#### Overview

Nonlinear Analysis in Midas NFX addresses three different types of nonlinearities:

- Material Nonlinearity: For materials that do not obey Hooke’s law
- Geometrical Nonlinearity: For cases where deformation is large
- Contact Nonlinearity: For problems where contact between two components changes as the analysis progresses.

#### Material Models

In many engineering problems, the behaviour of the material deviates from Hooke’s law, i.e. the relationship between load and deformation is not linear. Different materials exhibit different types of behaviour depending on their plastic properties, for instance ductile metals or rubbers and plastics.

The following nonlinear material models are available in Midas NFX:

Nonlinear Elasto-Plastic, Nonlinear Elastic, Nonlinear Hyperelastic (Mooney-Rivlin, Ogden, Blatz-Ko), Perfectly Plastic, Creep

#### Nonlinear Contacts

Midas NFX has an offering of two types of nonlinear contacts:

**Rough Contact:** Contact separation occurs in the normal plane but no sliding occurs along the plane of contact.**General Contact: **Contact separation occurs in the normal plane as well as along the plane of contact.

There is another case where the elements of the same mesh set come into contact with each other. Such phenomenon is known as self-contact, and is used in various applications.

#### Large Deformation

When the displacement/deformation in the structure is significantly large, Hooke’s law equation does not hold true. As the deformation is no longer infinitesimal, the deformation causes changes in shape, and consequently stiffness of the structure.

Hence, the nonlinear solver in Midas NFX re-calculates stiffness at small intervals to predict a more accurate account of the behavior of the structure. Newton-Raphson criterion is used to obtain convergence at every iteration.

#### Loads & Boundaries

In nonlinear static analysis, the iteration begins at the condition when no load is applied. Subsequently, load is gradually increased by equal intervals and stiffness is re-calculated at those intervals. This occurs for multiple iterations until the solver reaches the iteration at which the incremental load equals the input load.

Following load parameters can be assigned in Nonlinear Analysis:

- Displacement
- Force
- Pressure
- Follower force