Sources of Nonlinearity

We live in a complex, nonlinear world, but what are the sources of nonlinearity in finite element analysis (FEA)?

1. Contact Nonlinearity - is significant when the functioning of an assembly involves the interaction of parts.
2. Material Nonlinearity - such as time-dependent (visco) behaviours, plasticity and damage effects amongst many other characteristics commonly seen in nonlinear materials.
3. Geometric Nonlinearity - occurs when the structure experience large strain/large deformations (This is typically when strains are larger than 10%) which causes stress stiffening of structures.

Matrix Methods: Direct vs. Iterative

Direct vs. Iterative methods
The two approaches available for solving global stiffness matrix (K) in FEM are:

Implications on FEA solver

• For linear simulation e.g. KU = f , Gaussian elimination can be applied directly
• For nonlinear simulation e.g. K(u)U=f, stiffness is dependent on displacements (u). Therefore an iterative method must be used.

See also
The role of matrix solution in the FEM process