I'm running a few simulations for composite materials and accidentally let an explicit simulation run containing Standard C3D8R, so-called brick elements.
What is the difference in formulation between these Standard and Explicit elements?
Read this researchgate thread
https://www.researchgate.net/post/What_is_the_main_difference_between_implicit_and_explicit_analysis/amp
Hello Mahesh,
Thank you for your quick response.
Please note I'm not referring to the analysis procedure, but rather to what the difference is between the two element formulations. As far as I can tell from the Abaqus documentation, the stiffness is calculated in the same way.
Regards,
Fred
Dear Fred,
Explicit and implicit/standard analyses mainly are different because of their formulations. If you look at the Abaqus documentation, there are lots of elements that can be used either in explicit or standard analysis, such as C3D8 element. However, there are some elements that you use either in explicit or standard analysis, depeneding on your problem type.
Regards,
Imagine that you pick two points on a solution curve. When these two points get close enough to each other then the slope of the line between the two can be an estimate of the first derivative of the solution (finite difference estimate). Now the question is that this slope is a derivative estimate at the first point or at the second point? The right answer is "both".
However, depending on which one you take and plug the derivative estimate back into your differential equation it will turn your governing differential equation into two different formats;
1- an equation that has the unknown value of the solution at the second point on one side of the equation, explicitly in terms of the first point value on the other side of the equation. This means by having the value of the first point (as known) you explicitly can obtain the value of the second point solution (as the unknown) by just plugging the value of the first point into your equation. So you do not need to solve an algebraic equation. This is called Explicit solution which is basically a forward finite difference method and as long as you define the marching step size you will have the solution at the next step point whether in time domain or in space. Try to use linear elements with reduced integration for Explicit method.
2- an equation that provides an algebraic equation just in terms of the value of the unknown solution of the second point. To obtain the solution at this next increment (point) we need to solve the algebraic equation and this is called the Implicit method. The rest of the solution may need an iterative technique such as Newton-Raphson method. This is what sometimes referred to solving the equilibrium equation whereas in the Explicit method we did not have to solve a whole equation.
From this point of view, it might be better understood why in most of the cases with Explicit method, given that the size of the increments are small enough, the solution will converge. It is also faster and takes less disk space. On the other hand, in Implicit, since it has to solve the equation mostly with Newton-Raphson method, it may diverge such as when we have multiple roots to the equation. It needs larger disk space and it might be slower but it can handle any increment size.
Remember, these methods both can handle nonlinearity as well as static or dynamic problems and if modeling is carefully assigned both solutions should be almost the same. However, the "standard" solution is the Implicit which also is used to solve a linear equation, only with one step.
So there is no fundamental difference. The funny (and right) answer is try one of them, if did not work, try the other one.
The details of the element formulation are given in the theory manual. AFAIK, in explicit, hourglass control is done differently.
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