有限弹塑性变形的三维组集式本构模型

本文将文[1]中提出的三维组集式弹塑性本构模型推广应用于有限变形分析,导出了全量型和增量型本构关系在初始构形上的拉格朗日(Total Lagrange)形式和瞬时构形上的拉格朗日(Updated Lagrange)形式。文中对晶体单轴拉伸中的宏观剪切带进行了分析。预测结果与实验吻合。从而说明这种本构模型能够模拟有限变形中的几何非线性效应和晶体材料塑性变形中的宏观力学行为。     

饱和和非饱和介质的弹塑性损伤模型

针对饱和和非饱和工程材料变形和强度特点,给出了一个具体的弹塑性损伤本构方程,该本构方程可以描述材料性质的劣化过程（即损伤和软化）以及饱和程度对材料变形强度特性的影响。此外,还讨论了该弹塑性损伤本构方程的有限元实施方法,编制了专用的有限元程序。对常规三轴试伯进行了有限元分析,得出了一些具体的结果。     

一种描述形状记忆合金拟弹性变形行为的本构关系

本文给出一种描述形状记忆合金拟弹性变形现象的本构关系,可用于多晶材料在一般应力状态下及单晶材料在单轴应力下的变形情况。该本构关系采用弹性应变与相变应变迭加形式,物理意义明显,形式简洁。对 Cu-Zn-Sn 合金及 Ti-Ni 合金材料的变形行为进行了模拟计算,结果与实验值有较好的吻合。     

浅曲梁大挠度分析的余能有限元方法

以高玉臣提出的弹性大变形余能原理为基础,利用Lagrange乘子,放松平衡方程和力边界条件对余能泛函的约束,推导出广义的余能原理.根据极分解定理,将变形分为刚性转动和纯变形两部分,则余能也包含相应的两部分,一部分与刚性转动有关,而另一部分与纯变形有关.使用线弹性本构关系,建立了可用于几何非线性计算的有限元模型.应用更新的Lagrange列式法,给出了增量形式的有限元公式.数值计算结果表明,该方法可用于浅曲粱的几何大变形计算.     

有机玻璃在高应变率下的损伤型非线性粘弹性本构关系及破坏准则

对两种有机玻璃高应变率下的大变形和破坏行为进行了实验研究,通过改进文献[2]本构关系的非线性弹性项并引入损伤参量,建立了一个适用于更大变形范围、能描述应力平台及本构失稳的损伤型非线性粘弹性本构方程。相应地,从临界损伤量概念出发,提出以应变和应变率为控制变量的破坏准则。不论是本构关系还是破坏准则,理论计算均与试验结果吻合良好。     

形状记忆合金拟弹性行为的热力学描述

形状记忆合金是由马氏体和奥氏体组成并动态变化的两相材料 ,其拟弹性行为实质上是两相各自行为的动态组合。本文提出了形状记忆合金拟弹性行为的一种热力学描述。根据实验现象假设在感兴趣的温度和变形范围内 ,奥氏体相具有线弹性特性而马氏体相具有弹塑性特性 ,结合 Tanaka的相变描述 ,给出了小变形、初始各向同性和塑性不可压缩条件下形状记忆合金的三维本构方程。对不同温度下形状记忆合金材料的特性进行了描述 ,较好地预言了单调及循环加载下的响应和正、反相变行为及其温度影响 ,动态相变过程对应力响应的影响 ,高温相下的强度增加等。     

一种描述形状记忆合金拟弹性变形行为的本构关系

本文给出一种描述形状记忆合金拟弹性变形现象的本构关系,可用于多晶材料在一般应力状态下及单晶材料在单轴应力下的变形情况。该本构关系采用弹性应变与相变应变迭加形式,物理意义明显,形式简洁。对 Cu-Zn-Sn 合金及 Ti-Ni 合金材料的变形行为进行了模拟计算,结果与实验值有较好的吻合。     

钢方管截面柱考虑损伤的滞回性能分析

结构钢本构关系的精度直接影响分析结果的可靠度.根据能量等效性假设、热力学第二定律,推出损伤材料的弹性本构方程;采用混合强化准则,考虑Bauschinger效应、屈服平台、硬化(软化)效应及损伤和损伤演化影响,建立了的结构钢弹塑性各向异性损伤本构关系.结合构建的本构关系,采用八节点超参数壳体单元,推导了用U.L.格式及Cauchy应力描述的板壳双重非线性有限元方程,并编制了计算程序.利用U.L.格式的壳体大挠度双重非线性有限元分析方法,对钢方管截面短柱进行面内拉压循环荷载作用下的滞回性能分析.     

有初始几何缺陷的壳体弹塑性大变形分析

在等温小变形弹塑性内时本构方程偏量形式的基础上，导出了适用于大位移、小应变分析的弹塑性内时本构方程。并导出了带有初始几何缺陷的非线性弹塑性问题的有限元方程。文中给出的算例表明本方法是可行有效的。     

缝合式C/SiC复合材料非线性本构关系及断裂行为研究

C/SiC复合材料具有高比强度、高比模量和优良的热稳定性能等一系列优点, 广泛应用于航空航天领域中. 裂纹扩展进而引起的脆性断裂是其主要失效形式之一, 因而材料的断裂性能分析对材料的结构设计和应用有重要的指导意义. 本文开展了缝合式C/SiC复合材料简单力学试验和断裂试验, 研究了材料在不同载荷下的力学响应及断裂特征. 基于缝合式C/SiC复合材料简单力学试验, 建立了材料宏观非线性损伤本构方程, 并模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 本构方程采用简单函数描述了材料在复杂应力状态下的非线性应力-应变曲线, 并考虑了反向加载过程中造成的裂纹闭合. 基于商业有限元软件ABAQUS, 通过编写UMAT子程序实现非线性损伤本构方程, 采用单个单元验证了建立的本构方程的有效性. 在此基础上, 采用线弹性损伤本构和非线性损伤本构分别模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 采用非线性损伤本构方程模拟的力-位移曲线结果与试验结果更为吻合, 非线性损伤本构预测的失效载荷与试验失效载荷更为接近, 验证了所建立的非线性损伤本构方程的准确性, 为C/SiC复合材料断裂行为的研究提供了借鉴, 为缝合式C/SiC复合材料结构的设计和应用提供了理论基础.      

Prediction of extrudate swell in polymer melt extrusion using an Arbitrary Lagrangian Eulerian (ALE) based finite element method

Accurate prediction of extrudate (die) swell in polymer melt extrusion is important as this helps in appropriate die design for profile extrusion applications. Extrudate swell prediction has shown significant difficulties due to two key reasons. The first is the appropriate representation of the constitutive behavior of the polymer melt. The second is regarding the simulation of the free surface, which requires special techniques in the traditionally used Eulerian framework. In this paper we propose a method for simulation of extrudate swell using an Arbitrary Lagrangian Eulerian (ALE) technique based finite element formulation. The ALE technique provides advantages of both Lagrangian and Eulerian frameworks by allowing the computational mesh to move in an arbitrary manner, independent of the material motion. In the present method, a fractional-step ALE technique is employed in which the Lagrangian phase of material motion and convection arising out of mesh motion are decoupled. In the first step, the relevant flow and constitutive equations are solved in Lagrangian framework. The simpler representation of polymer constitutive equations in a Lagrangian framework avoids the difficulties associated with convective terms thereby resulting in a robust numerical formulation besides allowing for natural evolution of the free surface with the flow. In the second step, mesh is moved in ALE mode and the associated convection of the variables due to relative motion of the mesh is performed using a Godunov type scheme. While the mesh is fixed in space in the die region, the nodal points of the mesh on the extrudate free surface are allowed to move normal to flow direction with special rules to facilitate the simulation of swell. A differential exponential Phan Thien Tanner (PTT) model is used to represent the constitutive behavior of the melt. Using this method we simulate extrudate swell in planar and axisymmetric extrusion with abrupt contraction ahead of the die exit. This geometry allows the extrudate to have significant memory for shorter die lengths and acts as a good test for swell predictions. We demonstrate that our predictions of extrudate swell match well with reported experimental and numerical simulations.     

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.     

形状记忆合金管接头空间轴对称有限元分析

本文采用形状记忆合金（ＳＭＡ）的三维本构方程和有限变形理论，考虑拉、压不同应力状态对相变点移动的规律，编制了ＳＭＡ轴对称大变形的有限元程序，与单向拉伸下解析所得的应力、应变曲线相比，证实程序的正确性．文末计算一ＳＭＡ管接头，并指出按空间轴对称计算的必要性．     

局部弹性翼型非定常分离的动力学特性

对在低雷诺数下局部弹性翼型绕流中, 局部弹性导致的自激振动所产生的复杂非定常流动分离现象和描述方法进行了分析. 采用ALE-CBS方法数值模拟了具有可动边界的绕流流场问题, 同时采用Galerkin方法求解局部弹性结构的控制方程. 着重研究了翼型的局部弹性对流动分离和翼型性能的影响, 并分别从Eulerian和Lagrangian的角度分析了局部弹性结构导致的不同非定常分离现象, 其中Lagrangian角度可以方便地揭示出局部弹性翼型大幅度提高升力的机理和流动中的能量迁移. 结果表明翼型的局部弹性对非定常分离和分离泡的演化过程有着明显的影响, 可以使得流体质点由主流获取动量实现再附, 并且在一定的攻角下可以将固定分离转变为移动分离, 从而明显地提高了翼型的升力.      

A 3D finite volume scheme for solving the updated Lagrangian form of hyperelasticity

The finite volume discretization of nonlinear elasticity equations seems to be a promising alternative to the traditional finite element discretization as mentioned by Lee et al. [Computers and Structures (2013)]. In this work, we propose to solve the elastic response of a solid material by using a cell‐centered finite volume Lagrangian scheme in the current configuration. The hyperelastic approach is chosen for representing elastic isotropic materials. In this way, the constitutive law is based on the principle of frame indifference and thermodynamic consistency, which are imposed by mean of the Coleman–Noll procedure. It results in defining the Cauchy stress tensor as the derivative of the free energy with respect to the left Cauchy–Green tensor. Moreover, the materials being isotropic, the free‐energy is function of the left Cauchy–Green tensor invariants, which enable the use of the neo‐Hookean model. The hyperelasticity system is discretized using the cell‐centered Lagrangian scheme from the work of Maire et al. [J. Comput. Phys. (2009)]. The 3D scheme is first order in space and time and is assessed against three test cases with both infinitesimal displacements and large deformations to show the good accordance between the numerical solutions and the analytic ones. Copyright © 2016 John Wiley & Sons, Ltd.     

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。