混凝土轴拉加卸载随机损伤模型的建立与试验验证

为了分析及深入探讨混凝土在受拉加载及卸载情况下的力学特性,基于随机损伤本构关系提出了一种混凝土轴拉加卸载模型,推导出了混凝土加卸载的应力 应变关系表达式.为了印证理论表达式,进行了混凝土轴向拉伸及加卸载的试验研究,测得了混凝土的材料参数及其相应的轴拉加卸载应力-应变曲线.结合模型的计算结果,对混凝土的轴拉加卸载试验结果进行了对比分析,结果表明:混凝土轴拉加卸载模型能够预测混凝土的极限强度,同时能描述混凝土的强度软化、加载过程中的弹模折减及卸载后的塑性变形.     

三维非线性有限元与弹性边界元耦合数值方法

本文系统地讨论了以下三个问题:(1) 有限元与边界元耦合中的几个数值问题,其中包括:边界积分方程的凝聚、等效刚度矩阵的对称化及面力不连续的处理;(2) 弹塑性有限元与弹性边界元的耦合;(3) 弹粘塑性有限元与弹性边界元的耦合及数值计算稳定性条件。     

A theory of large-strain isotropic thermoplasticity based on metric transformation tensors

Summary A formulation of isotropic thermoplasticity for arbitrary large elastic and plastic strains is presented. The underlying concept is the introduction of a metric transformation tensor which maps a locally defined six-dimensional plastic metric onto the metric of the current configuration. This mixed-variant tensor field provides a basis for the definition of a local isotropic hyperelastic stress response in the thermoplastic solid. Following this fundamental assumption, we derive a consistent internal variable formulation of thermoplasticity in a Lagrangian as well as a Eulerian geometric setting. On the numerical side, we discuss in detail an objective integration algorithm for the mixed-variant plastic flow rule. The special feature here is a new representation of the stress return and the algorithmic elastoplastic moduli in the eigenvalue space of the Eulerian plastic metric for plane problems. Furthermore, an algorithm for the solution of the coupled problem is formulated based on an operator split of the global field equations of thermoplasticity. The paper concludes with two representative numerical simulations of thermoplastic deformation processes.     

具有损伤耦合效应的弹塑性蠕变问题结构分析的变分原理

本文基于连续介质损伤力学中有效应力的概念,研究弹塑性蠕变问题中的损伤耦合,并应用由最优控制理论基本思想发展起来的参变量变分原理建立起用于弹塑性蠕变损伤问题结构分析的变分原理.文中给出了原理的证明.该原理的物理意义明确,表达式简单且规范,容易为数值手段实现.     

Thermomechanical formulation of ductile damage coupled to nonlinear isotropic hardening and multiplicative viscoplasticity

In this paper, we present a thermomechanical framework which makes use of the internal variable theory of thermodynamics for damage-coupled finite viscoplasticity with nonlinear isotropic hardening. Damage evolution, being an irreversible process, generates heat. In addition to its direct effect on material's strength and stiffness, it causes deterioration of the heat conduction. The formulation, following the footsteps of Simó and Miehe (1992), introduces inelastic entropy as an additional state variable. Given a temperature dependent damage dissipation potential, we show that the evolution of inelastic entropy assumes a split form relating to plastic and damage parts, respectively. The solution of the thermomechanical problem is based on the so-called isothermal split. This allows the use of the model in 2D and 3D example problems involving geometrical imperfection triggered necking in an axisymmetric bar and thermally triggered necking of a 3D rectangular bar.     

有限元分析中硬化弹塑性本构方程积分算法

基于增量段上的应变关于塑性拉氏乘子的变化率为常矢量的假定,导出一种精确有效的、对有限元分析中线性混合硬化弹塑性本构方程的积分算法。以精确算例和等误差分布图的形式检验了本文方法以及其他两种常用方法的精度。     

基于微结构损伤的珠光体材料本构行为研究

珠光体材料由许多随机取向的珠光体团组成，每一珠光体团又由铁素体片和渗碳体片交替 叠合而成. 实验表明具有较小片层间距的珠光体材料具有较高的强度和寿命. 通过分析构成 珠光体团的各相及界面的损伤特征，利用损伤耗散功的概念，得到了铁素体、渗碳体与界面 损伤的具有统一形式的演化规律，将其嵌入基于细片层微结构和非经典塑性理论的珠光体团 的弹塑性本构方程，利用Hill自洽方法，得到了珠光体材料的损伤本构描述. 所得到的损 伤本构描述显含表征微结构特征的片层间距，容易证明具有较小片层间距的珠光体材料具有 较好的综合力学性能. 对珠光体材料的拉伸和循环拉压特性进行了分析，得到了与实验一 致的结果.     

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

We provide a global existence result for the time-continuous elastoplasticity problem using the energetic formulation. For this, we show that the geometric nonlinearities arising from the multiplicative decomposition of the strain can be controlled via polyconvexity and a priori stress bounds in terms of the energy density. While temporal oscillations are controlled via energy dissipation, the spatial compactness is obtained via regularizing terms involving gradients of the internal variables. Dedicated to Sir John Ball on the occasion of his 60th birthday.     

Analytical removal of singularity and direct evaluation of singular integrals in 3-D elastoplastic finite deformation analysis by BEM

As a further development of the present authors' research work [1,2], in this paper a method of the so-called quadratic pentahedron polar co-ordinate transformation and analytical removal of singularity of Cauchy principal value singular integrals is proposed to evaluate the strongly singular integrals in the sense of Cauchy principal values and the weakly singular integrals over quadratic internal cells in 3-D elastoplastic finite deformation analysis by BEM. First, a quadratic pentahedron polar co-ordinate transformation technique is used to reduce the order of singularity of the singular integrals. Then, a form of Gauss' theorem is introduced to remove the singularity in the Cauchy principal value singular integrals analytically. Therefore, the evaluation of all those strongly and weakly singular integrals can be carried out by standard Gaussian quadrature accurately and efficiently. Numerical examples of the 3-D elastoplastic problem and 3-D finite deformation problem are given to demonstrate that the method possesses good accuracy and numerical stability, and is convenient to implement. The method in this paper can be applied extensively to evaluating the singular integrals over cubic and higher order elements.