英语翻译1 Explain the notion of elasto-plastic constitutive laws

英语翻译
1 Explain the notion of elasto-plastic constitutive laws.The student is required to explain
the normality law,and why the flow potential takes the form of plastic criterion function (yield
function).Show one or two examples of the yielding functions,and how the isotropic
hardening and kinematic hardening are introduced.
2 In formulation of the elasto-plastic constitutive model,explain how to determine the
plastic multiplier λ,and how the rate of plastic strain is related to the flow potential function.
Then explain how the stress tensor can be determined.Show the procedures in constitutive
integration of the elasto-plastic law,according to an implicit algorithm.
3 Please explain what represents the global operations and local operations in finite element ．
methods.Indicate what type of operations are the global and linear ones,and what type of the
computation are the local and non-linear ones.How they are arranged in the algorithm to
realize the simulation of nonlinear problems.
4 Give a brief statement on description of the large deformation problems.Explain the ．
definition of.Explain why deformation gradient tensor is a two point tensor.Give the
definitions of different measurements for deformation,such as the right Cauchy-Green and left
Cauchy-Green tensors,Green-Lagrange and Euler Almansi tensors.
5 Show definition of the first and second Piola-Kirchhoff stress tensors.Write down the
equilibrium equations in weak form for the dynamic problems on actual and initial
configuration.Explain the key issue for integration of constitutive law in case of the large
deformation.
6 For solid problems with nonlinearity of the material properties,please make a brief ．
introduction on general procedures of the solution under the frame of quasi-static assumption.
Explain where and how the constitutive integration is used to satisfy the requirement for
analysis of the structure.
7 Show the general procedures of solution by dynamic explicit algorithm.Explain the key ．
issue to make explicit the solution.How the discretized vector (or column) of internal forces
can be determined.Make a brief description of the central difference method for time
integration of the dynamic equilibrium equation.

解释弹塑性本构规则的概念.学生需要解释正交定律,以及为何使用流动趋势来表示塑性准则方程（屈服方程）.给出一到两个屈服方程的例子,解释等向硬化现象和运动硬化现象.  
在弹塑性本构模型中,解释如何确定塑性因数 λ,以及塑性应变是如何和流动趋势相关的.然后解释如何确定应力张量.使用弹塑性法则的本构积分来表现这个过程,依据隐式算法.请解释全局运算和局部运算在有限元单元方法中是如何定义的.指出哪种运算使用全局线性运算,哪种计算方法使用局部非线性运算.这些运算在算法中应该如何安排来实现非线性问题的模拟.
对于大变形问题给出简单的描述.解释XX的定义.解释为什么变形梯度张量是一个两点的张量.给出对于变形不同测量方法的定义,例如右Cauchy-Green以及左Cauchy-Green张量,Green-Lagrange以及Euler Almansi张量. （这些名字没有翻译,如果需要的话 Cauchy是柯西,Green是格林,Lagrange是拉格朗日,Eluer是欧拉,Almansi是阿尔曼西）
给出第一和第二Piola-Kirchoff应力张量的定义.（Piola皮奥拉,Kirchoff基希奥夫）使用弱式关联规则写出动力学问题的平衡方程以及初始边界条件.解释在将本构方程在大变形问题下积分的主要问题.        对于非线性材料属性的实体单元问题,请在准静态假设的基础上对于推导结果的一般程序进行介绍.解释在哪里以及如何使用本构积分来满足对结构进行分析的要求.
给出使用显式动力学算法进行分析的一般过程.指出是计算结果显式的主要问题.结构内力的离散向量（柱子）是如何被决定的.（不清楚这里column是柱子还是矩阵的列）简单描述如何使用中心差分法对动力平衡方程进行时间积分.Note: 有一些专业名词我的翻译不一定准确,如果采用,请检查一下.