Makeswaran Jenothan, As per my understanding, in the implicit solver, the equilibrium equations are typically represented by the Newton-Raphson method, where the governing equation can be expressed as: K * Δu = F where: K is the global stiffness matrix, Δu is the incremental displacement vector, F is the nodal force vector.

While, in contrast, the explicit solver employs the central difference method to solve the equations of motion, which can be represented as: M * d^2u/dt^2 + C * du/dt + K * u = F where: M is the mass matrix, C is the damping matrix, K is the stiffness matrix, u is the displacement vector, F is the nodal force vector.

These two equations showcase the distinct approaches of the implicit and explicit solvers in Abaqus, highlighting the limitations in your approach, that why you are not able to get buckling modes effectively in your approach. Well, now you can understand that, the explicit solver in Abaqus is primarily designed for dynamic simulations and transient phenomena, making it less suitable for predicting local buckling failures accurately. Buckling analysis, especially local buckling, is better handled by the implicit solver in Abaqus, which is more adept at capturing the nonlinear behavior associated with buckling phenomena. While the explicit solver can be used for certain types of buckling analyses, it may not provide the level of accuracy needed for predicting local buckling failures due to its inherent characteristics focused on dynamic events rather than static stability issues.

If you still have issues, connect with me on WA: https://wa.me/+923440907874 to further discuss it.

Your explicit simulation will give you the dynamic response. If you simulate a quasi-static process in a severly reduced time(and thus a much higher loading rate), it's quite possible that you delay or prevent buckling phenomena.

I'd recommend running the simulation with a linear elastic material and check if you will eventually see some buckling. If nothing happens, try to apply the load more slowly (or reduce the mass scaling, if you used that).

Raffael Bogenfeld I've compared my kinetic energy to the total internal energy, and it's below 5%. Therefore, I've assumed that my loading rate is sufficient to see the local buckling failure mode. Do you think I should slow down the loading rate further?

Depends on where this kinetic energy comes from. Assuming a plate with pure in-plane compression load (and no buckling occuring) I'd consider 5% too much, as an emerging buckling deformation will incorporate a much higher kinetic energy than in-plane loading. 5% kinetic energy in case of buckling present would be totally fine.