基于对数应力率大应变本构关系的参数标定研究

在所有率型弹塑性本构模型中,只有对数应力率对应的本构模型能够满足自适应准则.基于对数应力率,采用实心圆轴扭转实验,对大应变弹塑性本构模型中的参数标定问题进行了讨论.推导出了考虑Swift效应时端部自由实心圆轴扭转变形的变形率、对数旋率、Kirchhoff应力及Kirchhoff应力的对数应力率.对于等向强化大应变弹塑性本构关系,给出了由实心圆轴扭转实验标定的、基于Kirchhhoff应力对数应力率的本构关系中塑性刚度函数的表达式.分析了扭转圆轴的Swift效应对塑性刚度函数的影响.结果表明,实心圆轴扭转的轴向伸长变形和径向变形对基于对数应力率大应变本构关系中的塑性刚度函数都有影响.当不考虑Swift效应时,所得塑性刚度函数表达式与不考虑Swift效应时基于Jaumann应力率的塑性刚度函数表达式相同.     

A Thermomechanically Consistent Constitutive Model for Polyoxymethylene

In this article tension, compression and torsion tests are presented using thin-walled tubes of polyoxymethylene (POM). These isothermal experiments show non-linear rate dependence, a tension–compression asymmetry and a pronounced relaxation behaviour. On the basis of the experiments carried out, a constitutive model of viscoplasticity with an equilibrium hysteresis in the small-strain regime is developed. Test calculations using finite elements based on the DAE approach show the capabilities of the thermomechanically consistent model. In particular, a very efficient stress algorithm can be derived which has no iteration on the element level. Moreover, it will be shown that time-adaptive finite elements could be of high importance if rate-dependent constitutive models are applied.     

Estimation of Fracture Toughness of Metallic Materials Using Instrumented Indentation: Critical Indentation Stress and Strain Model

We propose a generalized approach based on fracture mechanics and contact mechanics to estimate the fracture toughness in metallic materials from instrumented indentation testing. Models were developed for brittle and ductile fracture. Different criteria were applied to each model to determine the critical fracture point during indentation. For brittle fracture, the critical fracture point was defined in terms of the critical mean pressure; for ductile fracture, the critical fracture point was derived from fracture strain and critical plastic zone size. Each fracture criterion was used to determine the indentation fracture energy corresponding to the fracture energy required for crack extension. The fracture toughness was estimated for various metallic materials using each model and compared with standard fracture toughness tests.     

三轴加载下盐岩蠕变损伤特性的研究

基于不可逆热力学,采用内变量刻划岩石材料的不可逆变形历史,引入四阶损伤张量,建立了盐岩的蠕变损伤本构模型,对盐岩在复杂应力条件下的蠕变行为进行了描述,与实验结果比较表明该模型能较好的描述盐岩不同阶段的蠕变行为及其主要因素对盐岩蠕变特性的影响.     

蠕变——塑性交互作用的一种本构模型

基于热力学相容的本构模型并合理地定义广义时间，得到了描述蠕变、塑性及其交互作用的统一型本构方程。进而通过对在蠕变—塑性交互作用过程中材料内部子结构及其变化的分析，将材料的强化分解为对应于非弹性应变范围的强化和由蠕变变形导致的附加强化。对高温环境二维应力路径下３０４不锈钢的蠕变—塑性交互作用过程进行了分析，取得了与Ｏｈａｓｈｉ等的实验相吻合的结果。     

A Simple Hysteretic Constitutive Model for Unsaturated Flow

The present study covers the problem of rotation of a porous disk under a viscous incompressible fluid that fills the half-space above the disk, which is the generalization of the von Karman’s problem. It is found that, instead of solving the exact problem, which is rather complicated by coupling the motions of the free fluid and that contained inside the permeable disk, it is sufficient to solve a much simpler problem of the motion of the free fluid placed onto a permeable plane. Assuming the flow in the permeable disk is described by the Brinkman equations, we obtain a self-similar formulation of the problem. Employing this formulation, we also show that the boundary condition associated with continuity of the tangential strains and tangential velocity components is satisfied at the fluid–porous body interface. The coefficient for the vertical velocity component is furthermore obtained. Various extreme cases are identified.     

复杂应力状态下岩土材料非线性本构模型研究

基于统一强度理论,将洛德参数引入统一强度理论,推导出材料的统一强度参数,进而分析中间主应力以及主剪应力系数对材料统一强度参数的影响。在此基础上,对邓肯张双曲线模型进行改进,使得该模型能够反映复杂应力状态下的应力应变关系。采用粘土的平面应变试验进行验证,结果表明:在平面应变情况下,当b=0.4时,模型能够较好地反映粘土的应力应变关系,及其强度参数。分析了洛德参数以及中间主应力系数对模型的影响,进一步说明岩土材料存在主应力效应。该模型能够反映不同材料在复杂应力状态下的应力应变关系,有其更为广泛的适用性。     

混凝土单轴受拉的非局部本构模型

混凝土受拉本构行为存在很强的局部软化现象,使得单轴受拉试验无法给出应力-应变关系,而只能给出应力-位移关系。本文根据内变量理论和等效应变假设建立了基于真实应变的混凝土单轴受力本构方程,并根据Weibull分布可以描述混凝土等脆性材料断裂过程的试验现象,建立了关于弹性应变的损伤演化规律。然后,通过假设平均应变与真实弹性应变的函数关系,在应力-平均应变的本构关系中采用平均弹性应变以描述其非局部行为,而在材料的损伤演化规律中采用真实弹性应变以描述其局部行为,由此建立了单轴受拉荷载条件下的非局部本构模型。最后,对一个单调受拉试验和一个反复受拉试验的仿真结果表明所提出的非局部本构模型可以准确地模拟试验结果。     

Critical Evaluation of a Constitutive Model for Glassy Polycarbonate

Polycarbonate (PC) is an important amorphous glassy polymer whose intrinsic uniaxial response exhibits all the features like strain softening and hardening at large deformations characteristic of this class of materials. Polycarbonate is significantly ductile and is capable of sustaining large plastic deformation. Constitutive models of PC, in order to be useful, should be able to faithfully model its elastic as well as plastic behaviour with as few undetermined parameters as possible. We assess the efficacy of a particular model of glassy polymers by fitting its parameters through usual uniaxial tensile and compressive tests and then using those parameters to model a fracture specimen in 3-dimensions. A range of experimental techniques like digital image correlation, photoelasticity and x-ray tomography are used to make careful quantitative comparisons with computer simulations. Our results indicate that in view of the small scale yielding situation prevalent in PC specimens even at high loads, a faithful prediction of the elastic parameters are sufficient for reproducing most global responses and deformation fields away from the crack. However, to predict fracture initiation, the deformation state within the small but significant fracture process zone needs to be reproduced. This cannot be done unless the entire uniaxial response is modelled to a reasonable degree of accuracy.     

一种适合橡胶类材料的非线性粘弹性本构模型

借助非线性流变模型建立大变形情况非线性粘弹材料的本构关系,考虑到大多数橡胶类材料具有的几乎不可压缩性,以及体积响应和剪切响应的流变性能不同,将变形梯度乘法分解为等容部分和体积变形部分,给出了一种适合橡胶类材料的非线性粘弹性本构模型,并模拟了粘滞效应。对于极快或极慢的过程,该模型退化为橡胶弹性理论;在小变形情况下退化为经典的广义Maxwell粘弹性材料。模型与热力学第二定律相容,适合于大规模数值分析。     

有限元实现含应变非强化区的双面循环塑性模型

在有限单元方法的框架下,由广义径向返回法来实现含有应变非强化区的循双面环塑性本构模型.在小变形的假设下,本文详细描述了有限元方法实现率无关的双面循环塑性本构模型的完整算法.采用向后Euler隐式算法进行离散积分,其最终可化简为一个非线性方程,并且由Peg-asus方法来求解.对径向返回法进行线性化,可以得到切向刚度算子.最后,文中通过两个算例表征了离散积分的精确性和材料模型的正确性.     

岩体结构面非线性弹性-塑性软化本构模型研究

在总结评述现有岩体结构面本构模型的基础上,将非线性弹性模型和弹塑性模型结合起来,并采用起伏角磨损演化方程来定量描述结构面的磨损软化,建立了岩体结构面非线性弹性-塑性软化本构模型.利用新建立的模型对岩体结构面直剪试验进行了预测,模型预测结果与试验结果吻合良好,验证了模型的有效性和模拟能力.该模型概念清晰,参数易于确定,能够合理描述岩体结构面的非线性变形、塑性软化、弹塑性耦合、剪胀和磨损等主要力学特性.     

Finite Element Model Calibration for Ares I-X Flight Vehicle

Ares I-X is a flight test vehicle developed by NASA to demonstrate a new class of crew launch vehicle. For this first flight test, the first stage was a four segment solid rocket booster with mass simulators used to represent the other sections of the Ares I vehicle. Although this vehicle is significantly simpler than the Ares I, model calibration was required for the finite element model used in loads analysis and flight control evaluations before its maiden flight. The process of calibrating models involves updating parameters and reconciling predictions with test data. This work presents a probabilistic approach to the calibration process. The approach uses Analysis of Variance (ANOVA) for parameter sensitivity, nonlinear optimization to minimize the error between test and analysis, and multiple FEM models to bound the system response and to assess the probability of finding a reconciling solution. To reduce the computational burden associated with ANOVA, response surface models are used in lieu of computationally intensive finite element solutions. Uncertainty in the parameters and their effect on the frequency response function is studied in terms of Principal Values of the frequency response functions. Uncertainty bounds of the principal values are established across multiple models to allow one to determine the probability of finding a solution that reconciles analysis with test results. Results from applying this model calibration process to the Ares I-X project are described. Findings presented in the paper confirmed that the baseline model used for pre-flight assessments was within the acceptable range established for guidance and control.     

A Dynamic Micromechanical Constitutive Model for Frozen Soil under Impact Loading

By taking the frozen soil as a particle-reinforced composite material which consists of clay soil(i.e., the matrix) and ice particles, a micromechanical constitutive model is established to describe the dynamic compressive deformation of frozen soil. The proposed model is constructed by referring to the debonding damage theory of composite materials, and addresses the effects of strain rate and temperature on the dynamic compressive deformation of frozen soil. The proposed model is verified through comparison of the predictions with the corresponding dynamic experimental data of frozen soil obtained from the split Hopkinson pressure bar(SHPB) tests at different high strain rates and temperatures. It is shown that the predictions agree well with the experimental results.     

A Molecular-Statistical Basis for the Gent Constitutive Model of Rubber Elasticity

Molecular constitutive models for rubber based on non-Gaussian statistics generally involve the inverse Langevin function. Such models are widely used since they successfully capture the typical strain-hardening at large strains. Limiting chain extensibility constitutive models have also been developed on using phenomenological continuum mechanics approaches. One such model, the Gent model for incompressible isotropic hyperelastic materials, is particularly simple. The strain-energy density in the Gent model depends only on the first invariant I ₁ of the Cauchy–Green strain tensor, is a simple logarithmic function of I ₁ and involves just two material parameters, the shear modulus μ and a parameter J _m which measures a limiting value for I ₁−3 reflecting limiting chain extensibility. In this note, we show that the Gent phenomenological model is a very accurate approximation to a molecular based stretch averaged full-network model involving the inverse Langevin function. It is shown that the Gent model is closely related to that obtained by using a Padè approximant for this function. The constants μ and J _m in the Gent model are given in terms of microscopic properties. Since the Gent model is remarkably simple, and since analytic closed-form solutions to several benchmark boundary-value problems have been obtained recently on using this model, it is thus an attractive alternative to the comparatively complicated molecular models for incompressible rubber involving the inverse Langevin function. This revised version was published online in June 2006 with corrections to the Cover Date.     

A STRESS VECTOR-BASED CONSTITUTIVE MODEL FOR COHESIONLESS SOIL (Ⅱ)-APPLICATION

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一个考虑循环应变幅值历史效应的粘塑性本构模型

本文提出了一个考虑材料应变幅值历史效应的粘塑性本构模型。在该模型中，引入了三个具有不同演化速率的背应力演化方程；建立了非弹性应变幅值历史记忆模型，对各向同性变形阻力，引入了具有先前加载历史记忆的演化方程。将本文模型用于１Ｃｒ１８Ｎｉ９Ｔｉ不锈钢循环变形行为描述中，其预言结果与实验结果吻合得很好，表明该模型能很好地描述材料的循环应变幅值历史下的循环变形行为。     

循环加载作用下皮肤应力软化的连续介质模型

皮肤组织作为富含纤维的非均匀材料,具有复杂的力学特性．皮肤组织在循环加载作用下,随着循环次数的增加,加载过程的应力响应逐渐降低,并最终达到不随循环次数增加而改变的稳定状态,这种现象被称为应力软化行为．本文对加载过程中纤维的延展机制对宏观力学响应的影响进行研究,认为在外界载荷较小时该机制主导了宏观层次上的应力软化行为,随着外界载荷的增大,拉伸过程中微观结构损伤的演化开始产生影响,而且此时内部微观结构的演化由两种机制共同影响,据此建立了连续介质模型,将宏观尺度上应力软化行为和微观结构的演化相关联．将所获得的应力响应理论结果与猪离体头部皮肤在循环加载作用下的实验结果进行对比分析,证明了该模型能够合理地描述皮肤组织在循环加载作用下的应力软化行为．     

A Micromechanics-based Finite Element Model for the Constitutive Behavior of Polycrystalline Ferromagnets

A micromechanics-based finite element model for the constitutive behavior of polycrystalline ferromagnets is developed. In the model, the polycrystalline solid is assumed to comprise numerous single crystals with randomly distributed crystallographic orientations, and the single crystals, in turn, consist of ferromagnetic domains, each of which is represented by a cubic element. The dipole directions of the domains are randomly assigned to simulate the crystallographic nature of ferromagnetic polycrystals. A switching criterion for the domains is specified at the microscopic level. The macroscopic constitutive behavior is obtained by averaging the microscopic/local behavior of each domain. The developed model has been applied to the simulation of a ferromagnetic material. With appropriate material parameters adopted, hysteresis loops of the predicted magnetic induction versus magnetic field and those of the strain versus magnetic field are shown to agree well with experimental observations.The project supported by the National Natural Science Foundation of China (90205030, 10472088, 10425210), the National Basic Research Program of China (2006CB601202) and the State Administration of the Foreign Experts Affairs Through the “111” Project (B06024) The English text was polished by Yunming Chen.     

Enhancing the Bolzon–Schrefler–Zienkiewicz Constitutive Model for Partially Saturated Soil

This paper presents an enhanced version of the elasto-plastic model for partially saturated soil first proposed by Bolzon, Schrefler and Zienkiewicz in 1996, “BSZ” model, which uses the effective stress tensor and suction as independent stress variables. It is recalled that the effective stress tensor proposed by Lewis and Schrefler in 1982 is thermodynamically consistent and, compared with other choices of stress tensors, results particularly suitable for partially saturated soil mechanics. A hydraulic constitutive relationship and a hydraulic hysteresis are introduced in the model, to take into account the irreversible deformation during cyclic drying and wetting until structural collapse. For this reason the plastic rate of strain is split into the sum of two components: one depending on the effective stress tensor and the other one on suction. This is the new feature of the BSZ model. This enhanced model is then cast into a thermodynamical framework at macroscopic level and it is shown that it is possible to derive the constitutive law from the Helmholtz free energy and a dissipation function, both for associative and non- associative plasticity. Finally the model predictions have been compared with experimental data for Sion slime, with particular emphasis on the deviatoric part, and model predictions of hysteretic behaviour have been investigated in case of a wetting and drying cycle on compacted betonite–kaolin.