Crash Timestep Basics
- 1. 1 TIMESTEP In the context of explicit analysis, time step is the time required for a shock wave to propagate across the smallest distance of the element. A run is a single model simulation and it starts at time zero and continues till the user defined endpoint is reached. The basic time unit in the run is the time step. Time step should not exceed beyond 0.5E-06 IN very rough terms, time step is proportional to (element size)/sound speed. So you can see how a smaller element size would reduce the time step. Material sound speed is proportional to 1/sqrt(density). So you can see how mass (=density/volume) would affect the time step. The smaller the time step, the more steps it takes to complete the analysis. More time steps means longer run time, solution will converge, more the accuracy. Solver don’t understand the real scenario, it is like if we enter 1 it will show 1, if we enter 99 it will show 99. Time step is a control card. We are controlling the time taken by shock wave to transfer before the sound wave going to hit on the node. In some cases what happen if element length is small and time step value is not enough to pass through the element then solver will add some mass to the elements (Mass Scaling) and run through it. For a crash solver percentage of increase of mass allowed in 2% to %5. Beyond that solution will not converge which gives unphysical results.
- 2. 2 Physical scenario explanation Whenever vehicle get into crash. Structure experience high impact loads due to which deformation starts. Nodes starts to displace so strain develops because of that stress develops. So it starts to transfer the load, displacement from node to node through the smallest element length within very short period of time. That fraction of time is called as time step. Numerical Explanation Remember-1. Crash happens within milliseconds, 2. All fem results we find at nodes and elements. Just imagine if there is no time step. The crash happens, displacements starts and solver starts to transfer the load and displacements with shortest nodal distances here we didn’t assigned it transfer the displacement with particular time. It takes its own time to transfer the displacement. In fem all elements will not be having equal length, for every element it will take different time to transfer the displacements. Which is unphysical and we cannot guess the solution time it will take very long time. This is the reason we specify the particular time that the wave should pass through the element. That time is called as time step. Some study tells that maximum possible time to transfer the loads and displacements with adjacent nodes should not exceed beyond 0.5E-06 seconds. Funny Explanation - Assume I am the time step. Read the case below. 1. My manager assigned me a job and informed me to finish task within 2 days. What I will do I concentrate more and somehow I will try to extend finish mesh connection everything quickly without wasting my time for tea and snacks. And deliver the model with 80-90 of accuracy. 2. Same job assigned me with no time bond. I may finish in 2 days or I may take 1 week. On comparing above, case 2 is very unphysical. Compare with real scenario of crash since we know that in very fraction of time crash event will happen. Accordingly very less time step we keep and impose the solver to finish the task within that time. Prepared By Satish Gombi
- 3. 3 Reference LS Dyna solver calculates your solution by running over all the nodes in the model at each time step. In a very simplified explanation, LS-DYNA will look at the total force on each node from the previous time step, use that to find the acceleration of that node, and then to find the displacement of that node. The node is then moved by this much. The calculation then updates the strain on the connecting element. This then goes through the material constitutive equation to get stress, which is applied as a force on the neighbouring node in the next time step. You can imagine this series of calculations behaving like a wave, propagating through your mesh. The critical thing, however, is you want to calculate all the node positions of your model at the same time, without it being affected by the calculations from the previously calculated node. This basically means that you need to set your time increment such that the code can calculate the displacements of the next node before the wave from the previous node calculation can hit it. For instance, if my boundary conditions on the mesh shown below were along the left and bottom edges, and I applied a downward load at node 25, the calculations at t=0 would go as follows: F at N25 = 0. This gives acceleration (from F=ma, with mass at 1/4th the mass on element 16). From acceleration, I calculate displacement for my next time step and move N25.
- 4. 4 Now, the movement of this node imposes a strain on element 16, which generates a stress in element 16 (from the material law) which will apply a force on N20. However, I still haven't calculated the displacement of N20 at t=0. I must do this before the wave propagating from N25's displacement hits N20. This wave travels through the material at the speed of sound through that material, which depends directly on density, Young's modulus and Poisson's ratio of that material. The wave propagation velocity in a 2D shell element is given below: So the speed of sound through my material, and my mesh size determines how much time I have before I need to calculate N20 displacements. (Note, I am using N20 as an example. LS-DYNA also needs to calculate N19 and N24 as the wave is propagating in all directions). I would also like to have a little margin for safety. If I set my time step to exactly the time for the wave to hit N20, it would be a little risky and can lead to instability. Therefore, LS-DYNA has a parameter in the *CONTROL_TIMESTEP card called TSSFAC, which is set to a default of 0.9. This is basically a scale factor on the calculated time step to ensure that N20 is calculated well in advance of the wave front. Now, that makes sense for a regular mesh (I hope). All the elements have the same time-step, and everything works out great. What happens if my mesh is not regular? I have some smaller elements, some larger elements, different materials (affecting wave speeds), etc. This is unavoidable in real parts because of the necessity of capturing the geometry accurately. Then LS-DYNA will use the smallest time step calculated over all the elements to ensure that none of the elements get unstable because of the above-explained phenomenon. That means if you have one element with a tiny time step, the time-step of your entire model is dictated by that one element, necessitating a lot more calculations than are necessary. Which is why a uniform mesh is strove for when meshing an LS-DYNA model. And materials with a high wave propagation speed (generally metals) are meshed more coarsely than materials with low propagation speeds (plastics, rubbers) when used together in the same model. However, even that can only go so far.
- 5. 5 The list of your hundred lowest time steps is given in the d3hsp file. Search for the term 'smallest' and you should be able to find it in the file once your deck starts to run through the time steps (after estimated run time is given in your stdout). Use this list to see if you can re-mesh locally to remove small elements. The other alternative is called mass-scaling. Here, I artificially increase the mass of my smallest elements, and so increase the density of that element, without affecting any other property. This then means that my wave propagation speed gets artificially reduced, increasing the time step for that element. Looking at this in reverse, if I have a target time step for my entire model, LS-DYNA can look at which elements are below that time step, and apply just enough mass to those elements to ensure that their time-steps hit your target. You can set a time step manually in the *CONTROL_TIMESTEP card under the dt2ms field. Note, you need to input this value as a negative of your timestep. (There are different ways to mass-scale. Read the manual for the different definitions.) Just because this method allows you to set your own time step does not mean that you can set whatever value you want. Remember, you are artificially increasing the mass in a dynamic simulation as the analysis is progressing. This means that your kinetic energy of that element is artificially going up. LS-DYNA is essentially creating energy from nothing. LS-DYNA will output how much your mass-scaling is in the stdout at the beginning of the run. I would suggest a mass scaling value (as percentage of original mass of your model) of not more than 2%. Note this is just the initial mass scaling. The amount of mass added may go up through the simulation (as elements deform). At the end of the run, check the glstat file for mass-scaling over time. If it is a relatively flat curve and stays under 2% at all times, your result should be close enough to the ideal result (without mass-scaling). Of course, the best way would be to run one case without mass scaling and compare the results to make sure the level of mass scaling still gives you accurate results. I hope this helps in giving an intuitive sense of how LS-DYNA calculates the time step, and how you can control your mesh size to maximize your time step (within reason), and how mass scaling can allow a higher time step when you have small elements you cannot clean up.