Both material and geometric non-linearity are handled in the same way in FEA. The idea is to go by small increments of loads. For a small increment of load, the material is assumed to behave linearly, corresponding to the local tangent modulus (see figure).
The change in the shape is calculated. If so needed, the new shape is taken as a different structure, and the additive stresses due to another small increment in load is calculated,.. and so on, until the full applied load is reached. Due to the iterative nature of calculations, the non-linear FEA is time-consuming, and uses up computer resources, but reflects the real life conditions more accurately than a linear analysis.
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