Crysal Plasticity Finite Element Simulations based on Continuum Dislocation Dynamics

Plastic deformation of crystalline materials is the result of the motion and interaction of dislocations. Continuum dislocation dynamics (CDD) defines flux-type evolution equations of dislocation variables which can capture the kinematics of moving curved dislocations. Coupled with Orowan's law, which connects the plastic shear rate to the dislocation flux, CDD defines a dislocation density based material law for crystal plasticity. In the current work we provide simulations of a micro-bending experiment of a single crystal and compare the results qualitatively to those from discrete dislocation simulations from the literature. We show that CDD reproduces salient features from discrete dislocation simulations regarding the stress distribution, the dislocation density and the accumulated plastic shear, which would be hard to obtain from more traditional crystal plasticity constitutive laws. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite Element Simulations of Magnetic Liquids with Free Boundaries

The main objective of this paper is to present an algorithm for finite element simulations of the dynamic behaviour of magnetic liquids with free boundaries. Starting with the governing equations we describe the discretization and solution strategy. As an example the shape of an oscillating drop is investigated where for a simplified problem an analytical approximation is available.     

Particle Finite Element Simulations of Cutting Processes in Manufacturing

The cutting of metals is an important process in manufacturing and challenges established methods in the field of computational mechanics. The particle finite element method (PFEM) combines the benefits of particle based methods and the standard finite element method (FEM) to account for large deformations and separation of material. In cutting simulations the workpiece is realised as a set of particles, whose boundary is detected by the α-shape method. After the boundary detection, the particles are meshed with finite elements. Since metals show a plastic behavior under large deformations, a suitable material model needs to be considered. Numerical examples show the effect of the choice of the parameter α on the cutting force. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Variational Finite Element Model for Large-Eddy Simulations of Turbulent Flows

The authors introduce a new Large Eddy Simulation model in a channel,based on the projection on finite element spaces as filtering operation in its variational form,for a given triangulation{Th}h>0.The eddy viscosity is expressed in terms of the friction velocity in the boundary layer due to the wall,and is of a standard sub grid-model form outside the boundary layer.The mixing length scale is locally equal to the grid size.The computational domain is the channel without the linear sub-layer of the boundary layer.The no-slip boundary condition(or BC for short)is replaced by a Navier(BC)at the computational wall.Considering the steady state case,the authors show that the variational finite element model they have introduced,has a solution(vh,ph)h>0that converges to a solution of the steady state Navier-Stokes equation with Navier BC.     

带复合型摩擦裂纹的圆盘动态断裂实验有限元分析

为验证考虑裂纹面接触和动态荷载时,中心裂纹巴西圆盘（CCBD）试件用于分离式Hopkinson压杆（SHPB）系统中测量脆性材料复合型动态断裂韧度的可行性,以及研究裂纹面接触对动态断裂韧度实验结果的影响.通过有限元法建立SHPB CCBD三维有限元模型,计算了不同加载条件下CCBD试件的动态应力强度因子（DSIF）.结果表明:在实验中,将考虑裂纹面接触的应力强度因子(SIF)准静态公式推广为动态公式,需要判定断裂时间是否达到应力平衡的时间条件;压剪复合型加载时,裂纹面接触导致裂纹面应力变化,会对Ⅱ型裂纹的DSIF产生显著影响,不考虑裂纹面接触的影响将会导致Ⅱ型DSIF的测试值偏大.     

Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System

A moving mesh method is proposed for solving reaction-diffusion equations. The finite element method is used to solving the partial different equation system, and an efficient scheme is applied to implement mesh moving. In the practical calculations, the moving mesh step and the problem equation solver are performed alternatively. Serveral numerical examples are presented, including the Gray-Scott, the Activator-Inhibitor and a case with a growing domain. It is illustrated numerically that the moving mesh method costs much lower, compared with the numerical schemes on a fixed mesh. Even in the case of complex pattern dynamics described by the reaction-diffusion systems, the adapted meshes can capture the details successfully.     

人工机械心瓣启闭过程的ALE有限元分析

本文采用任意拉格朗日－欧拉（ＡＬＥ）有限单元法，将血液视为不可压缩粘性流体，同时将人工机械瓣简化为定轴转动刚体，建立了机械心瓣－血液耦合运动二维计算模型，解决了人工机械瓣启闭过程的计算问题．对Ｓｔ．Ｊｕｄｅ瓣启闭过程的数值分析表明：１．Ｓｔ．Ｊｕｄｅ瓣启闭过程包括四个阶段，即：Ⅰ．开启相；Ⅱ．开启保持相；Ⅲ．关闭相；Ⅳ．关闭保持相．２．Ｓｔ．Ｊｕｄｅ瓣关闭时回流明显，伴有显著水击效应．３．在启闭过程中，高剪力区位于两瓣叶间及瓣环附近．本文的研究突破了以非耦合的方法研究心瓣启闭过程的局限性．     

Temperature and Rate effects in Finite Viscoplasticity of Glassy Polymers at Different Deformation Modes: Experiments and Simulations

The non–linear inelastic response of glassy polymers is highly influenced by the three–dimensional deformation state, the temperature and the strain rate at which they are deformed. The contribution presents new experiments for different deformation modes which are carried out at different temperatures and rates on commercial bis–phenol A polycarbonate. Emphasis is put not only on the experimental results by themselves but also on the setup and the technique employed in the obtention of the data. The effect of temperature on the velocity with which the neck propagates along the gaged section of a flat specimen under tension is studied means a facility based on photogrammetry. From the homogeneous compression experiments a single set of material parameters appearing in a constitutive model based on the distributed free volume theory under the frame work of additive kinematics will be identified. The inhomogeneous experimental results serve then as a validation for 3–D simulations since the non–uniform strain distribution on the surfaces of both, simulations and experiments, can be compared. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Evaluation of HPF and MPI Approaches and Performance in Unstructured Finite Element Simulations

The High Performance Fortran (HPF) language and the Message Passing Interface (MPI) are two widely used methods to achieve parallelism on today's clusters and multiprocessor supercomputers. HPF is a distinct language providing extensions to Fortran 90/95 to express parallel execution paths and regions. MPI is a library of communication calls that can be inserted into modern high-level languages (C and Fortran). This paper discusses the use of the two approaches in a parallel finite element application for liquid composite manufacturing process modeling. The unstructured nature of the code provides an excellent opportunity to test both the computation and communication effectiveness of the two approaches. We discuss performance results based on implementations conducted on a modern massively parallel computing platform with a highly tuned processor interconnection network.     

Fracture Mechanical Analysis of Cracks in Ice Shelves using the Finite Element Method and Configurational Forces

Ice shelves are important elements of the climate system and sensitive to climate changes. The disintegration of large Antarctic ice shelves is the focus of this fracture mechanical analysis. Ice is a complex material which, depending on the context, can be seen as a viscous fluid or as an elastic solid. A fracture event usually occurs on a rather short time scale, thus the elastic response is important and linear elastic fracture mechanics can be used. The investigation of the stress intensity factor as a measure of crack tip loading is based on a 2-dimensional analysis of a single crack with a mode-I type load and additional body loads. This investigation is performed using configurational forces. Depth dependent density and temperature profiles are considered. The relevant parameters are obtained by literature, remote sensing data analysis and modeling of the ice dynamics. The criticality of wet surface cracks is investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

小参数常微分方程的有限元格式

在这篇短文中作者构造了特殊的有限元格式,研究了此格式的收敛性.     

Finite Element Analysis of Eigendynamics of Rolling Tires

The eigenvalue analysis of rolling tires is one part of the simulation of tire rolling noise radiation for the reduction of traffic noise. In this paper the general strategies of numerical eigenvalue analysis for nonsymmetric matrices are shown. The special effects observed on rotating bodies are discussed in details. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite Element Analysis of Free Material Optimization Problem

Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.     

粘-弹性介质中渗流的有限元法分析

R.S.Sandhu和E.L.Wilson提出了弹性介质中渗流分析的有限元法[1],可以用来分析较复杂的工程问题,本文将此方法推广到粘-弹性介质情况.当土骨架是粘-弹性介质时,应力与应变的关系随时间变化,增加了问题的复杂性.本文提出了折算弹性张量的概念,即当有限元法计算中的时间间隔Δt预先给定时,在此间隔内应力增量和应变增量可以近似表示为线性关系.这些线性比例常数将称为折算弹性张量.Sandhu和Wilson方法仅能用于弹性介质情况,根据折算张量概念,本文方法适用范围推广到粘-弹性介质情况.     

非协调有限元的全塑性分析

本文采用满足相容条件的非协调有限元模型以解决全塑性分析中有限元解的数值精度问题.文中讨论了该模型适用于全塑性分析的机理和判据,还设计了一个确定塑性极限载荷的算法.     

Stokes流动的罚-杂交有限元分析*

本文建议了一种用于分析Stokes流动的罚-杂交变分原理,其中,偏应力张量和静水压力事先满足线动量平衡.建立了相应的有限元模型.由此,压力可在列式过程中消去,使得有限元矩阵方程仅以节点速度作为唯一的求解未知量.推导了几种4-节点和8-节点四边形单元.通过数值算例,显示了单元性能.     

轴对称弹性体的有限元分析

轴对称弹性力学问题的有限元分析长期以来都是采用三角圆环有限元和线性形状函数.由于积分困难,常用近似积分求得刚度矩阵,这种近似积分对于靠近旋转对称轴的元素,误差很大,所以,长期以来,被认为不满意的办法.也有用精确积分计算刚度矩阵的.但本文指出,这种积分只适用于有中孔的轴对称体.对于实心的轴对称体而言,这种刚度矩阵都不收敛,计算是无效的.本文提出了一种新的形状函数,当径向座标r接近于零时,这种形状函数的径向位移u自然地接近于零.如果用这种新的形状函数,则由此计算求得的刚度矩阵,不论三角圆环有限元的位置是否靠近轴线.都是存在的.这种有限元,就能用于计算实心的轴对称体的问题.     

Finite Element Analysis of General Magnetomechanical Coupling Phenomena

In this paper we consider the derivation of a finite element model for fully–coupled magneto–mechanical boundary value problems based on a vector–valued magnetic potential. The formulation allows for the incorporation of nonlinear, anisotropic and hysteretic constitutive response. A piezomagnetic inclusion problem is computed to test the implementation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)