Nonlinear FEA

Nonlinear Finite Element Analysis (FEA) is required when structural response cannot be assumed proportional to applied loads. Unlike linear analysis, the principle of superposition does not hold. Nonlinearity arises from three main sources: (1) material nonlinearity, where the stress-strain relationship is nonlinear (plasticity, hyperelasticity, viscoelasticity, creep); (2) geometric nonlinearity, where large deformations or rotations alter stiffness and equilibrium paths; and (3) boundary condition nonlinearity, such as contact problems or changing constraints. Nonlinear FEA requires incremental-iterative solution strategies, most commonly the Newton-Raphson method, where equilibrium is enforced at each load step by updating the tangent stiffness matrix. Convergence criteria are based on residual forces or displacement norms. Practical applications include buckling, plastic collapse, crash simulations, and contact mechanics. Limitations include high computational cost, sensitivity to load stepping strategy, and potential convergence difficulties.