Stable time step and mass scaling

[Prasad Reddy]

I am working on high deformation impact problems in ABAQUS. 
After some increments the step time (delta t) is reducing to a very small value due to high distortions in the elements. 
Shall some body give me the mathematical formula for calculating initial stable step time in ABAQUS.
And if I use mass scaling it increases step time. How does mass scaling increases step time in ABAQUS (can some body please provide mathematical explanation).

Best Regards,
Prasad.

[Non-text portions of this message have been removed]

[fcn_public]

Hello Prasad,
 

Post by Prasad Reddy
After some increments the step time (delta t) is reducing to a very
small value due to high distortions in the elements. 
Shall some body give me the mathematical formula for calculating
initial stable step time in ABAQUS.

There is no documented formula for that. However, the ABAQUS/Explicit manual gives an overview of the factors it considers to compute the stable time increment. Essentially, it computes a rough estimate of the resonant frequency w=sqrt(k/m), with k=stiffness and m=mass, and scales the time step so that a wave with that frequency can propagate at most one element in that time.

Therefore, for a given mesh, increasing the mass will decrease the frequency, and thus increase the time step.

Hope this helps,
Fernando