三维轮轨法向接触力学行为弹塑性理论分析

基于Hertz接触理论和双线性强化模型,建立了轮轨法向接触弹塑性理论分析模型,分析了轮轨法向接触力学响应特征,讨论了轴重对接触压力和接触变形的影响规律。同时,基于三维轮轨接触有限元模型模拟了轮轨接触力学行为,并引入理论误差系数分析了弹性模型和双线性强化模型对轮轨接触力学响应预测结果的差异性。结果表明,轮轨最大接触压力和接触变形量均随轴重的增大而增大;双线性强化模型的理论误差系数较小,采用双线性强化分析模型能较准确地预测轮轨接触弹塑性力学行为。研究结果可为轮轨系统安全服役和损伤评估提供理论和技术支持。     

Time-independent anisotropic plastic behavior by mechanical subelement models

The paper describes a procedure for modelling the anisotropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are considered as piecewise linear for simplicity. The model is incorporated in a finite element analysis program which is based on the assumed stress hybrid element and the viscoplasticity theory.     

Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

Analytical solutions for the dynamic cylindrical cavity expansion in a com-pressible elastic-plastic cylinder with a finite radius are developed by taking into account of the effect of lateral free boundary, which are different from the traditional cavity expan-sion models for targets with infinite dimensions. The finite cylindrical cavity expansion process begins with an elastic-plastic stage followed by a plastic stage. The elastic-plastic stage ends and the plastic stage starts when the plastic wave front reaches the lateral free boundary. Approximate solutions of radial stress on cavity wall are derived by using the Von-Mise yield criterion and Forrestal’s similarity transformation method. The effects of the lateral free boundary and finite radius on the radial stress on the cavity wall are discussed, and comparisons are also conducted with the finite cylindrical cavity expansion in incompressible elastic-plastic materials. Numerical results show that the lateral free boundary has significant influence on the cavity expansion process and the radial stress on the cavity wall of metal cylinder with a finite radius.     

Measurement of elastic-plastic stresses by scattered-light photomechanics

Several birefringent materials were studied for their suitability for use in three-dimensional photoplasticity. This study resulted in the selection of cellulose propionate as model material. Its close match in index of refraction with ordinary mineral oil makes cellulose propionate suitable for scattered-light photomechanics. Viscoelastic behavior of the material is used to simulate elastic-plastic behavior of metals. The stress, strain and optical behavior of the material has been studied under slow loading in finite steps. A successful solution of an elastic-plastic torsion problem was obtained, demonstrating the applicability of the techniques of scattered-light photoplasticity to three-dimensional problems. This experimental method does not require the unloading and slicing of the model, avoiding any errors that might be introduced by residual stresses due to unloading. A major advantage of the method is the use of live loading, which allows the investigation of several load levels with the same model. Stress- and strain-concentration factors for the grooved shaft in torsion showed excellent agreement with Neuber's analytical results. Distributions of shear stress and shear strain across the minimum section of the model were compared to elastic theory. Integration of the shear-stress distributions showed good agreement with the measured values of applied torque.     

The simple shear oscillation and the restrictions to elastic-plastic constitutive relations

Based on the definitions of hardening, softening and ideal plastic behavior of elastic-plastic materials in the true stress tensor space, the phenomena of simple shear oscillation are shown to be relative to the oscillatory occurrence of hardening and softening behavior of elastic-plastic materials, namely the oscillation of hardening behavior, by analyzing a simple model of rigid-plastic materials with kinematical hardening under simple shear deformation. To make the models of elastic-plastic materials realistic, must be satisfied the following conditions: for any constitutive model, its response stresses to any continuous plastic deformation must be non-oscillatory, and there is no oscillation of hardening behavior during the plastic deformation.     

Analytical dynamic model of elastic-plastic pipe-on-pipe impact

The dynamic response of pipe-on-pipe impact is described by an analytical model. The model considers the impact of a whipping pipe with one end hinged and the other end free on a simply-supported target pipe at its midpoint. Combining with the contact theory, the Laplace transformation, and the inverse Laplace transformation method, an analytical model based on the tubular beam theory is proposed to study the elastic-plastic behavior of a target pipe laterally impacted by a whipping pipe. Numerical simulations using the explicit finite element code MSC/DYTRAN are also performed. The results are coincident with the theoretical prediction.     

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF HETEROGENEOUS MATERIALS WITH VORONOI FINITE ELEMENT METHOD

The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.     

脉冲载荷作用下钢梁动力响应及反常行为的应变率效应

为了讨论率敏感材料软钢钢梁受矩形脉冲载荷作用下的动力响应问题,通过直接离散有限变形弹塑性连续体最小加速度原理中的Lee泛函得到基本控制方程,并将包含应变率的Cowper-Symonds方程嵌入应力-应变关系方程,使该计算模型计及材料的应变率效应,因而能够准确描述钢梁受爆炸和冲击载荷作用下的动力响应问题。该计算模型的有效性通过与通用有限元程序ABAQUS比较而得到了验证,并进一步与已有的刚塑性解做了对比。利用该计算模型进行数值计算,分析了均布和集中脉冲载荷作用下钢梁动力响应的应变率效应,结果发现对于钢梁存在新的异常行为响应模式,应变率导致异常区域偏移和扩大,已有的刚塑性解在一定载荷强度范围内不能准确预报钢梁的实际位移。     

固体火箭发动机滚动球窝喷管弹塑性摩擦接触承载性能分析

固体火箭发动机滚动球窝喷管的弹塑性摩擦接触承载性能,属于复杂结构在复杂载荷作用下的弹塑性摩擦接触问题,它直接决定着系统的结构设计和功能发挥。为保证系统在承受极端工作载荷时,喷管不产生大的轴向位移,阴球、阳球与滚动体间具有一定的接触强度,同时不产生过量的塑性变形,设计阶段,基于计算精度高的三维摩擦接触问题的Lagrange乘子法,解决了与弹塑性耦合的算法问题;在滚动体运动分析及摩擦测试的基础上,模拟系统冷试车冲压试验,充分考虑材料表面强化层,建立了各构件间的弹塑性摩擦接触模型。有限元计算结果及冷试车分解试验、系统作动力矩测试试验结果表明,系统弹塑性摩擦接触承载性能满足结构设计要求,有限元建模及计算结果正确。     

Experimental and FEM study of windshield subjected to high speed bird impact

Both experimental and finite element model (FEM) results are presented for the dynamic strength behavior of windshield subjected to bird impact. The experimental data taken from a series of high speed photographs are compared with the numerical results predicted by using FEM in which the windshield was modeled entirely with solid elements and the bird body was approximately simulated by an elastic-plastic material with failure element behavior. Effective plastic strain and element pressure were adopted as the failure criteria and once the pressure or the effective plastic strain of an element reached the critical value, the element would lose the tensile resistance capability completely. The deflection and stress distribution in the windshield were obtained. It is shown that the result from the finite element analysis agrees with those from the full-scale bird impact test. The project supported by the National Natural Science Foundation of China (10272011)     

A damage model for crack initiation and growth

A damage accumulation model is presented for the study of the problem of crack initiation and stable growth in an elastic-plastic material. A centre-cracked specimen subjected to a uniform stress perpendicular to the crack plane is considered. A coupled stress and failure analysis is performed by using a finite element computer program based on J₂-plasticity theory in conjunction with the strain energy density theory. After initial yielding, each material element follows a different equivalent uniaxial stress-strain behavior depending on the amount of energy dissipation by permanent deformation. A host of uniaxial stress-strain curves constituting parts of the same stress-strain curve were assigned to material elements for each increment of loading. The path-dependent nature of the onset of crack initiation and growth was revealed. The proposed model predicts faster crack growth rates than those obtained on the basis of a single uniaxial stress-strain curve and is closer to experimental observation.     

Flange earing and its control on deepdrawing of anisotropy circular sheets

The Hill's quadric anisotropy yield function and the Barlat-Lian anisotropy yield function describing well anisotropy sheet metal with stronger texture are introduced into a quadric-flow corner constitutive theory of elastic-plastic finite deformation suitable for deformation localization analysis. And then, the elastic-plastic large deformation finite element formulation based on the virtual power principle and the discrete Kirchhoff shell element model including the yield functions and the constitutive theory are established. The focus of the present research is on the numerical simulation of the flange earing of the deep-drawing of anisotropy circular sheets, based on the investigated results, the schemes for controlling the flange earing are proposed. Supported by NSFC(No. 19832020) and National Automobile Dynamic Simulation Laboratory of China.     

On the bifurcation and postbifurcation analysis of elastic-plastic solids under general prebifurcation conditions

In this work we have studied the bifurcation and postbifurcation of elastic-plastic solids whose behavior near the critical point could not be idealized as hypoelastic and thus the “hypoelastic comparison solid” concept of R. Hill's theory is no longer applicable. First a simple continuous model is considered in order to illustrate the different possibilities in the stability behavior of the structures considered here. Next, a general three-dimensional stability analysis for a broad class of rate independent elastic-plastic solids is presented. It is found that for all the constitutive theories considered and for all possible prebifurcation solutions, the bifurcation functional is a simple generalization of Hill's. A completely different postbifurcation analysis is needed, however, in the case where the “hypoelastic comparison solid” concept cannot be used.     

复合地基承载特性的弹塑性分析

对桩及承台采用线弹性有限元模型,对承台下桩周土采用弹塑性有限元模型,对群桩以外的土体采用线弹性无限元模型,在桩土接触面上设置接触面单元,利用三维弹塑性有限元对桩%D土%D承台相互作用进行了分析。得出了如下结论 :承台下桩顶反力总体表现出角桩最大,边桩次之,中桩最小的分布规律,随着作用在承台上的荷载增大,桩顶反力趋于均匀分布,承台下桩侧摩阻力是由桩端向桩顶逐渐发展的,承台对桩上部侧摩擦阻力存在“削弱作用”。为了验证本文方法的可行性,对承台下有九桩的情况进行了静载试验,将试验结果与本文计算结果进行了比较。     

Corotational rates in constitutive modeling of elastic-plastic deformation

The principal axes technique is used to develop a new hypoelastic constitutive model for an isotropic elastic solid in finite deformation. The new model is shown to produce solutions that are independent of the choice of objective stress rate. In addition, the new model is found to be equivalent to the isotropic finite elastic model; this is essential if both models describe the same material.

The new hypoelastic model is combined with an isotropic flow rule to form an elastic-plastic rate constitutive equation. Use of the principal axes technique ensures that the stress tensor is coaxial with the elastic stretch tensor and that solutions do not depend on the choice of objective stress rate. The flow rule of von Mises and a parabolic hardening law are used to provide an example of application of the new theory. A solution is obtained for the prescribed deformation of simple rectilinear shear of an isotropic elastic and isotropic elastic-plastic material.     

ELASTIC-PLASTIC DYNAMIC RESPONSE OF FULLY BACKED SANDWICH PLATES UNDER LOCALIZED IMPULSIVE LOADING

An analytical model is developed to assess the elastic-plastic dynamic response of fully backed sandwich plates under localized impulse load.The core is modeled as an elastic-perfectly plastic foundation.The top face sheet is treated as an individual plate resting on the foundation.The elastic-plastic analysis for the top face sheet is based on a minimum principle in dynamic plasticity associated with the finite difference technique.The effects of spatial and temporal distributions of the impulsive loading on the dynamic response of sandwich plates are discussed.The model can be used to predict the impulse-induced local effect on fully backed sandwich plates.     

A weighted residual method for elastic-plastic analysis near a crack tip and the calculation of the plastic stress intensity factors

In this paper,a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample.The elastic-plastic solutions of the crack tip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field,to calculate the plastic stress intensity factors,are also developed.Therefore,a complete analysis based on the calculation both for the crack tip field and for the whole crack body field is provided.     

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS OF COSSERAT CONTINUUM

A new algorithm is developed based on the parametric variational principle for elastic-plastic analysis of Cosserat continuum. The governing equations of the classic elastic-plastic problem are regularized by adding rotational degrees of freedom to the conventional translational degrees of freedom in conventional continuum mechanics. The parametric potential energy principle of the Cosserat theory is developed, from which the finite element formulation of the Cosserat theory and the corresponding parametric quadratic programming model are constructed. Strain localization problems are computed and the mesh independent results are obtained.     

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.     

基于参数变分原理的Cosserat连续体弹塑性分析

基于参数变分原理,提出了Cosserat模型弹塑性计算的算法,给出了基于Cosserat理论的参数最小势能原理,基于所提出的变分方程,建立了Cosserat理论弹塑性分析的参数二次规划模型,进一步将算法应用于平面应变软化问题计算中,获得的结果具有良好的非网格依赖性.