混凝土黏塑性动力损伤本构关系

从静力弹塑性损伤本构关系的基本框架出发, 综合考虑塑性应变与损伤 演化的率敏感性, 建立了能够较为全面地描述混凝土在动力加载条件下非线性性能的混凝土 黏塑性动力损伤本构模型. 为了考虑塑性应变的率敏感性, 基于Perzyna理论推导了有效应 力空间黏塑性力学基本公式, 采用改进的Perzyna型动力演化方程, 将损伤静力演化方程推 广到动力加载情形. 基于并联弹簧模型, 从概率论的角度推导给出了一维损伤静力演化方程, 并基于能量等效应变的基本概念将其推广到多维损伤演化. 利用数值模拟, 计算得到了 混凝土在不同应变率下的应力应变全曲线, 同时得到了一维动力提高因子和二维动力强度包 络图, 数值结果与试验结果的对比表明了该模型的有效性.     

岩体介质渐进破坏的弹塑性本构关系

本文把作者和曲圣年提出的岩体介质的应变软化,非关联和弹塑性耦合的本构关系推广到独立作用加载面的情况.并应用这种理论,具体地给出了具有强化帽和渐进破坏屈服面的岩体介质本构关系.     

基于模糊集的塑性理论

本文提出一个描述各种材料的循环加载行为的一般理论,它在数学上以模糊集理论为基础。根据建立本构模型的观点,它跟以往的许多循环塑性模型有密切关系。它不是利用两个或两个以上的屈服面或界面,而是在由应力与一个从属函数(membership function)所生成的空间里引入一个更一般的曲面。这个概念使我们可以在同一个数学框架中定义许多不同的模型。借助于几个一维的例子考察这一理论的若干可能情形。本文考虑了有记忆与无记忆的以及记忆衰减的本构模型,这些模型有各向同性的和随动硬化的,以及无硬化的。用模糊集的表述法,描述了循环加载过程中的各种现象,如滞后回路,循环稳定效应,弹性-塑性的光滑转变,等等。这些现象都用适当的例子作了说明。     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

拉－扭复合加载下不锈钢的弹塑性本构关系——Ⅱ．理论

提出应力是塑性应变空间内蕴几何学参数的泛函．一般情况下，塑性应变空间是非欧几何空间，而其度量张量是塑性应变和其历史的函数，但在初始各向同性和不可压的情况下可取成欧氏空间．本文在Ｉｌｙｕｓｈｉｎ理论，和Ｖａｌａｎｉｓ理论的基础上，提出在拉－扭复合加载下的εｐ１－εｐ３空间中新的积分型弹塑性本构关系，所建理论预测的结果和实验［１］相当一致，表明理论是合理的     

拉－扭复合加载下不锈钢的弹塑性本构关系——Ⅱ．理论

提出应力是塑性应变空间内蕴几何学参数的泛函．一般情况下，塑性应变空间是非欧几何空间，而其度量张量是塑性应变和其历史的函数，但在初始各向同性和不可压的情况下可取成欧氏空间．本文在Ｉｌｙｕｓｈｉｎ理论，和Ｖａｌａｎｉｓ理论的基础上，提出在拉－扭复合加载下的εｐ１－εｐ３空间中新的积分型弹塑性本构关系，所建理论预测的结果和实验［１］相当一致，表明理论是合理的     

材料的弹粘塑性本构关系和应力波的演化

试验表明，大多数工程材料在冲击载荷作用之下的变形一般都同时包含有可恢复的瞬态性弹性变形和不可恢复的粘滞性塑性变形，即其本构关系可以用弹粘塑性模型来描述。本文从内变量理论出发，探讨了时率相关材料的弹粘塑性本构关系的一般特性，建立了增量型的弹粘塑性本构关系的一般理论框架和普适的表达式，并且对两种最常用的本构模型——Bodner-Partom模型和Johnson-Cook模型给出了在一维应变条件下的具体形式。通过计算和讨论一维应变粘塑性靶板中冲击波的衰减机制和应力波的演化规律，特别是考察各种粘塑性本构模型中的材料参数对冲击波的衰减和应力波的演化的影响，得出了一些可以直接应用或具有一定借鉴价值的结果，为研究应力波的其他衰减机制以及在人防工程中智能防护层设计时新材料的选取奠定了基础。     

各向同性率无关材料本构关系的不变性表示

在内变量理论的框架下,针对各向同性率无关材料,使用张量函数表示理论建立了塑性应变全量及增量本构关系的最一般的张量不变性表示. 它们均由3个完备不可约的基张量组合构成,这3个基张量分别是应力的零次幂、一次幂和二次幂. 因此得出,塑性应变、塑性应变增量与应力三者共主轴. 通过对基张量的正交化,给出了本构关系式在主应力空间中的几何解释. 进一步,全量(或增量)本构关系中3个组合因子被表达为应力、塑性应变(或塑性应变增量)的不变量的函数. 当塑性应变(或塑性应变增量)的3个不变量之间满足一定关系时,所给出的本构关系将退化为经典的形变理论(或塑性势理论).最后,还讨论它与奇异屈服面理论的关系,当满足一定条件时,两者是一致的.      

运动硬化材料本构关系的精确积分及其推广应用

考虑到弹塑性有限元分析中的每一增量步长或迭代之后,需要对材料本构关系进行积分,本文导出了运动硬化材料本构关系的精确积分。算法步骤简洁。将它推广应用于各向同性硬化材料和混合硬化材料时,对于径向加载情况,此积分仍是精确解;对于非径向加载情况,此积分是具有很高精度的近似解。计算结果表明本文提出的算法在精度和效率上改进了现行的子增量法的数值积分方案。     

线性强化材料弹塑性分析的自然单元法

自然单元法(NEM)是一种求解偏微分方程的无网格数值方法,其形函数兼具无网格法的特点和传统有限元法的优点.本文基于塑性增量理论,将自然单元法应用于弹塑性问题的分析计算中.为实现近似函数在非凸边界上的线性变化,采用约束的自然单元法(C-NEM)进行形函数计算.给出了增量切线刚度法求解非线性控制方程的相关公式,并对加载状态的确定和过渡状态下比例因子的计算方法等问题进行了深入的研究.编制了Von-Mises屈服准则下线性强化材料模型的二维弹塑性分析计算程序.算例分析表明,用自然单元法分析弹塑性力学问题是可行的,具有前处理过程简单、可以方便地准确施加本质边界条件等优点.     

Nonproportional loading effects on elastic-plastic behavior based on stress resultants for thin plates of strain hardening materials

A stress resultant constitutive law in rate form is constructed for power-law hardening materials. The change of plate thickness is considered in the constitutive law. The elastic-plastic behavior of a plate element based on the stress resultant constitutive law under uniaxial combined tension and bending is determined under a limited number of nonproportional and unloading paths. The results based on the stress resultant constitutive law and the through-the-thickness integration method are compared within the context of both the small-strain and finite deformation approaches. The results indicate that the selection of the normalized equivalent stress resultant and the corresponding work-conjugate normalized equivalent generalized strain is appropriate for describing the hardening behavior in the stress resultant space. However, the hardening rule in a power law form must be modified for low hardening materials at large plastic deformation when finite deformation effects are considered.     

受轴向冲击薄壁圆管的几何畸变相似律研究

对于受轴向冲击载荷作用的薄壁圆管动态响应的相似律问题,由于圆管的薄壁特性导致厚度无法与高度和半径按相同的比例进行结构缩放,从而产生模型的几何畸变,此时传统的相似律已无法描述原型与畸变模型之间的动态响应规律。基于薄壁圆管轴向冲击问题的控制方程,通过能量守恒和量纲分析,推导了考虑几何畸变条件下轴向冲击载荷作用的理想弹塑性薄壁圆管动态响应的相似律。通过在给定应变与应变率区间上建立比例模型预测的流动屈服应力与原型流动屈服应力的最佳逼近关系,将几何畸变相似律进一步推广至包含应变率和应变硬化的材料。通过数值方法验证了提出的几何畸变模型相似律的适用性。分析结果表明,提出的考虑厚度畸变的受轴向冲击薄壁圆管的相似律可用于预测原型结构的冲击动态响应,并显著降低比例模型与原型结构平均载荷和能量的偏差。     

A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials is derived. The evolution equation for the active yield surface with reference to the memory yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function for pressure insensitive and sensitive materials. Detailed incremental constitutive relations for materials based on the Mises yield function, the Hill quadratic anisotropic yield function and the Drucker–Prager yield function are derived as the special cases. The closed-form solutions for one-dimensional stress–plastic strain curves are also derived and plotted for materials under cyclic loading conditions based on the three yield functions. In addition, the closed-form solutions for one-dimensional stress–plastic strain curves for materials based on the isotropic Cazacu–Barlat yield function under cyclic loading conditions are summarized and presented. For materials based on the Mises and the Hill anisotropic yield functions, the stress–plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. For materials based on the Drucker–Prager and Cazacu–Barlat yield functions, the stress–plastic strain curves do not close and show the ratcheting effect under uniaxial cyclic loading conditions. The ratcheting effect is due to different strain ranges for a given stress range for the unloading and reloading processes. With these closed-form solutions, the important effects of the yield surface geometry on the cyclic plastic behavior due to the pressure-sensitive yielding or the unsymmetric behavior in tension and compression can be shown unambiguously. The closed form solutions for the Drucker–Prager and Cazacu–Barlat yield functions with the associated flow rule also suggest that a more general anisotropic hardening theory needs to be developed to address the ratcheting effects for a given stress range.     

Spring-back evaluation of automotive sheets based on isotropic-kinematic hardening laws and non-quadratic anisotropic yield functions: Part I: theory and formulation

In order to improve the prediction capability of spring-back in automotive sheet forming processes, the modified Chaboche type combined isotropic-kinematic hardening law was formulated based on the modified equivalent plastic work principle to account for the Bauschinger effect and transient behavior. As for the yield stress function, the non-quadratic anisotropic yield potential, Yld2000-2d, was utilized under the plane stress condition. Besides the theoretical aspect of the constitutive law including the general plastic work principle for monotonously proportional loading, the method to determine hardening parameters as well as numerical formulations to update stresses were developed based on the incremental deformation theory and the consistency requirement as summarized in Part I, while the characterization of material properties and verifications with experiments are discussed in Part II and III, respectively.     

非比例加载下两相介质弹塑性特性的有限元分析

在Ｉｌｙｕｓｈｉｎ五维应变空间下,利用弹塑性有限变形的有限元法。研究了两相介质在非比例加载下的弹塑性特性,提出了应力模、延迟角随应变路径、转折角变化的近似计算公式,计算结果还表明,工程材料的许多复杂本构特性都是由第二相介质引起的．     

Constitutive modeling of cyclic plasticity deformation of a pure polycrystalline copper

Cyclic plasticity experiments were conducted on a pure polycrystalline copper and the material was found to display significant cyclic hardening and nonproportional hardening. An effort was made to describe the cyclic plasticity behavior of the material. The model is based on the framework using a yield surface together with the Armstrong–Frederick type kinematic hardening rule. No isotropic hardening is considered and the yield stress is assumed to be a constant. The backstress is decomposed into additive parts with each part following the Armstrong–Frederick type hardening rule. A memory surface in the plastic strain space is used to account for the strain range effect. The Tanaka fourth order tensor is used to characterize nonproportional loading. A set of material parameters in the hardening rules are related to the strain memory surface size and they are used to capture the strain range effect and the dependence of cyclic hardening and nonproportional hardening on the loading magnitude. The constitutive model can describe well the transient behavior during cyclic hardening and nonproportional hardening of the polycrystalline copper. Modeling of long-term ratcheting deformation is a difficult task and further investigations are required.     

An integral elasto-plastic constitutive theory

This paper proposes an integral elasto-plastic constitutive equation, in which it is considered that stress is a functional of plastic strain in a plastic strain space. It is indicated that, to completely describe a strain path, the arc-length and curvature of the trajectory, the turning angles at the corner points and other characteristic points on the path must be considered. In general, the plastic strain space is a non-Euclidean geometric space, hence its measure tensor is a function of not only properties of the material but also the plastic strain history. This recommended integral elasto-plastic constitutive equation is the generalization of Ilyushin, Pipkin, Rivlin and Valanis theories and is suited to research the responses of material under the complex loading path. The predictions of the proposed theory have a good agreement with the experimental results.     

The inelastic behavior of metals subject to loading reversal

One of the consequences of memory effects in the plastic deformation of metals is the Bauschinger effect (Civilingenieur 27 (1881) 289–348), which manifests itself as a difference in the values of the yield stress in tension and compression for a material that has undergone plastic deformation. The Bauschinger effect has been modeled with the kinematic hardening rules e.g., Ziegler (Quart. Appl. Math. 17 (1959) 55) and Chaboche (Int. J. Plasticity 2 (1986) 149). These models, though, are not able to reproduce the stress-strain response accurately at points of loading reversal: it has been observed (Acta Metall. 34 (1986) 1553; Mater. Sci. Engineering A113 (1989) 441) that, for some materials, the stress has a plateau after the loading is reversed. This is not reflected by the kinematic hardening rule nor by its modifications. In this paper we will develop a general three dimensional model that is able to reproduce the stress–strain response at loading reversals and can be applied also to more general changes of loading direction. The central idea of our model is to link the hardening behavior of the material to thermodynamical quantities such as the stored energy due to cold work and the rate of dissipation. The predictions of the theory show good agreement with the stress–strain curve and also with the manner in which the stored energy varies with the inelastic strain, as obtained from experiments (Progress in Materials Science (1973) Vol. 17. Pergamon, Oxford; Trans. Met. Soc. AIME 224 (1962) 719).