Masterarbeit (abgeschlossen)

Ting Yang

Numerical differentiation for local and global tangent operators in computational plasticity

The main goal of this thesis is to that numerical differentiation is a useful tool to achieve the conver-gence in computational plasticity. It is applied to integrate plastic constitutive laws and to calculate the responding tangent operators. There are two types of problem need to be solved: 1. the inte-gration of the constitutive law at each Gauss point(local problem); 2. The boundary value problem (global problem).
Those two types of problem, the derivatives one of significant composition of the Jacobian of the residual (local problem) and the consistent elastoplastic moduli (global problem). For a global prob-lem, is usually calculated by an incremental approach. By using the Newton-Raphson method to a nonlinear equations system and achieve the convergence at each load increment. In any case, the consistent tangent matrix must be used. In this thesis, I use “Matlab” to compute with the elasto-plastic model.
The resulting algorithm maintains the characteristic convergence of the Newton-Raphson method, gives that the effective difference schemes and step sizes are chosen. It is powerful and computa-tionally efficient in both sides.