This is most common error, and it's most of the time happen due to

• Incorrectly define material data
• Incorrect mesh size or mesh pattern
• Involving in large deformation/Non-linear behavior 
• Load -Boundary condition & time stepping

As common good practice do the following changes ang you get lucky enough to get solution.

Static Structural 

1. Simplify the model as much as possible and remove the unwanted section or features that are not affect to analysis.
2. Check the material model. Whether material data correctly defined and all the require material data defined for the analysis type. 
3. For initial test analysis scale down the model or get the half or section depending on the symmetric and start getting result. Then you can expand the FEA setting for actual model/or section.
4. Define the mesh size and element order based on solver, analysis type, model, Try to use Multizone meshing
5. Check for the contacts/contacts types and evaluate the initial contact setting with "Contact Tools" correct them
6. If the one body undergo a displacement, then split the analysis time to small interval and define the displacement for that particular time interval. (ex if the analysis time is 0.001 and displacement 10 mm, then split the time 0.0001, 0.0002,0.0003,....0.001 and displacement 1 mm, 2 mm, 3 mm,....10 mm)
7. For non-linear simulation, it's always better to have Finer mesh
8. Set ON for Large Deflection
9. Set the 0.0001s "End Time" and with result fine tune
10. If the one section or body undergo a large deformation, and you are doing Static Structural Simulation define the,  "Nonlinear Adaptive Region"    Nonlinear Control -> Newton-Raphson Option ->Unsymmetrical & Nonlinear Control -> Stabilization -> ON
11. Use the "Automatic Mass Scaling -> ON" and keep the total mass scaling less than 5% for accuracy
12. Start with Program Controlled setting if you don't know the really what setting need to set and expand the correct setting when evolve the solution

Sometimes some of the Explicitly Dynamic, LS-Dyna solution can be archive via Statics Structural method. But it's always not easy.

Explicit Dynamic / Ansys LS-Dyna 

1. Simplify the model as much as possible and remove the unwanted section or features that not affect to analysis.
2. Check the material model. Whether material data correctly defined and all the require material data defined for the analysis type. For LS-Dyna / or Explicit dynamic make sure failure criteria defined,..
3. Define the mesh size and element order based on solver, analysis type, model,...
4. For non-linear simulation, it's always better to have Finer mesh
5. coarse mesh used to to gain the insight
6. Set the 0.01s "End Time" and with result fine tune
7. If you are running Explicitly Solver, assign the element erode card
8. Use the "Automatic Mass Scaling -> ON" and keep the total mass scaling less than 5% for accuracy

Awesome...!