1440 Timberwolf Drive, PO Box 964, Holland, OH 43528-0964 USA | 1 (419) 867-5400 | Email Us

1440 Timberwolf Drive, PO Box 964, Holland, OH 43528-0964 USA
1 (419) 867-5400 | Email Us

Simulations Are Not Straight Forward

Linear and non-linear. You may have heard one or both of these terms before when having simulation work done. “We ran this simulation linear because...” That’s great, and they sound like they know what they are talking about, but what does that actually mean and how does it apply to your DA Blog Image 1analysis?

Linear analyses are applicable for small deformations only. Small deformations here is twofold in that one, you aren’t straining the material enough to exceed its elastic limit (material linearity), and two, that you aren’t affecting the geometric response of your model (geometric linearity). Great!  It’s one of those definitions that needs more definitions.

Material linearity can be observed by comparing a rubber band vs. silly putty. Stretch a rubber band 2x and let it go and it will snap back and smack your hand whilst returning to its original shape. The load you put on it didn’t exceed its elastic limit, so all deformation was recoverable and the load vs stretch was rather consistent throughout the pull. This is an example of a linear material model. Now do the same to the silly putty. It stretches out and just sits there. You very quickly exceeded the material’s elastic region, entering plastic, or permanent, deformation. Its load vs displacement curve will be very irregular, and also time dependent with a heavy viscoelastic response, but that’s a rabbit hole for another day. This is a prime example of a nonlinear material response.

Geometric linearity works similarly to material linearity in that the load vs displacement response of the geometry needs to be consistent. Loading a spring under compression is a very linear geometric response, as you squeeze it with X load it shortens by Y. Let it go and it springs right back out. This is a great example of geometric linearity. What happens if you take that too far though? If you keep compressing said spring until you bottom the coil out, your load vs displacement starts to skyrocket at a MUCH steeper rate than in its linear region. You have now entered that geometry’s nonlinear area.

Linear analyses are accurate and have a great computation time but adhere to the stipulation that their applicability starts to decay fast if you exceed either the material or geometry’s linear regions. Nonlinear analyses take it from there with much more heavy computation times, but can handle both material and geometric nonlinearity, as you probably guessed from the name. The trick to a nonlinear analysis once you cook everything down is that it is basically a lot of small linear analyses back to back that piece together the complicated response from a bunch of tiny simple responses, like trying to draw a circle using a series of short lines.DA Blog Image 2

So, which type of analysis is applicable for your simulation need? That all depends on what you need modeled. Applying a small load to observe the stress development in your design? Linear. Usually helpful when studying every day usage loads. Smashing something until it breaks? Definitely nonlinear. Taking anything to excessive distortion, breaking, buckling, or blowing up, nonlinear is where it’s at.


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Daniel Applegate


Predictive Modeling Engineer

Graduated Magna Cum Laude from the University of Toledo with a B.S. in Mechanical Engineering in 2009 and shortly thereafter started his career at Plastic Technologies, Inc. Daniel’s expertise spans the processing platforms of reheat stretch blow molding, injection stretch blow molding, and extrusion blow molding.  His primary role has been to develop and execute package performance simulation, analyzing the results, and engineering solutions or improvements for the containers based on the outcomes.