What is nonlinear analysis

What is linear and non-linear analysis in FEA? - Femto engineering

Nonlinear analysis

A non-linear analysis is always necessary when non-linear effects occur. These include, for example, geometric non-linearities, such as a very large deformation. Other effects are plastic material behavior (often with plastics) or contact between several components. In contrast to the linear static analysis, the stiffness matrix for these problems cannot be constant during the application of the load. As a result, a different solution strategy is required, and therefore a different solver in the FEM context.

Modern FEM software is able to achieve adequate results even with complex non-linear problems. Nevertheless, greater know-how is necessary in order to make the right assumptions and to be able to assess the plausibility of the results. Understanding the underlying problem, a planned and logical approach to building the model, and a careful choice of solution parameters will go a long way towards achieving a successful result.

In the following you will find a more detailed description of the possible types of non-linear influences:

Geometric non-linearity:
In a linear analysis, the effects of deformations in the solution process itself are not taken into account, as they are usually too small to have a sufficiently large effect on the result. In the non-linear simulation, however, the continuous shifts in the formulation of the constitutive condition and in the equilibrium condition are taken into account. This is the case, for example, with metal forming, the analysis of tires or the examination of medical devices, where large deformations typically occur. Non-linear analyzes can also be useful for small deformations, for example when examining the behavior of cables, sheaths or hoses.

Material non-linearities:
Material nonlinearity includes the nonlinear behavior of a material based on current deformation, deformation history, deformation rate, temperature, pressure and other parameters. Examples of nonlinear material models are visco-plasticity and hyper-elasticity (rubber and plastics).

Nonlinear boundary conditions and contact
A nonlinear boundary condition occurs when the model is influenced by kinematic constraints. The kinematic degrees of freedom of a model can be restricted by movement restrictions. If there is contact between components in the course of a deformation, the force flow within the system can suddenly change due to the support of the parts, which is also a non-linearity.