Solution Mode: Linear vs. Nonlinear

With the linear solution mode, there is a direct, linear relationship between the applied loads and the induced response of the system. With the nonlinear solution mode, the response of the system is determined by continuously updating the stiffness of the system and iterating to find the solution.

Linear solution mode provides better performance (speed) and greater robustness (the simulation will always converge on a solution). Linear solution mode is preferable in situations where the model stiffness changes minimally during the simulation.

For example, if a linear spring extends statically by 1 mm under a load of 10 N, it will extend by 2 mm under a load of 20 N. Therefore in a linear simulation the flexibility of the structure need only be calculated once.

Nonlinear solution mode is necessary to obtain an accurate solution in situations where the stiffness of the model changes substantially throughout the course of the simulation, such that the initial linear relationship between the applied loads and the induced response does not remain valid. These kinds of stiffness changes can be caused by:

• Large displacements and rotations
• Large deformations
• Changes in contact
• Nonlinear material behavior such as material yielding

Nonlinear solution mode provides accurate solutions to these more challenging simulations, with a corresponding decrease in performance and robustness.

A nonlinear structural problem is one in which the structure's stiffness changes as it deforms. While all physical structures exhibit nonlinear behavior, a linear simulation is a convenient approximation that is often adequate for design purposes. It is inadequate, however, for many structural simulations involving large displacements, contact changes, and/or complex material behavior such as metal plasticity. A simple example is a spring with a nonlinear stiffening response, as shown below.

Since the stiffness is now dependent on the displacement, the initial flexibility can no longer be multiplied by the applied load to calculate the spring's displacement for any particular load.

In nonlinear solution mode, the response of the system is determined by continuously recalculating the stiffness of the system and iterating to find the solution. This is more time-consuming than a linear simulation.