extent, and the frozen active layer had a restraining effect on the propagation of seismic waves. In addition, the transition layer (the unfrozen interlayer between the frozen active layer and the permafrost layer) during the cold season undergoes compaction during the nonlinear deformation stage. In the event of strong earthquakes, different soil layers exhibited selective amplification effects, and the frozen active layer exhibited an obvious influence on the filtering effect of the lower soil layers. These results can provide a reference basis for the seismic risk analysis of free field in permafrost regions.

Seismic Characteristics of a Geotextile Tube-Reinforced Embankment and Shallow Foundations Laid on Liquefiable Soil

The ground in Saemangeum has a high water level and is mostly composed of silty soil and sand, which makes it susceptible to liquefaction and seepage effects. To investigate the seismic response of a geotextile tube-reinforced embankment and shallow foundations laid on a liquefiable soil, a simple spring type shaking table apparatus was developed. The variation in the response acceleration and shear stress-strain relationship were investigated, and the effect of soil improvement and reinforcement were explored, wherein one of the shallow foundations was laid on a coarse sand layer and reinforced by a polyester geotextile. The results showed that the main cause of damage to the embankment was seepage-induced liquefaction. Excessive surface accelerations were observed in the embankment soil due to lateral spreading, indicating the importance of analyzing the liquefaction potential of soils not only at the site area but also near embankments. Lastly, the inclusion of geotextile reinforcement and soil improvement only resulted in the slight reduction of shallow foundation settlement.

One-dimensional fiber beam-column model and two-dimensional fixed crack model for numerical simulation of UHPC structures

Ultra-high performance concrete (UHPC), with much higher compressive strength, tensile strength and ultimate tensile strain than normal concrete, has been experimentally investigated and applied in engineering structures more and more widely. However, there are few numerical models appropriate for the accurate and efficient simulation of UHPC or reinforced UHPC (R/UHPC) flexural members including beams and columns as well as shear-critical members such as shear walls till now, which brings obstacles to the analysis and design of UHPC structures. In this study, the uniaxial skeleton and hysteretic rules for UHPC under tensile and compressive loads are first proposed and verified by material tests. The formulas to calculate all the basic parameters in the model are put forward for convenient use. Then the fiber beam-column model for flexure-dominated UHPC members is established in ABAQUS 2017 software and six R/UHPC column specimens subjected to cyclic load are simulated. Based on simulation results, the equations of transition curves in the uniaxial rules are determined, which have significant influence on the predicted hysteresis curves. On the other hand, a new two-dimensional fixed crack based constitutive model for shear-critical UHPC members is further proposed and implemented in ABAQUS 2017 software by considering the compressive softening due to principal tensile strain and shear stress–strain relationship along cracks of UHPC. Finally, ten R/UHPC shear wall specimens under cyclic loads as well as four R/UHPC deep beams under monotonic loads are simulated and the accuracy of the proposed 2D model for UHPC is validated.

Insight on bulk shear strength parameters of clay using discrete element approach incorporating physics-based interparticle force model

This paper aims to provide insight on factors affecting the bulk shear strength parameters of clay, i.e., the cohesion and internal friction as well as the effects of memory of preconsolidation pressure. A unique Discrete Element Method (DEM) model is built on platy particles with customized particle interaction force model. The particle interaction force model considers non-contact forces (such as the long-range electrostatic repulsion, short-range van der Waals attraction) as well as the direct contact force. The long-range electrostatic forces are calibrated by measurement with Atomic Force Microscope (AFM). Parameters for direct particle contacts of the regular DEM contact model, such as the contact stiffness and the friction coefficient, are calibrated by use of experimental consolidation and direct shear testing data. Computational simulations are conducted on digital clay specimen subjected to virtual direct shear tests. The predicted experimental responses of the digital specimens are consistent with typically observed in experiments including the shear stress-shear strain relationship, volumetric contraction and dilation, shear band formation, etc. From the stress–strain curves, the soil strength parameters are obtained with common experimental criteria. The DEM simulation results show that higher preconsolidation pressure drives more particles to overcome non-contact force into direct contacts and consequently bonding by van der Waals force. Consequently, the bulk cohesion of clay increases with increasing preconsolidation pressure. The results show that bulk cohesion strength is mainly attributed to the attractive interparticle force as well as the interlocking of platy particle, while the bulk internal friction angle is affected by the particle friction coefficient and particle fabric. Overall, the simulation results indicate the experimentally observed macroscopic shear strength parameters c and φ are linked to the microscope characteristics of soil particles and their mutual interactions. The results offer insight on the microscopic properties of particles on the bulk macroscopic strength behaviors. Besides, this work demonstrates a new strategy for simulation-based prediction of bulk soil strength parameters, by incorporating microscale characterization of the interparticle interactions and particle fabric into the particle-based DEM model.

Circumferential pure shear test of thin-walled aluminum alloy tubes

In order to obtain the pure shear deformation characteristics along the circumferential direction of tubes, a circumferential shear test for thin-walled tubes is proposed in this paper. The experimental device consists of a tubular sample and two cylindrical mandrels with shear plates. The torque along the circumferential direction was applied to the tubular sample by the two shear plates to make the pre-set shearing zone of the sample under a circumferential pure shear stress state. The two cylindrical mandrels support the inner wall of the tube to avoid buckling so that the pure shear stress state can be maintained during the whole deformation process. A 5052 aluminum alloy tube with an outer diameter of 50 mm and a wall thickness of 1.2 mm was used in the test. It is shown through simulation and experiment that shear deformation is concentrated in the pre-set shearing zone. This test can be used to obtain the circumferential pure shear stress-strain relationship.

Interaction between a complex fluid flow and a rotating cylinder

The flow of a thixotropic Bingham material past a rotating cylinder is studied under a wide range of Reynolds and Bingham numbers, thixotropic parameters, and rotational speeds. A microstructure transition of the material involving breakdown and recovery processes is modeled using a kinetic equation, and the Bingham- Papanastasiou model is employed to represent shear stress-strain rate relations. Results show that the material’s structural state at equilibrium depends greatly on the rotational speed and the thixotropic parameters. A layer around the cylinder resembling a Newtonian fluid is observed, in which the microstructure is almost completely broken, the yield stress is negligibly small, and the apparent viscosity approximates that of the Newtonian fluid. The thickness of this Newtonian-like layer varies with the rotational speed and the Reynolds number, but more significantly with the former than with the latter. In addition, the lift and moment coefficients increase with the rotational speed. These values are found to be close to those of the Newtonian fluid as well as of an equivalent non-thixotropic Bingham fluid. Many other aspects of the flow such as the flow pattern, the unyielded zones, and strain rate distribution are presented and discussed.

Numerical modeling of single closed and open-ended pipe pile embedded in dry soil layers under coupled static and dynamic loadings

Abstract For the design of a deep foundation, piles are presumed to transfer the axial and lateral loads into the ground. However, the effects of the combined loads are generally ignored in engineering practice since there are uncertainties to the precise definition of soil–pile interactions. Hence, for technical discussions of the soil–pile interactions due to dynamic loads, a three-dimensional finite element model was developed to evaluate the soil pile performance based on the 1 g shaking table test. The static loads consisted of 50% of the allowable vertical pile capacity and 50% of the allowable lateral pile capacity. The dynamic loads were taken from the recorded data of the Kobe earthquake. The current numerical model takes into account the material non-linearity and the non-linearity of pile-to-surrounded soil contact surfaces. A lateral ground acceleration was adapted to simulate the seismic effects. This research emphasizes modeling the 1 g model by adapting MIDAS GTS NX software. This will, in turn, present the main findings from a single pile model under a combined static and dynamic load. Consequently, the main results were first validated and then used for further deep investigations. The numerical results predicted a slightly higher displacement in the horizontal and vertical directions than the 1 g shaking table. The shear stress–shear strain relationship was predicted. Positive frictional resistance for the closed-ended pile was captured during the first 5 s when low values of acceleration were applied and, consequently, the pile resistance decreased and became negative. Internal and external frictional resistance was captured for the open-ended pipe pile. Overall, frictional resistance values were decreased with time until they reached the last time step with a minimum value. As a result, the evaluation of the current study can be used as a guide for analysis and preliminary design in engineering practice.

An indirect method to determine nonlinearly elastic shear stress-strain constitutive relationships for nonlinear torsional vibration of nonlinearly elastic shafts

PurposeIn this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.Design/methodology/approachIn this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.Findings The effect of four variables, namely dimensionless fundamental vibration amplitude , radius and length , and nonlinear-elasticity intensity factor , on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. , , and , cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.Originality/valueThe study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

Undrained anisotropic behaviour of K 0-consolidated marine clay under cyclic stresses

To investigate the effect of major principal stress direction angles on the cyclic response of soft marine clays, a series of directional shear tests with different major principal stress direction angles on undisturbed Wenzhou marine clay were conducted in the undrained condition by using a hollow cylinder testing apparatus. The dynamic responses of the marine clays were analysed, along with the shear stress-strain relationship, octahedral strain and excess pore water pressure. Results indicate that the specimens exhibit remarkable anisotropic deformation under various major principal stress direction angles, and a larger angle causes a smaller octahedral strain of specimen under the same cyclic stress level. With the increase in the major principal stress direction angle, the excess pore water pressure decreases. At β > 45°, the increment shear stress starts dominating, which causes the sign of generated pore water pressure to change from negative to positive.

Influencing factors of scale effects in large-scale direct shear tests of soil-rock mixtures based on particle breakage

In studies of soil-rock mixtures (SRM), scale effect due to limitations of particle size often causes laboratory research results to differ from on-site measurements. To explore the specific impacts of scale effect on the shear behaviours of SRM, large-scale laboratory direct shear tests and numerical simulations using the discrete element method (DEM) were thus performed. The accuracy of the numerical simulations was verified with a comparison of test and simulation results. The results suggest that scaling has only a minor influence on the shear stress–strain relationship of SRM, while Mixing Method was shown to be the optimum scaling method for studying shear behaviours in SRM under laboratory conditions. Based on this, a value of 0.9 times the shear strength of a relevant sample treated using the Mixing Method is suggested as the representative shear strength of actual scale SRM on site. There are some obvious differences in stone content and porosity factor in scaled samples treated by different scaling methods, however, which can lead to further dissimilarities in shear strength and other strength parameters under high normal pressure. In SRM more generally, the bulk shrinkage of the SRM samples is obvious during shear, and the shrinkage rate gradually decreases. The normal pressure and stone content have significant effects on the bulk shrinkage.

Assessment of shear strength and compressibility characteristics of a newly developed lunar highland soil simulant (LSS-ISAC-1) for Chandrayaan lander and rover missions

The engineering properties (shear strength and compressibility) of lunar soils influence the design of landers, rovers, and their mobility behavior on the lunar surface. Assessing such properties is important for any lunar-based studies, and it is usually being determined by using suitable lunar soil simulants. This paper explains the shear strength parameters, stress-strain relationships, and volume change behavior of the newly developed lunar highland soil simulant (LSS-ISAC-1), apart from particle size distribution, which have a profound influence on the engineering behavior. In addition, to the above, other engineering properties such as critical state of the angle of internal friction, dilatancy angle, Young's modulus, Poisson's ratio, internal erodibility, small-strain shear wave velocity, and shear modulus have also been evaluated and presented. Mohr-Coulomb and friction-dilatancy theories are considered as a base for the analysis with the use of statistical predictive equations. The relative density and confining pressures are used as functions in the predictive equation to assess the behavior of the LSS-ISAC-1. The comparison of properties with the actual lunar highland soil samples of the Apollo 16 mission reveals a reasonable similarity of LSS-ISAC-1 with the lunar highland soils.

Measurement of Pure Shear Constitutive Relationship From Torsion Tests Under Quasi-Static, Medium, and High Strain Rate Conditions

Abstract Torsion tests provide important shear stress and shear strain relationships to reveal the fundamental plastic flow response of a material. Bespoke torsion techniques complemented by digital image correlation are developed to accurately measure the shear stress–strain relationship at quasi-static, medium rate 9/s, and high strain rate above 1000/s. The equipment used includes a screw-driven mechanical system, a hydraulic Instron machine and a Campbell thin-walled tube split Hopkinson torsion bar equipped with an ultrahigh-speed camera. A near alpha Ti3Al2.5V alloy was used as a model material in this study. A four-camera digital image system has been constructed to monitor the material deformation and failure during a low rate torsion test, to gain further insight into plastic deformation of the tubular specimen. Shear stress–strain relationship of the Ti3Al2.5V alloy exhibits noticeable strain rate sensitivity. Observations of the strain hardening rate evolution indicate that the hardening capacity of Ti3Al2.5V is both strain and strain rate dependent. High strain rate torsional stress–strain relationship shows lower strain hardening, compared to the response obtained from a shear compression specimen. The present techniques are demonstrated to be suitable for the measurement of pure shear constitutive relationship, including rate sensitivity and failure of the material.