Stop Changing the Conversation – Nonlinear Simulation

What is nonlinear simulation? Most people don’t know. So, I’ll lay it out as simply as I can.

First, let’s talk about the linear solver. When the linear solver runs, it solves for the end result. Only the end result. The solver doesn’t recognize any of the in-between steps. Most people notice this when they create an animation where you would expect some intermediate interaction between parts. “Why didn’t the hook go over the latch?” Is a question I hear all too often when customers create animations from linear simulations. When you have a hook going over a latch, you would expect some interaction between the two components. The reason the two components don’t move like you would expect is because a linear solver only focuses on the end result. So, we only have two points to work with – The start point and the end point. The animation interpolates between the two. The middle is missing.

The nonlinear solver goes about the problem in a different way. Instead of having two points, A and B, the nonlinear solver will solve the in-between steps. The solver marches through time solving these intermediate steps. However, this time isn’t real time. It’s merely a parameter used to describe the relation between the intermediate steps. So, it’s often referred to as pseudo time. This approach comes in handy in a few different situations.

Boundary nonlinearity – Just like the latch example. You have two parts that interact with one another. When the situation arises where you would like to study the steps in-between start and finish, you might want to treat the simulation nonlinearly.

Geometric nonlinearity – When a part deforms so much that its spacial orientation significantly changes, it often helps to solve with little steps. This sort of nonlinear simulation can be dealt with using Simulation Standard. To turn this option on, click, “Large displacement” under properties.

Material nonlinearity – When a material doesn’t have a straight stress-strain curve, you can’t go from point A to point B without the in-between steps. This is because the path from point A to point B is crooked. Have you ever stretched rubber so far that it became easier to stretch? Well, how could you ever solve THAT with a linear solver? You have one force and two or more displacements. Think about it. There are a few different types of material non-linearity, so I won’t go into it too deeply. but they apply to rubbers, plastics, metals after yield and so forth.

So, when someone tells you, “This problem is nonlinear,” don’t change the subject. It’s not as complicated as it sounds.