# Nonlinearities in Structure

When the force-displacement relation of the system is linear, then that particular type of system is named as “linear system.” The simplest example of such a system is mass-spring mechanical assembly. In this mechanical system, the stiffness of a spring remains constant. But in real-world problems, the stiffness of a system is not linear; however, it may be idealized as linear to make analysis simple. In non-linear systems, the stiffness of a system varies with deformation and does not remain constant.

## Types of Nonlinearities:

There are the following types of non-linearities that exist in a system and are responsible for changing the stiffness of a system with deformation.

1. Large deformations or Geometric Nonlinearity
2. Material Nonlinearity
3. Contact Nonlinearity
1. Large deformations or Geometric Nonlinearity: This type of nonlinearity exists in a structure due to large deformation or large rotation. This type of nonlinearity is responsible for the change in the geometry of a structure due to large rotation/large deformation.

The geometric nonlinear problems can be solved in the FE commercial packages by keeping the nonlinear switch on.

2. Material Nonlinearity: This type of nonlinearity exists in a structure when the material’s stress-strain curve is non-linear. In the case of mild steel, the stress-strain curve is not linear after the elastic limit point, and in the case of some non-metals, the stress-strain curve is not linear even from the origin itself. The non-linear behavior is present in all the engineering materials, but we can consider only the linear portion for simpler analysis.
3. Contact Nonlinearity: This type of nonlinearity comes into picture when one body is in contact with another body due to the sudden change in the stiffness. The simulation of the contact nonlinear problems can be performed by considering the gap between the two bodies which are in contact with each other.

## Issues arise in Nonlinear FE analysis:

1. The convergence is the biggest challenge in the nonlinear analysis.
2. The solution is expensive in terms of time and memory requirement.
3. There is a difficulty in the validation of the nonlinear analysis results due to the increase in the complexity.
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