Finite Element Simulation of the Non-remanent Straining Ferroelectric Material Behaviour Based on the Electrostatic Scalar Potential:Convergence and Stability
The applicability of the Newton–Raphson iteration scheme to an electric scalar potential formulation of a ferroelectric/ferroelastic constitutive model within the framework of a finite element simulation is analysed methodically. Since the specific shape of the polarisation hysteresis is recognised as the principal reason of numerical problems, the considerations given here are limited to the non-remanent straining ferroelectric material model. Three approaches to gain convergence are discussed. Besides the known Line Search two other methods are presented, which are applied locally for each integration point. While the main idea of the first is to modify the vector of the internal dielectric displacement, the second approach affects the tangent modulus. An additional scaling of the tangent modulus is proposed in order to suppress numerical instabilities which may arise as a consequence of an over-compensation of numerical errors. To identify the remanent polarisation an enhanced Return Mapping algorithm based on an implicit backward Euler method is used. The applicability of the modified numerical iteration procedure is demonstrated by two examples.
KeywordsTangent Modulus Raphson Method Remanent Polarisation Switching Surface Maximum Relative Deviation
The authors greatly acknowledge the support from the Deutsche Forschungsgemeinschaft (DFG) under Contract No. Ba 1411/12.