ANSYS contact theory in transient analysis

This project was awarded to SmartEngineer974 for $30 CAD.

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I have used ANSYS transient analysis to solve the contact problem of a crack two surfaces. I need to write down all the theoretical work done by ANSYS and the equations. I have used augmented Lagrangian as a penalty method. How can I re-write my finite element using augmented Lagrange?

I also need to know what ANSYS used for solving the time integration

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