Self-consistent Eulerian rate type elasto-plasticity models based upon the logarithmic stress rate

The objective of this article is to suggest new Eulerian rate type constitutive models for isotropic finite deformation elastoplasticity with isotropic hardening, kinematic hardening and combined isotropic-kinematic hardening etc. The main novelty of the suggested models is the use of the newly discovered logarithmic stress rate and the incorporation of a simple, natural explicit integrable-exactly rate type formulation of general hyperelasticity. Each new model is thus subjected to no incompatibility of rate type formulation for elastic behaviour with the notion of elasticity, as encountered by any other existing Eulerian rate type model for elastoplasticity or hypoelasticity. As particular cases, new Prandtl-Reuss equations for elastic-perfect plasticity and elastoplasticity with isotropic hardening, kinematic hardening and combined isotropic-kinematic hardening, respectively, are presented for computational and practical purposes. Of them, the equations for kinematic hardening and combined isotropic–kinematic hardening are, respectively, reduced to three uncoupled equations with respect to the spherical stress component, the shifted stress and the back-stress. The effects of finite rotation on the current strain and stress and hardening behaviour are indicated in a clear and direct manner. As illustrations, finite simple shear responses for the proposed models are studied by means of numerical integration. Further, it is proved that, among all possible (infinitely many) objective Eulerian rate type models, the proposed models are not only the first, but unique, self-consistent models of their kinds, in the sense that the rate type equation used to represent elastic behaviour is exactly integrable to really deliver an elastic relation. ©     

A computational study of a model of single-crystal strain-gradient viscoplasticity with an interactive hardening relation

The behavior of a model of single-crystal strain-gradient viscoplasticity is investigated. The model is an extension of a rate-independent version, and includes a new hardening relation that has recently been proposed in the small-deformation context (Gurtin and Reddy, 2014), and which accounts for slip-system interactions due to self and latent hardening. Energetic and dissipative effects, each with its corresponding length scale, are included. Numerical results are presented for a single crystal with single and multiple slip systems, as well as an ensemble of grains. These results provide a clear illustration of the effects of accounting for slip-system interactions.     

A thermodynamic consistent damage and healing model for self healing materials

Thermodynamics of the damage and the healing processes for viscoplastic materials is discussed in detail and constitutive equations for coupled inelastic-damage-healing processes are proposed in a thermodynamic consistent framework. Small deformation state is utilized and the kinematic and the isotropic hardening effects for the damage and healing processes are introduced into the governing equations. Two new yield surfaces for the damage and healing processes are proposed that take into account the isotropic hardening effect. The computational aspect for solving the coupled elasto-plastic-damage-healing problem is investigated, and the mechanical behavior of the proposed polymeric based self healing system is obtained. Uniaxial compression tests are implemented on a shape memory polymer based self healing system and the damage and the healing are captured by measurement of the changes in the modulus of elasticity. It is concluded that the proposed constitutive equations can model the damage and healing effectively and the mechanical behavior of a shape memory polymer based self healing system can be precisely modeled using this formulation.     

考虑尺寸效应的多晶金属循环塑性分析

采用多晶塑性分析方法,设材料单元包含一定数量的各向异性单晶晶粒并考虑晶粒尺寸的影响,利用Taylor假设计算材料单元的应力和应变.模型引入考虑尺寸效应的晶体滑移硬化函数,同时针对晶体滑移引入背应力及其方向性硬化的描述,以反映不同晶粒尺寸材料在循环加载条件下的力学行为,利用该模型,论文第一作者采用显式格式编制了与ABAQUS商用有限元软件接口的用户材料子程序(VUMAT),实例计算证实该模型可以反映和描述多晶金属材料在反复加载条件下的循环塑性行为与尺寸效应.     

一种新的多轴非比例低周疲劳寿命预测临界面模型

工程结构在服役过程中往往承受着复杂的多轴非比例循环荷载,在长期动力载荷作用下结构构件的失效主要为多轴非比例疲劳破坏. 文中基于圆管薄壁试件在拉-扭复合加载情况下的多轴疲劳试验结果,对比了广泛讨论的Kandil-Brown-Miller (KBM) 模型和Fatemi-Socie (FS) 模型对多轴非比例疲劳寿命的预测能力,分析了非比例加载条件引起多轴疲劳附加损伤的原因;针对FS 模型对不存在非比例附加强化的材料多轴疲劳寿命预测的不足,提出了一个能考虑非比例加载路径变化和材料附加强化效应双重作用的非比例影响因子,参照FS 准则提出了一种新的多轴非比例低周疲劳寿命预测临界面模型. 利用5 种材料的多轴非比例疲劳试验数据对该模型进行了试验验证,结果表明:采用文中提出的临界面模型预测的多轴非比例疲劳寿命与试验结果符合较好,预测精度优于FS 模型;同时,该模型对不存在非比例附加强化的材料的多轴疲劳寿命预测表现出更好的适用性,且能有效的提高不同类型材料的多轴非比例疲劳寿命预测精度.      

显式方法精确模拟形状记忆合金循环荷载下的变形行为

本文提出全新的有限弹塑性J2流方程,用来显式、精确地模拟SMAs（形状记忆合金）材料在循环加载-卸载条件下从塑性逐渐转变为伪弹性的变形行为．首先,改进流动法,使得本构方程耦合屈服中心的移动和屈服面的增大,并改进背应力演化方程,使模型可以产生强烈的包辛格效应,从理论上具备模拟SMAs独特变形行为的能力;其次,构造全过程下的统一硬化函数显式表达式,代入本构方程后能得到符合要求的形函数;再次,利用选定的数据点构造统一光滑的上屈服函数,再利用上下屈服应力之间的一种线性关系,推导得到下屈服阶段的形函数;最后,只需要给定一个参数就可以得到单个循环结果,利用拉格朗日插值方法构建参数随循环次数变化的函数,就可以模拟任意循环荷载下的变形行为．通过模型结果和实验数据对比证明新方法的有效性．     

Development of a family of explicit algorithms for structural dynamics with unconditional stability

A new family of explicit integration algorithms is developed based on discrete control theory for solving the dynamic equations of motion. The proposed algorithms are explicit for both displacement and velocity and require no factorisation of the damping matrix and the stiffness matrix. Therefore, for a system with nonlinear damping and stiffness, the proposed algorithms are more efficient than the common explicit algorithms that provide only explicit displacement. Accuracy and stability properties of the proposed algorithms are analysed theoretically and verified numerically. Certain subfamilies are found to be unconditionally stable for any system state (linear elastic, stiffness softening or stiffness hardening) that may occur in earthquake engineering of a practical structure. With dual explicit expression and excellent stability property, the proposed family of algorithms can potentially solve complicated nonlinear dynamic problems.     

A crystal plasticity model for strain-path changes in metals

A model is proposed that deals with the transient mechanical anisotropy during strain-path changes in metals. The basic mechanism is assumed to be latent hardening or softening of the slip systems, dependent on if they are active or passive during deformation, reflecting microstructural mechanisms that depend on the deformation mode rather than on the crystallography. The new model captures the experimentally observed behaviour of cross hardening in agreement with experiments for an AA3103 aluminium alloy. Generic results for strain reversals qualitatively agree with two types of behaviour reported in the literature – with or without a plateau on the stress–strain curve. The influence of the model parameters is studied through detailed calculations of the response of three selected parameter combinations, including the evolution of yield surface sections subsequent to 10% pre-strain. The mathematical complexity is kept to a minimum by avoiding explicit predictions related directly to underpinning microstructural changes. The starting point of the model is a combination of conventional texture and work hardening approaches, where an adapted full-constraints Taylor theory and a simple single-crystal work-hardening model for monotonic strain are used. However, the framework of the model is not restricted to these particular models.     

Unified simulation of hardening and softening effects for metals up to failure

Applied Mathematics and Mechanics - Toward accurately simulating both hardening and softening effects for metals up to failure, a new finite strain elastoplastic J2-flow model is proposed with the...     

Multiscale modeling of irradiated polycrystalline FCC metals

We propose a set of models for the post-irradiation deformation response of polycrystalline FCC metals. First, a defect- and dislocation-density based evolution model is developed to capture the features of irradiation-induced hardening as well as intra-granular softening. The proposed hardening model is incorporated within a rate-independent single crystal plasticity model. The result is a non-homogeneous deformation model that accounts for defect absorption on the active slip planes during plastic loading. The macroscopic non-linear constitutive response of the polycrystalline aggregate of the single crystal grains is then obtained using a micro–macro transition scheme, which is realized within a Jacobian-free multiscale method (JFMM). The Jacobian-free approach circumvents explicit computation of the tangent matrix at the macroscale by using a Newton–Krylov process. This has a major advantage in terms of storage requirements and computational cost over existing approaches based on homogenized material coefficients in which explicit Jacobian computation is required at every Newton step. The mechanical response of neutron-irradiated single and polycrystalline OFHC copper is studied and it is shown to capture experimentally observed grain-level phenomena.     

An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation

In a search for a constitutive model for ratcheting simulations, the models by Chaboche, Ohno–Wang, McDowell, Jiang–Sehitoglu, Voyiadjis–Basuroychowdhury and AbdelKarim–Ohno are evaluated against a set of uniaxial and biaxial ratcheting responses. With the assumption of invariant shape of the yield surface during plastic loading, the ratcheting simulations for uniaxial loading are primarily a function of the plastic modulus calculation, whereas the simulations for multiaxial loading are sensitive to the kinematic hardening rule of a model. This characteristic of the above mentioned models is elaborated in this paper. It is demonstrated that if all parameters of the kinematic hardening rule are determined from uniaxial responses only, these parameters primarily enable a better plastic modulus calculation. However, in this case the role of the kinematic hardening rule in representing the ratcheting responses for multiaxial loading is under-appreciated. This realization motivated many researchers to incorporate multiaxial load dependent terms or parameters into the kinematic hardening rule. This paper evaluates some of these modified rules and finds that none is general enough to simulate the ratcheting responses consistently for the experiments considered. A modified kinematic hardening rule is proposed using the idea of Delobelle and his co-workers in the framework of the Chaboche model. This new rule introduces only one multiaxial load dependent parameter to the Chaboche model, but performs the best in simulating all the ratcheting responses considered.     

Modeling multi-axial deformation of planar anisotropic elasto-plastic materials,part I: Theory

In sheet metal forming processes local material points can experience multi-axial and multi-path loadings. Under such loading conditions, conventional phenomenological material formulations are not capable to predict the deformation behavior within satisfying accuracy. While micro-mechanical models have significantly improved the understanding of the deformation processes under such conditions, these models require large sets of material data to describe the micromechanical evolution and quite enormous computation expenses for industrial applications. To reduce the drawbacks of phenomenological material models under the multi-path loadings a new anisotropic elasto-plastic material formulation is suggested. The model enables the anisotropic yield surface to grow (isotropic hardening), translate (kinematic hardening) and rotate (rotation of the anisotropy axes) with respect to the deformation, while the shape of the yield surface remains essentially unchanged.Essentially, the model is formulated on the basis of an Armstrong–Frederick type kinematic hardening, the plastic spin theory for the reorientation of the symmetry axes of the anisotropic yield function, and additional terms coupling these expressions. The capability of the model is illustrated with multi-path loading simulations in ‘tension-shear’ and ‘reverse-shear’ to assess its performance with ‘cross’ hardening and ‘Bauschinger’ effects.     

循环硬化材料本构模型的隐式应力积分和有限元实现

针对新发展的、能够描述循环硬化行为应变幅值依赖性的粘塑性本构模型,讨论了它的数值实现方法。首先,为了能够对材料的循环棘轮行为（Ratcheting）和循环应力松弛现象进行描述,对已有的本构模型进行了改进;然后,在改进模型的基础上,建立了一个新的、全隐式应力积分算法,进而推导了相应的一致切线刚度（Consistent Tangent Modulus）矩阵的表达式;最后,通过ABAQUS用户材料子程序UMAT将上述本构模型进行了有限元实现,并通过一些算例对一些构件的循环变形行为进行了有限元数值模拟,讨论了该类本构模型有限元实现的必要性和合理性。     

Modeling the Bauschinger effect for sheet metals,part I: theory

It is essential to model the Bauschinger effect correctly for sheet metal forming process simulation and subsequent springback prediction when material points are subjected to cyclic loading conditions. The combined nonlinear hardening model for time independent cyclic plasticity, proposed by Chaboche and co-workers, is examined and a simple modification is suggested for the isotropic part of the hardening rule to utilize the conventional tensile test data directly. This modification is useful for the materials whose reverse loading curves saturate to the monotonic loading curve. In addition, an anisotropic nonlinear kinematic hardening model (ANK model) is proposed in an attempt to represent the Bauschinger effect more realistically. Possible offset in flow stress is modeled by treating the back stress evolution during reverse loading differently from the initial loading. This strategy coupled with the modified isotropic hardening rule seems to provide a way to model the Bauschinger effect consistently over multiple cycles. Two types of auto-body alloys are examined in this paper. Associated material parameters are determined by employing available tension-compression test data and multi-cycle bend test data. A developed finite element formulation is applied to analyze simple validation type of problems. The cyclic stress–strain curves generated from the proposed ANK model match remarkably well with measured data.     

A two parameter elasto-plastic formulation for hardening pressure-dependent materials

A new pressure-dependent yield function is proposed by introducing a plastic Poisson's ratio within the theoretical formulation of the plastic potential. In analogy with other classical models, an equivalent stress and an equivalent plastic strain increment are defined. Then, according to these definitions, the equivalent stress–strain curve is derived and an exponential hardening law is introduced. The advantage of the proposed formulation over alternative approaches relies in explicit closed-form expressions of the flow rules and of the plastic multiplier.     

显式模拟类橡胶材料Mullins效应滞回圈

通过显式、直接的方法提出一个多轴可压缩应变能函数,用来模拟类橡胶材料在加载——卸载作用下,由于Mullins效应而产生的应力——应变滞回圈. 本文的创新点在于将表征能量耗散的变量引入到应变能函数.新的弹性势具有以下两个特点:第一,在加载情况下,新引入的变量不会对弹性势产生任何影响,因此,只要给出合适的形函数显式表达,3个基准实验,包括单轴拉伸和压缩,等双轴拉伸和压缩,以及平面应变,都可精确模拟;第二,新引入的变量在卸载情况下将被激活.在不同的卸载应力下,变量将发生改变,从而影响弹性势,使其最终产生不同的应力——应变关系卸载曲线,与对应的加载曲线共同构成应力——应变滞回圈.通过对Mullins效应实验数据进行分析和研究,得出了卸载形函数在不同卸载应力下变化的规律,并预测不同卸载应力下的应力——应变关系.最后,我们将得到精确匹配实验数据的数值模拟结果,从而证明本文方法不仅可以精确匹配至少3个基准实验,还可以模拟和预测类橡胶材料在加载——卸载作用下由于Mullins效应而产生的滞回圈.      

考虑路径相关性的非比例循环塑性本构模型

根据非比例加载下金属材料响应的延迟特性及加载路径相关性,选取沿应力迹法向的塑性应变的累积量作为非比例加载影响的度量,相应给出反映非比例附加强化的变量,并假设其模量和强化率与加载路径的几何参数相关．为反映由于非比例加载而引起的材料强化的异向效应,在Valanis的塑性内时响应方程中引入与加载路径几何性质有关的应力项,构成非比例循环塑性本构关系．对316和304不锈钢材料在一些典型非比例循环加载路径下的应力响应进行了理论预测,与Benallal等及McDowell的实验结果取得了良好的一致．     

用伪应力函数法求解幂硬化材料柱体的扭转问题

本文引用伪应力函数使得幂硬化材料的任意形状等截面柱体和变直径圆截面柱体扭转问题的定解方程具有弹性柱体扭转问题的相应形式,从而可用类似于求解弹性柱体扭转的方法或直接利用已知的弹性解答求解对应的幂硬化材料柱体的扭转问题,本文用这种方法求得了幂硬化材料椭圆截面柱体及含球形空腔的圆轴扭转问题的解析解。     

Constitutive equation with fractional derivatives for the generalized UCM model

A fundamental problem on the constitutive equation with fractional derivatives for the generalized upper convected Maxwell model (UCM) is studied. The existing investigations on the constitutive equation are reviewed and their limitations or deficiencies are highlighted. By utilizing the convected coordinates approach, a mathematically rigorous constitutive equation with fractional derivatives for the generalized UCM model is proposed, which has an explicit expression for the stress tensor. This model can be reduced to the linear generalized Maxwell model with fractional derivatives, the UCM model and some other existing models. In addition, the rheological properties of this proposed model in the start-up of simple shear and elongation flows are investigated. It is shown that this generalized UCM model can describe the various stress evolution processes and the strain hardening effect of the viscoelastic fluids.