Conditional stability of the explicit method

With the explicit method the state of the model is advanced through an increment of time, Δt, based on the state of the model at the start of the increment at time t. The amount of time that the state can be advanced and still remain an accurate representation of the problem is typically quite short. If the time increment is larger than this maximum amount of time, the increment is said to have exceeded the stability limit. A possible effect of exceeding the stability limit is a numerical instability, which may lead to an unbounded solution. It generally is not possible to determine the stability limit exactly, so conservative estimates are used instead. The stability limit has a great effect on reliability and accuracy, so it must be determined consistently and conservatively. For computational efficiency Abaqus/Explicit chooses the time increments to be as close as possible to the stability limit without exceeding it.