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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.
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.
