率相关晶体塑性模型的塑性各向异性分析

在Sarma和Zacharia的工作基础上,改进了单晶晶体弹粘塑性本构模型的积分算法,并采用改进的欧拉法结合迭代方法求解,特点是稳定性好计算效率较高．然后用上述模型及算法研究了:1）在单向拉伸和平面应变压缩变形下单晶塑性各向异性的特点;2）晶体模型中的主要材料参数（应变率敏感指数m和潜硬化比率q）和加载应变率对单晶塑性各向异性的影响;3）沿不同的晶体方向加载对滑移系启动的影响．     

梯度增强的弹塑性损伤非局部本构模型研究

简要介绍了几种主要的梯度增强非局部模型．基于“能量耗散梯度依赖”原则,在连续介质热力学框架内推导了梯度增强损伤与塑性耦合的本构关系,同时给出了一个基于塑性的损伤模型的梯度依赖本构的具体形式．在数值计算方面,结合移动最小二乘法和泰勒级数展开方法,建立了损伤场（有限元高斯积分点上）的Laplace值的近似求解格式,分别给出了二维和三维情况下的相关公式．给出的二维的韧性断裂的梯度依赖损伤塑性的数值应用,表明了格式的有效性和实用性．还讨论了内部长度的意义及取值问题．     

加筋碟形薄壳的塑性屈曲分析

本文采用非线性前屈曲一致理论分析均布外压下加筋碟形薄壳的塑性屈曲问题，建立了这类壳体的能量表达式和屈曲方程，给出了简明的计算格式，数值分析结果表明，所导出的算法具有较好的精度，计算过程也简单方便。     

基于复杂网络的黏性土颗粒边坡堆积体失稳研究

对颗粒边坡堆积体模型在金属板向下持续作用时的失稳破坏过程进行了颗粒离散元模拟,得出了二维边坡堆积体土颗粒速度总矢量、边坡堆积体失稳破坏时滑移开裂面的角度以及边坡堆积体坡顶y方向的平均速度等宏观响应过程.构建了自然堆积下边坡堆积体颗粒的法向力链无向网络模型,研究其滑移面出现的位置,并与实验结果做对比.最后,用复杂网络方法对边坡堆积体坡顶颗粒接触力链网络的拓扑特征进行了分析,得到平均度、簇聚系数和平均最短路径在边坡堆积体失稳过程中的演化规律,并结合强度折减法验证其准确性.研究结果表明,平均最短路径可以对边坡堆积体失稳破坏进行较为有效的预警.采用复杂网络理论研究边坡堆积体宏观响应与其力链网络介观结构之间的相互关系,为边坡失稳研究提供了一种全新的数学分析方法.     

基于等效滑移与潜在硬化机制的多晶金属亚宏观弹塑性模型

将多晶材料中晶片之间与晶粒界面上的滑移作为消耗塑性功的主要物理机制,提出一个由亚宏观滑移系作为耗能构元的材料模型,并用功共轭方法得到了亚宏观滑移系的等效滑移剪切率.重新给出了滑移系自身运动硬化、潜在硬化及Bauscninger效应的力学描述,导出了本构方程.在探讨材料性质参数对后继屈服面形状及尺寸变化影响的基础上,论述了模型的基本性质.与以晶粒为基本构元的多晶体自洽理论比较,所得到的本构方程具有简洁的数学表达,而且能精确有效地预测多晶金属材料在复杂加载条件下的宏观弹塑性力学行为.     

基于数值流形法的降雨入渗与坡面径流耦合算法研究

降雨时坡地的入渗-产流分析，是降雨型滑坡、泥石流等地质灾害机理研究中的重要课题之一.为实现边坡降雨-入渗-产流的全过程数值模拟，进一步提高计算效率，考虑将降雨入渗面视作坡面径流与坡体渗流的内部域，基于一维运动波方程和二维压力水头格式的Richards方程建立耦合模型，并推导出其总体控制方程，采用数值流形法(numerical manifold method, NMM)实现其数值求解，通过编制相应的计算程序分析了边坡降雨产流过程.数值分析结果表明：所建模型的计算结果与试验数据及前人模拟结果吻合良好，验证了该文模型及计算方法的有效性与可靠性；降雨强度越大，产流时间越早，坡面积水深度越大，对坡体内的水分分布影响范围越广.研究表明，所建模型能真实反映边坡降雨-入渗-产流全过程，可为降雨诱发的各类地质灾害分析提供计算依据.     

溢流体形的数值模拟

本文论述了自由面问题的有限元泛函极值,加权余量法离散格式,自由面调整方案,变换函数交替方向差分法迭代原理和边界层计算方程等问题。并得到水利工程中各种溢流坝坝面形状的流量系数、流速和压强分布、边界层厚度等方面的结果,与实验比较一致。     

基于非关联流动法则的圆形隧洞滑移线解答

圆形隧洞的滑移线方程早在20世纪中期苏联学者已给出解答,并在国内广泛应用．推导过程中假设滑移线与速度矢量方向夹角为45°-φ/2是错误的,理论上滑移线与速度矢量方向的夹角与采用的流动法则有关．该文分别从关联流动法则和非关联流动法则出发,推导了圆形隧洞的滑移线方程和水平方向破裂体深度的表达式．通过与模型试验结果进行对比,对岩土材料应采用基于非关联流动法则的滑移线解答.     

圆柱体不可压粘性流体非定常绕流的数值模拟

在本文中通过由计算机产生随机扰动并在物理模型中考虑随机扰动影响的做法,我们从非定常的NS方程出发,采用作者所发展的部分解析解格式以及一种保证壁面无滑移条件严格满足的新的确定壁面涡量边界条件的精确方法,仔细地计算了圆柱体不可压粘性流体非定常绕流的Karman涡街、数值结果与实验观察相符合。在计算中,我们还考虑了圆柱的起动过程。     

随机调幅Rattling系统建模

本文研究了一个随机调幅Ｒａｔｌｉｎｇ系统·代替常用的数值分析方法,采用非高斯截断技术,导出一个由三维平均映射描述的离散的随机模型·实测指出该模型能揭示浑沌随机性质,故更适于用以模拟齿轮箱噪声源     

Rigid‐plastic hybrid element analyses of the plane strain upsetting

A rigid‐plastic hybrid element method (HEM) for simulation of metal forming is developed. This method is a mixed approach of the rigid‐plastic domain‐BEM and the rigid‐plastic FEM based on the theory of compressible plasticity. Because the compatibilities of not only velocity but also velocity's derivative between the adjoining boundary elements and finite elements can be met, the velocities and the derivatives of the velocity can be calculated with the same precision for the rigid‐plastic HEM. Then, it is considered that the rigid‐plastic HEM is a more precise method in formulation than the conventional rigid‐plastic FEMs for which the compatibilities of velocity's derivative cannot be met. The plane strain upsetting processes with two friction factors are analyzed by the rigid‐plastic HEM in this article. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 726–737, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10031.     

Hybrid-conventional finite element for gradient-dependent plasticity

The hybrid-conventional finite element method is applied to the analysis of quasi-static, gradient-dependent elastoplastic problems in solid mechanics. The stresses within the element domain and the displacements on the boundary are simultaneously and independently approximated using Trefftz constraints, which lead to boundary integrals. The plastic multipliers are conventionally approximated with regard to C₀ continuity of the multiplier field of the gradient-dependent plasticity. The finite element formulation is derived using a Galerkin-weighted residual approach. The plastic boundary conditions are examined and plastic radiations are set to zero on the plastic boundaries. The effectiveness of the present method is demonstrated with three numerical applications.     

Analysis of a thermo‐viscoplastic model with Lipschitz continuous constitutive equations

We study a thermo‐mechanical model, where the mechanical inelastic model with a Lipschitz–continuous constitutive relation for the plastic strain is coupled with a heat equation. The main results are the local‐in‐time existence and uniqueness of the solution to the considered model and the existence of the solution for an arbitrarily long time interval for the sufficiently small given data. Copyright © 2013 John Wiley & Sons, Ltd.     

Solving a classification task by spiking neural network with STDP based on rate and temporal input encoding

This paper develops local learning algorithms to solve a classification task with the help of biologically inspired mathematical models of spiking neural networks involving the mechanism of spike-timing-dependent plasticity (STDP). The advantages of the models are their simplicity and, hence, the potential ability to be hardware-implemented in low-energy-consuming biomorphic computing devices. The methods developed are based on two key effects observed in neurons with STDP: mean firing rate stabilization and memorizing repeating spike patterns. As the result, two algorithms to solve a classification task with a spiking neural network are proposed: the first based on rate encoding of the input data and the second based on temporal encoding. The accuracy of the algorithms is tested on the benchmark classification tasks of Fisher's Iris and Wisconsin breast cancer, with several combinations of input data normalization and preprocessing. The respective accuracies are 99% and 94% by F1-score.     

非对称的Lax-Milgram引理对非关联塑性的一个应用

在塑性势和屈服面的广泛假设下,研究了非关联塑性的某些性质.对强化材料,通过使用非对称的Lax-Milgram引理,证明了当强化参数A>‖?F/?σ‖?Q/?σ‖-时,应力位移增量分布的存在唯一性.     

FEM solutions for plane stress mode-I and mode-II cracks in strain gradient plasticity

The strain gradient plasticity theory is used to investigate the crack-tip field in a power law hardening material. Numerical solutions are presented for plane-stress mode I and mode II cracks under small scale yielding conditions. A comparison is made with the existing asymptotic fields. It is found that the size of the dominance zone for the near-tip asymptotic field, recently obtained by Chen et al., is on the order 5% of the intrinsic material lengthI. Remote from the dominance zone, the computed stress field tends to be the classical HRR field. Within the plastic zone only force-stress dominated solution is found for either mode I or mode II crack.     

正交异性理想塑性材料平面应力问题的裂纹尖端应力场

本文在裂纹尖端场的应力分量仅仅是θ的函数的假设下,利用Hill屈服准则和平衡方程导出了正交异性理想塑性材料平面应力问题中裂纹尖端场的微分方程;在允许应力不连续线存在的情况下,把解析表达和数值计算法结合起来,得到了Ⅰ型和Ⅱ型裂纹尖端的应力场.     

用于应变局部化行为分析的弹塑性损伤耦合本构研究

在已有的损伤塑性耦合本构模型基础上,进行了本构意义上的参数辨识,对不同参数取值时的材料行为进行了数值模拟,并对损伤演化律提出了改进措施．应用改进了的模型,在结构意义上进行了数值检验,模拟了简单试件拉伸时的变形局部化．数值结果表明这一理论模型有更好的数值稳定性,能较为准确地模拟金属韧性断裂的变形局部化现象．