Simulation of Metal Forming Processes

  • A. E. Tekkaya
Part of the Engineering Materials book series (ENG.MAT.)


The term process simulation describes all methods by which one or more of the process parameters of a real physical process or process family is or are predicted approximately before its or their actual happening, [7.1]. The aim of the determination of these parameters in case of metal forming processes is usually one or more of the following:
  • Checking the feasibility of the process design for producing a workpiece,

  • Evaluating the product properties for service use,

  • Increasing the insight about the real process in order to optimize the production sequence.

The simulation in production processes aims to manufacture products economically. Therefore, the application of process simulation must be always more economical than the application of the real process.


Sheet Metal Flow Curve Equivalent Plastic Strain Versus Versus Versus Versus Bulk Metal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Special Symbols




Shape function matrix for the rate of deformation components


Rate of deformation tensor


Young’s modulus of elasticity


Green Lagrangian finite strain tensor


Force vector


Deformation gradient tensor


Shear modulus of elasticity


Kirchhoff stress tensor


2nd Piola Kirchhoff stress tensor


Identity tensor


Jacobian determinant


Velocity gradient tensor


Normal unit vector


Shape function matrix for the velocities


Penalty factor


1st Piola Kirchhoff stress tensor






Cauchy (true) stress tensor


Displacement vector


Velocity vector






Spin tensor


Position vector


Yield stress


Flow stress


Virtual change


Infinitesimal strain tensor


Lagrangian function


Coulomb coefficient of friction


Poisson’s number


Plastic potential



\(\bar \varepsilon \)

Equivalent plastic strain (Umformgrad)

Nabla operator


Element related








Initial state related


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  • A. E. Tekkaya

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