基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程

岩石材料的粘弹性和粘塑性变形是与时间相关的能量耗散行为。在Rice不可逆内变量热力学框架下,引入两组内变量分别用来描述在粘弹性和粘塑性变形过程中材料的内部结构调整。通过给定比余能的具体形式和内变量的演化方程,推导出内变量粘弹-粘塑性本构方程。粘弹性本构方程具有普遍性,能涵盖Kelvin-Voigt和Poynting-Thomson在内的经典粘弹性模型的本构方程。并指出热力学力与应力呈线性关系是组合元件模型为线性模型的根本原因。粘塑性本构方程能较好地刻画岩石材料在粘塑性变形过程中的硬化现象。对模拟岩石的模型相似材料进行单轴加卸载蠕变试验,将蠕变过程中的粘弹性和粘塑性变形分离并根据试验数据对本构方程的材料参数进行辨识。试验数据和理论曲线对比结果表明该文提出的本构方程能很好地模拟材料的蠕变行为。该类型的本构方程能为岩石工程的长期稳定性的预测、评价以及加固分析提供基础。     

基于能量的弹塑性损伤实用本构模型

建立一个实用的弹塑性损伤本构模型。在有效应力空间采用经验公式计算塑性变形,能将模型塑性部分与损伤部分解耦,降低模型的数值处理复杂性,同时大大简化模型塑性应变的计算。结合不可逆热力学理论,基于损伤能量释放率建立损伤准则,损伤能量释放率由修正后的弹性Helmholtz自由能导出,模型中将弹性Helmholtz自由能分解为应力球量部分和应力偏量部分,将其应力球量部分产生的损伤取为零,同时根据应力状态引入折减系数对其应力偏量部分进行修正,使得模型能较为准确的模拟混凝土材料在双轴加载下的本构行为。将应力张量谱分解为正、负两部分以分别定义材料受拉、受压损伤演化,并采用受拉损伤变量、受压损伤变量分别模拟混凝土材料在拉、压加载下的本构特性。引入一个加权损伤变量使得模型能较准确的反映混凝土材料的“拉-压软化效应”。最后该文给出初步试验验证,证明了该文模型的有效性。     

粘弹塑性理论在混凝土变形中的应用

首先文章介绍了粘弹塑性统一本构模型的基本方程,根据混凝土的特点对统一本构模型进行了简化,简化后的模型对混凝土的无损伤段的变形模拟,取得了满意的结果。之后应用粘弹塑性统一本构模型对混凝土进行跳跃实验预测,同样获得了预期效果,证明粘弹塑性统一本构模型在混凝土的变形预测中的应用是成功的。     

混凝土坝地震动力损伤分析

基于塑性损伤本构理论,将损伤变量作为内变量,在Drucker-Prager本构模型中引入损伤变量,考虑材料损伤引起的材料劲度的退化,基于非关联流动法则计算材料的塑性应变,根据材料的有效塑性应变计算损伤量,考虑到张开裂缝闭合时材料弹性劲度的恢复,推导了考虑塑性损伤的混凝土动态本构关系,并给出了内变量的计算步骤和动力方程的迭代格式。最后利用建立的动态本构模型对Koyna重力坝进行了非线性地震响应时程分析,并给出了关键时刻坝体最大受拉损伤分布,结果表明在坝颈和坝基处出现了较大的损伤,坝颈处的损伤最终形成由下游向上游的开裂破坏,这与该坝的实际震害较为一致。     

复合材料非线性本构关系的机算机模拟

本文对单向连续纤维增强复合材料的弹塑性本构关系进行了数值模拟。首先提出了基于统一弹粘塑性本构理论的有限无法,然后利用微观力学模型研究了弹性纤维增强弹粘塑性基体的复合材料应力——应变关系。     

Drucker-Prager材料一致率型本构模型

根据一致粘塑性模型理论,结合所做的混凝土单轴动力特性试验,对常用的混凝土本构模型Drucker-Prager模型进行改进,引入应变率的影响,推导了Drucker-Prager材料的一致率型本构模型;并与试验的应力应变曲线进行比较,结果表明本文模型能够较好地反映混凝土的动力特性;最后,通过对一平面梁进行计算,并与线弹性及率无关塑性结果进行比较,结果表明考虑了应变率的影响后梁的动力特性发生了较大的变化。     

复合材料非线性本构关系的机算机模拟

本文对单向连续纤维增强复合材料的弹塑性本构关系进行了数值模拟。首先提出了基于统一弹粘塑性本构理论的有限无法,然后利用微观力学模型研究了弹性纤维增强弹粘塑性基体的复合材料应力——应变关系。      

三轴围压下砂浆弹塑性损伤变形过程的细观力学分析

基于对泛函势和Cauchy-Born准则,抽象出弹簧束构元和体积构元,组集两种构元的力学响应,给出了材料的弹性损伤本构关系;考虑滑移作为主要的塑性变形机制,提出了滑移构元,给出了材料的塑性本构关系;利用变形分解机制,得到了由三种构元共同描述的弹塑性损伤本构关系。阐述了在给定应变条件下弹塑性损伤本构关系的计算迭代流程。利用单轴拉伸算例详细阐述了模型参数的标定过程。对有围压作用下砂浆材料的压缩行为进行了模拟,从材料细观变形角度解释了随着围压增加,材料承载能力增加的现象。模型预测结果与试验结果符合较好,初步验证了模型具有处理非比例加载问题的能力。     

孔隙固体超弹性本构模型与应用

油气井封固、核废料填埋与浅层地热能利用等问题是能源岩土领域的研究热点。土体、岩石、混凝土材料的多场耦合本构模型理论是这些研究热点问题的核心所在。传统固体弹塑性力学、岩土力学与孔隙固体力学理论相比,由于其基本假设或构建手段的局限性,其关于岩石与混凝土材料的变形计算往往会产生较大误差,且理论扩展性不强。该文分别从饱和岩土力学理论、经典Biot孔隙弹性力学理论出发,阐述其在孔隙固体材料本构理论的相关研究工作,并进行梳理与对比;其后运用严格物理热力学理论框架,建立孔隙固体材料的超弹性本构模型;最后针对石灰石与水泥石的既有试验数据,验证孔隙固体超弹性本构模型的有效性。     

五种本构模型在钢管混凝土有限元中的比较

采用Von Mises、Mohr Coulomb和Drucker Prager三种经典模型、以及两种适用于混凝土材料的Smeared Cracking模型和Damaged Plasticity模型,分别对带约束拉杆和无约束拉杆的方形、矩形钢管混凝土短柱轴压承载力进行有限元分析,简述每种本构模型的特点,并与已有的47个钢管混凝土短柱轴压试验结果对比。结果表明与静水压力无关且忽略混凝土塑性体积膨胀的VonMises模型无法考虑钢管对混凝土的约束作用以及约束拉杆的作用,采用相关流动法则而低估了塑性体积膨胀的Smeared Cracking模型分析结果略低于试验结果,其他三种考虑静水压力并采用不相关流动法则的模型更符合试验结果,而且三者计算结果很接近。     

Large viscoplastic deformations of shells. Theory and finite element formulation

The paper is concerned with large viscoplastic deformations of shells when the constitutive model is based on the concept of unified evolution equations. Specifically the model due to Bodner and Partom is modified so as to fit in the frame of multiplicative viscoplasticity. Although the decomposition of the deformation gradient in elastic and inelastic parts is employed, no use is made of the concept of the intermediate configuration. A logarithmic elastic strain measure is used. An algorithm for the evaluation of the exponential map for nonsymmetric arguments as well as a closed form of the tangent operator are given. On the side of the shell theory itself, the shell model is chosen so as to allow for the application of a three-dimensional constitutive law. The shell theory, accordingly, allows for thickness change and is characterized by seven parameters. The constitutive law is evaluated pointwise over the shell thickness to allow for general cyclic loading. An enhanced strain finite element method is given and various examples of large shell deformations including loading-unloading cycles are presented.     

Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading

A viscoplastic constitutive equation for polyethylene that properly describes significant strain recovery during unloading was proposed. The constitutive equation was formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading–unloading criterion was then introduced using the loading surface. Moreover, a new parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which has some value only during unloading. Experimental results for polyethylene were simulated by using the modified constitutive equations, and cyclic inelastic deformation in both uniaxial and biaxial states of stress was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equation and the deformation were discussed.     

板壳非线性分析的新理论新方法

提出了板壳非线性分析的新理论新方法。首先建立了下列几个新的本构关系:塑性应变向量增量与总应变向量增量的新关系,热塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系,粘塑性应变向量增量与总应变向量增量的新关系,热粘塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系。这些关系分别称为弹塑性应变增量理论、热弹塑性应变增量理论、弹粘塑性应变增量理论及热弹粘塑性应变增量理论,避开了屈服曲面、加载曲面、流动法则及复杂的非线性应力应变关系。其次建立了非线性样条无网格法,这种方法是以新的本构关系、几何非线性理论、变分原理、广义变分原理、加权残数法及样条离散化为基础建立的,避免了经典本构关系及有限元法带来的巨大困难及缺陷,不仅计算简便,而且精度高,收敛速度很快。建立了板壳非线性分析的统一格式,对板壳的几何非线性分析、材料非线性分析及双重非线性分析都适用。     

Crack tip fields in a viscoplastic solid: monotonic and cyclic loading

The asymptotic stress and strain field near the tip of a plane strain Mode I stationary crack in a viscoplastic material are investigated in this work, using a unified viscoplastic model based on Chaboche (Int J Plast 5(3):247–302, 1989). Asymptotic analysis shows that the near tip stress field is governed by the Hutchinson–Rice–Rosengren (HRR) field (Hutchinson in J Mech Phys Solids 16(1):13–31, 1968; Rice and Rosengren in J Mech Phys Solids 16(1):1–12, 1968) with a time dependent amplitude that depends on the loading history. Finite element analysis is carried out for a single edge crack specimen subjected to a constant applied load and a simple class of cyclic loading history. The focus is on small scale creep where the region of inelasticity is small in comparison with typical specimen dimensions. For the case of constant load, the amplitude of the HRR field is found to vanish at long times and the elastic K field dominates. For the case of cyclic loading, we study the effect of stress ratio on inelastic strain and find that the strain accumulated per cycle decreases with stress ratio.     

Three-dimensional, finite deformation, viscoplastic constitutive models for polymeric materials

A general methodology for developing three-dimensional. finite deformation, viscoplastic constitutive models for polymeric materials is presented. The development begins with the presentation of a one-dimensional spring and dashpot construction which exhibits behavior typical of polymeric materials, namely strain-rate dependence, stress relaxation, and creep. The one-dimensional construction serves as a starting point for the development of a three-dimensional, finite deformation, viscoplastic constitutive model which also exhibits typical polymeric behavior. Furthermore, the three-dimensional constitutive model may be easily generalized to incorporate an arbitrary number of inelastic processes, representing (inelastic) microstructural deformation mechanisms operating on different time scales. Strain-rate dependence, stress relaxation, and creep phenomena are discussed in detail for a simple version of the constitutive model. Test data for a particular polymer is used to validate the simple model. It is concluded that the methodology provides a flexible approach to modeling polymeric materials over a wide range of loading conditions.     

Prediction of crack growth in a nickel-based superalloy under fatigue-oxidation conditions

Prediction of oxidation-assisted crack growth has been carried out for a nickel-based superalloy at elevated temperature based on finite element analyses of oxygen diffusion, coupled with viscoplastic deformation, near a fatigue crack tip. The material constitutive behaviour, implemented in the finite element code ABAQUS via a user-defined material subroutine (UMAT), was described by a unified viscoplastic model with non-linear kinematic and isotropic hardening rules. Diffusion of oxygen was assumed to be controlled by two parameters, the oxygen diffusivity and deformation-assisted oxygen mobility. Low frequencies and superimposed hold periods at peak loads significantly enhanced oxygen concentration near the crack tip. Evaluations of near-tip deformation and oxygen concentration were performed, which led to the construction of a failure envelop for crack growth based on the consideration of both oxygen concentration and accumulated inelastic strain near the crack tip. The failure envelop was then utilised to predict crack growth rates in a compact tension (CT) specimen under fatigue-oxidation conditions for selected loading ranges, frequencies and dwell periods. The predictions from the fatigue-oxidation failure envelop compared well with the experimental results for triangular and dwell loading waveforms, with marked improvements achieved over those predicted from the viscoplastic model alone. The fatigue-oxidation predictions also agree well with the experimental results for slow-fast loading waveforms, but not for fast-slow waveforms where the effect of oxidation is much reduced.     

A generalized micromechanics model with shear-coupling

Summary A unified mathematical framework for a higher-order transverse shear-normal stress coupled micromechanical model is presented. The model is developed based on the analysis of a repeating unit cell in a doubly periodic array of fibers. The behavior in subregions within the unit cell is modeled using an expansion for the displacement field. The order and form of the displacement expansions in the subregions are arbitrary. The higher-order terms in the displacement expansion result in coupling between the transverse shearing and the normal deformation responses (shear coupling). The formulation is sufficiently general to allow generic elastic, plastic, viscoelastic, viscoplastic, or damage constitutive models (within the context of infinitesimal strain theory) for history-dependent behavior to be incorporated into the micromechanical framework. The proposed approach is analytical and provides closed-form expressions for the effective macroscopic behavior of a continuous fiber composite.The model is validated by comparison with existing micromechanics models. The agreement between the predicted effective moduli obtained from the current model and other existing models indicates that the current formulation accurately predicts the effective elastic behavior of a composite. Furthermore, comparison with existing data for the local elastic stress distributions around the inclusion indicates that the current model correctly captures the trends and magnitudes in these distributions. The predictions obtained from the current theory are shown to be more accurate than the corresponding MOC predictions. The ability to more accurately capture the spatial stress distributions can be directly attributed to the incorporation of the shear-coupling phenomena.Finally, the influence of the presence of shear coupling on the local field distributions is considered for the simple macroscopic loading cases of transverse tension and transverse shearing. It is shown that signficant coupling between the local transverse shearing and normal deformation responses exists even when the composite is subjected to a macroscopically simple loading field. The existence of this coupling has potentially significant implications in the implementation of history-dependent constitutive models.     

The strain path dependence of multiaxial cyclic hardening behaviour

The small-strain, isotropic deformation theory is used in incremental form to model an additional cyclic hardening for any arbitrary loading path. The theory is of the unified type and does not employ yield or loading/ unloading criteria. The scalar-valued functions involved in the tensorial constitutive equations as well a growth law for these functions are identified based on idea of the equivalent state. Definitions of equivalent stress and equivalent strain have been developed to correlate step by step loading programmes taking the history of deformation into account. Use is made of the total work increment together with an interpolation method for tensor functions to generalize the simple state to a multiaxial behaviour in the strain space for a given strain increment. For the demonstration of model capability, the numerical simulation is undertaken on cyclic nonproportional paths in two-dimensional axial-shear strain space. The results are verified for stainless steel and brass by comparison with the material response experimentally obtained in the stress space.