A bounding surface visco-plasticity model considering generalized spacing ratio of soils

The non-unique critical state of soils with time-dependent behaviors is a significant issue in geotechnical engineering problems.However,previous bounding surface plasticity models cannot predict accurately the non-unique critical state of soils,because the distance between the compression line and critical state line charged by strain-rate effect is basically neglected.To fill this gap,a generalized spacing ratio of soils is defined in the elasto-viscoplastic framework,and a bounding surface visco-plasticity model is formulated and verified,which can consider the generalized spacing ratio.Specifically,the generalized spacing ratio of soils reflects the distance between the compression line and the critical state line of soils with time-dependent behaviors.Then,the generalized spacing ratio is introduced into an improved anisotropic bounding surface.A new expression of the visco-plastic multiplier is derived by solving the consistency equation of an anisotropic bounding surface.In the expression,a strain rate index is proposed to account for the strain-rate effect on visco-plastic strain increment,and a visco-plastic hardening modulus is derived to predict the visco-plastic response of soils in overconsolidation conditions.The model is then verified through constant strain rate tests and creep tests.Notably,it can capture the non-unique critical states of soils with time-dependent behaviors due to the generalized spacing ratio and the creep rupture of soils due to the visco-plastic multiplier that considers the stress ratio and visco-plastic strain rate.

Fatigue properties and damage constitutive model of salt rock based on CT scanning

To investigate the macroscopic fatigue properties and the mesoscopic pore evolution characteristics of salt rock under cyclic loading,fatigue tests under different upper-limit stresses were carried out on salt rock,and the mesoscopic pore structures of salt rock before and after fatigue tests and under different cycle numbers were measured using CT scanning instrument.Based on the test results,the effects of the cycle number and the upper-limit stress on the evolution of cracks,pore morphology,pore number,pore volume,pore size,plane porosity,and volume porosity of salt rock were analyzed.The failure path of salt rock specimens under cyclic loading was analyzed using the distribution law of plane porosity.The damage variable of salt rock under cyclic loading was defined on basis of the variation of volume porosity with cycle number.In order to describe the fatigue deformation behavior of salt rock under cyclic loading,the nonlinear Burgers damage constitutive model was further established.The results show that the model established can better reflect the whole development process of fatigue deformation of salt rock under cyclic loading.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

Constitutive Laws for Visco-plastic Porous Medium Shaped by Regularly Distributed Circular Particles

A numerical study is presented,using a homogenization technique to consider the plain strain problem of visco-plastic porous medium shaped by regularly distributed circular particles. Based on a rigid plastic material,the paper derives the macroscopic constitutive laws for homogenous equivalent medium. By changing the shape parameter of circular particles,the effect of pore shape on macroscopic constitutive laws is explored. Yield surfaces with different pore shapes are obtained. About voids,a two-scale conception is introduced,which regards main void as macroscopic scale and secondary cavities as microscopic scale. The macroscopic potential involving main and secondary voids is achieved. The proposed macroscopic constitutive law taking microscopic features as influence factors is helpful for exploring the macroscopic mechanical properties of porous medium when numerical simulation is required.

A macroscopic multi-mechanism based constitutive model for the thermo-mechanical cyclic degeneration of shape memory effect of NiTi shape memory alloy

A macroscopic based multi-mechanism constitutive model is constructed in the framework of irreversible thermodynamics to describe the degeneration of shape memory effect occurring in the thermo-mechanical cyclic deformation of NiTi shape memory alloys (SMAs). Three phases, austenite A, twinned martensite and detwinned martensite , as well as the phase transitions occurring between each pair of phases (, , , , and are considered in the proposed model. Meanwhile, two kinds of inelastic deformation mechanisms, martensite transformation-induced plasticity and reorientation-induced plasticity, are used to explain the degeneration of shape memory effects of NiTi SMAs. The evolution equations of internal variables are proposed by attributing the degeneration of shape memory effect to the interaction between the three phases (A, , and and plastic deformation. Finally, the capability of the proposed model is verified by comparing the predictions with the experimental results of NiTi SMAs. It is shown that the degeneration of shape memory effect and its dependence on the loading level can be reasonably described by the proposed model.

Review on cyclic plasticity of magnesium alloys:Experiments and constitutive models

Fatigue analysis has always been a concern in the design and assessment of Mg alloy structure components subjected to cyclic loading,and research on the cyclic plasticity is fundamental to investigate the corresponding fatigue failure.Thus,this work reviews the progress in the cyclic plasticity of Mg alloys.First,the existing macroscopic and microscopic experimental results of Mg alloys are summarized.Then,corresponding macroscopic phenomenological constitutive models and crystal plasticity-based models are reviewed.Finally,some conclusions and recommended topics on the cyclic plasticity of Mg alloys are provided to boost the further development and application of Mg alloys.

Constitutive model for monotonic and cyclic responses of loosely cemented sand formations

This paper presents a model to simulate the monotonic and cyclic behaviours of weakly cemented sands.An elastoplastic constitutive model within the framework of bounding surface plasticity theory is adopted to predict the mechanical behaviour of soft sandstone under monotonic and cyclic loadings. In this model, the loading surface always passes through the current stress state regardless of the type of loading. Destruction of the cementation bonds by plastic deformation in the model is considered as the primary mechanism responsible for the mechanical degradation of loosely cemented sands/weak rock.To model cyclic response, the unloading plastic and elastic moduli are formulated based on the loading/reloading plastic and elastic moduli. The proposed model was implemented in FLAC2D and evaluated against laboratory triaxial tests under monotonic and cyclic loadings, and the model results agreed well with the experimental observations. For cyclic tests, hysteresis loops are captured with reasonable accuracy.

Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking

In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters.

Constitutive Model of Saturated Soft Clay with Cyclic Loads under Unconsolidated Undrained Condition

An equivalent visco-elastic model of saturated soft clay was studied under unconsolidated undrained (UU) condition, which can be used to evaluate the stability of ocean foundation. Cyclic triaxial compression and extension tests were conducted to study the parameters of the model. Results showed that the relationships of the damping ratio and the octahedral shear modulus with the octahedral cyclic shear strain were nearly unique, when the initial octahedral shear stress ratios of specimens were equal to 0.3, 0.5 and 0.7. The relationships of the damping ratio and the octahedral shear modulus with the octahedral cyclic shear strain determined from the cyclic triaxial compression tests were basically the same as those determined from the cyclic triaxial extension tests. Furthermore, the relationships were not related to the initial stress condition, the test stress state and the octahedral cyclic shear stress ratio. The relationships determined from the cyclic triaxial tests under no deviatoric stress were basically the same as those determined from the cyclic triaxial tests under deviatoric stress. The change of the octahedral cyclic accumulative strain with the number of cycles was unique under different tests stress states. An equivalent visco-elastic constitutive model of saturated soft clay under UU condition was initially established.

Experimental study of the damage characteristics of rocks containing non-penetrating cracks under cyclic loading

The damage evolution process of non-penetrating cracks often causes some unexpected engineering disasters.Gypsum specimens containing non-penetrating crack(s)are used to study the damage evolution and characteristics under cyclic loading.The results show that under cyclic loading,the relationship between the number of non-penetrating crack(s)and the characteristic parameters(cyclic number,peak stress,peak strain,failure stress,and failure strain)of the pre-cracked specimens can be represented by a decreasing linear function.The damage evolution equation is fitted by calibrating the accumulative plastic strain for each cycle,and the damage constitutive equation is proposed by the concept of effective stress.Additionally,non-penetrating cracks are more likely to cause uneven stress distribution,damage accumulation,and local failure of specimen.The local failure can change the stress distribution and relieve the inhibition of non-penetrating crack extension and eventually cause a dramatic destruction of the specimen.Therefore,the evolution process caused by non-penetrating cracks can be regarded as one of the important reasons for inducing rockburst.These results are expected to improve the understanding of the process of spalling formation and rockburst and can be used to analyze the stability of rocks or rock structures.

Numerical Analysis of Fiber Reinforced Polymer-Confined Concrete under Cyclic Compression Using Cohesive Zone Models

This paper examines the mechanical behavior offiber reinforced polymer(FRP)-confined concrete under cyclic compression using the 3D cohesive zone model(CZM).A numerical modeling method was developed,employing zero-thickness cohesive elements to represent the stress-displacement relationship of concrete potential fracture surfaces and FRP-concrete interfaces.Additionally,mixed-mode damage plastic constitutive models were pro-posed for the concrete potential fracture surfaces and FRP-concrete interface,considering interfacial friction.Furthermore,an anisotropic plastic constitutive model was developed for the FRP composite jacket.The CZM model proposed in this study was validated using experimental data from plain concrete and large rupture strain(LRS)FRP-confined concrete subjected to cyclic compression.The simulation results demonstrate that the pro-posed model accurately predicts the mechanical response of both concrete and FRP-confined concrete under cyc-lic compression.Lastly,various parametric studies were conducted to investigate the internal failure mechanism of FRP-confined concrete under cyclic loading to analyze the influence of the inner friction plasticity of different components.

CONSTITUTIVE MODELLING OF NONPROPORTIONAL CYCLIC PLASTICITY

A multiplicative hardening function and a unified evolution rule of the hardening factors are proposed.The hardening factor f_1 is introduced to describe cyclic hardening with respect to the plastic strain range,while f_2 and f_3 describe,respectively,instantaneous and hereditary additional hardening with respect to the nonproportionality of the plastic strain path.Two material dependent memory parameters α_1 and α_3 are introduced to keep the memory of the largest cyclic and additional hardening in the previous plastic deformation history.Different hardening mechanisms are then embedded into a thermomechanically consistent constitutive equation through the hardening function.The constitutive response of 304 and 316 stainless steels subjected to biaxial nonproportional cyclic loading is analyzed and the proposed model is critically verified by comparing the results with experimental results obtained by Tanaka et al.,and Ohashi et al.

A NONPROPORTIONAL CYCLIC VISCOPLASTIC CONSTITUTIVE MODEL

A viscoplastic constitutive model is introduced,which takes into account nonproportional cyclic additional hardening and the effects of nonproportional cyclic loading history and inelastic strain amplitude history.In the model,a variable q of memory on the inelastic strain amplitude during loading is introduced,a new nonproportionality is defined,a cyclic saturated isotropic deformation resistance parameter Q,is given,and the evolution equations of the isotropic deformation resistance with the memory on the previous loading history are proposed.The present model is applied to the description of the complex cyclic deformation behavior of 1Cr18Ni9Ti stainless steel,and the predictions are in good agreement with the experimental results.This shows that the model describes the deformation behavior of nonproportional cyclic loadings and their histories very well.

Constitutive Model for Multiaxial Ratcheting Predictions of Cyclic Softening Weld Metal

A series of fully reversed axial, torsional strain-controlled cyclic tests and two multiaxial ratcheting tests were conducted on weld metal specimens using an Instron8521 tension-torsional servo-controlled testing machine. The weld metal showed clear cyclic softening under axial, torsional and multiaxial loading. A modified kinematic hardening rule was proposed in which a multiaxial-loading-dependent parameter incorporated the radial evanescence term of the Burlet-Cailletaud mode with the Ohno-Wang kinematic hardening rule to predict the multiaxial ratcheting effects. The introduction of yield stress evolved with accumulated plasticity strain enables the model to predict cyclic plasticity behavior of cyclic softening or cyclic hardening materials. Thus modified model considers the isotropic hardening as well as kinematic hardening of yield surface, and it can present description of plasticity behavior and ratcheting of cyclic softening and cyclic hardening materials well under multiaxial loading.

Theoretical investigation on axial cyclic performance of monopile in sands using interface constitutive models

Cyclic loads generated by environmental factors,such as winds,waves,and trains,will likely lead to performance degradation in pile foundations,resulting in issues like permanent displacement accumulation and bearing capacity attenuation.This paper presents a semi-analytical solution for predicting the axial cyclic behavior of piles in sands.The solution relies on two enhanced nonlinear load-transfer models considering stress-strain hysteresis and cyclic degradation in the pile-soil interaction.Model parameters are calibrated through cyclic shear tests of the sand-steel interface and laboratory geotechnical testing of sands.A novel aspect involves the meticulous formulation of the shaft loadtransfer function using an interface constitutive model,which inherently inherits the interface model’s advantages,such as capturing hysteresis,hardening,degradation,and particle breakage.The semi-analytical solution is computed numerically using the matrix displacement method,and the calculated values are validated through model tests performed on non-displacement and displacement piles in sands.The results demonstrate that the predicted values show excellent agreement with the measured values for both the static and cyclic responses of piles in sands.The displacement pile response,including factors such as bearing capacity,mobilized shaft resistance,and convergence rate of permanent settlement,exhibit improvements compared to non-displacement piles attributed to the soil squeezing effect.This methodology presents an innovative analytical framework,allowing for integrating cyclic interface models into the theoretical investigation of pile responses.

A NONCLASSICAL CONSTITUTIVE MODEL FOR CRYSTALPLASTICITY AND ITS APPLICATION

A nonclassical constitutive description for a slip system is formulated by using a simple mechanical model consisting of a spring and a plastic dashpot-like block. The corresponding constitutive model for a single crystal and the analysis for polycrystalline response is proposed based on the KBW's self-consistent theory. The constitutive model contains no yield criterion, so the corresponding numerical analysis is greatly simplified because it involves no additional process to search for the activation of slip systems and slip direction. A mixed averaging approach is proposed to obtain the response of polycrystalline material, which consists of the Gaussian integral mean for the omega which varies continuously within each face of the isosahedron and arithmetic mean for the spatially uniformly distributed twenty sets of 0 and phi determined by the normal of each face of the isosahedron. The main features 316 stainless steel subjected to typical biaxial nonproportional cyclic strain paths are well described. Calculation also shows that the developed model and the corresponding analytical approach are of good accuracy and efficiency.

循环载荷作用下煤岩复合结构宏-细观破坏特征及能量-损伤本构模型

煤炭深部开采过程中,周期性开采扰动行为会使邻近煤层的煤岩复合结构承受循环载荷的作用,因此,研究不同循环载荷作用下煤岩复合试样的力学响应行为及宏-细观失效特征具有重要工程意义。选取3种不同的加(卸)载速率,开展了2种循环加卸载路径下的单轴循环压缩试验(同步测定声发射信号),分析了煤岩复合试样的损伤失效特征;基于能量耗散原理,构建了煤岩复合试样在循环载荷作用下的能量-损伤本构模型,最后结合试验实测数据进行验证。结果表明:加(卸)载速率与复合试样的峰值强度呈正相关,当加(卸)载速率从0.05 mm/min增大到0.15 mm/min时,恒定下限逐步循环加卸载路径(路径I)、变上下限等幅循环加卸载路径(路径II)下,试样的峰值应力分别增加了22.44%和28.89%;高加(卸)载速率下,试样的内部裂纹扩展越快,煤岩复合试样中煤组分的破碎程度加剧,分形维数随之增大,试样的内部裂纹扩展越快;随着加(卸)载速率的增大,煤组分中沿基质破坏增多。循环分级跨度大的路径(路径I)有助于试样内部的应力传递,为试样内部裂纹的发育提供了有利条件,导致对应试样的破坏程度更高。试验曲线和能量-损伤本构理论曲线具有较强的一致性,表明所建的能量-损伤本构模型能够很好地描述煤岩复合试样在循环加卸载过程中的变形行为。

超高性能混凝土单轴拉、压循环作用下力学性能及其本构模型研究

超高性能混凝土(ultra-high performance concretre,UHPC)是一种新型材料,具有抗拉、抗压强度高、开裂后应变硬化等特点,在装配式结构领域具有较为广阔的应用前景。为了明确UHPC在单轴循环荷载下的受力性能并提出适合的本构关系,通过大量的试验建立循环荷载下UHPC的本构模型,设计具有不同钢纤维掺量的棱柱体和狗骨直拉试件,开展不同加载制度的单轴压缩试验,分析试验结果以明确钢纤维掺量、养护方式和加载制度对UHPC单轴拉压力学性能的影响情况。试验结果表明,在受压方面,钢纤维体积含量为2%的UHPC峰值压应变明显高于钢纤维体积含量为1%和3%的UHPC峰值压应变。各UHPC试件的弹性模量明显大于普通混凝土的弹性模量。在受拉方面,UHPC呈现出一定的应变硬化现象,且达到峰值后拉应力下降较为缓慢,展现出一定的受拉延性。钢纤维体积含量和蒸养处理对UHPC试件的抗拉强度有明显的提高作用。最后,在试验数据的基础上,提出了UHPC受压和受拉的骨架曲线和滞回准则,并拟合了卸载(再加载)的计算公式,可用于有限元计算中UHPC的基本本构方程。

循环加载下压实黄土的边界面塑性本构模型

压实黄土的动应力应变关系预测是黄土高原平山填方工程长期运营涉及的关键问题之一,已有模型预测压实黄土的动本构关系难度较大。该文在边界面塑性框架下,引入动态映射法则,提出了一个反映应变累积的循环加载塑性模量表达式,构建了循环加载条件下压实黄土边界面塑性本构模型,分析了循环应力比与围压对应力应变关系与模量的影响规律,采用压实粉质黄土动三轴试验结果进行了验证。结果表明,该循环加载塑性模量基本反映了压实黄土的应变累积行为,所构建的本构模型考虑了循环应力比对动应力应变关系与模量的影响,可为填方压实黄土长期变形分析提供参考。

用于金属阻尼器的Q235钢材循环硬化应变幅相关特性

金属阻尼器作为一种成本较低的减震构件被广泛应用于各类工程结构之中,通常采用低强度高延性钢材制作。在地震作用下,金属阻尼器会经历随机的循环塑性变形历程,其材料力学性能会发生变化,产生循环硬化或软化。为了探究常用于金属阻尼器的Q235钢材在各类循环应变幅下的力学性能,该文对Q235钢材在常应变幅、升应变幅与降应变幅循环荷载下的力学性能进行了试验研究,最大应变幅达到10%,分析了加载应变幅值和应变历史对钢材硬化性能的影响。结果表明,Q235钢材的硬化能力与加载应变幅相关,较大应变幅下积累的塑性变形会提高后续较小应变幅下钢材的硬化量,升应变幅荷载下钢材的硬化能力与加载历史无关。在此基础上,通过MATLAB优化工具箱标定了各个常应变幅试件的最优化CHABOCHE模型参数,参数结果表明仅考虑各向同性硬化的应变幅依赖效应即可准确反映Q235钢材在各个应变幅下的循环力学响应。以剪切阻尼器为例,基于有限元软件ABAQUS,通过编制子程序USDFLD考虑了材料硬化的应变幅依赖效应,分析对比了是否考虑钢材硬化应变幅依赖特性对阻尼器性能预测的影响。分析表明Q235钢材的循环硬化的应变幅相关特性对阻尼器性能分析影响很大,需要在分析中考虑。