Finite-Elemente-Implementierung konstitutiver nichtlinearer Stoffgesetze für piezokeramische Werkstoffe

Abstract

The objective of the thesis is the finite element implementation of constitutive material models for piezoceramic materials. First, experimental investigations of piezoceramic materials are presented to verify the material models and their finite element implementation. Especially, the behaviour under multi-axial, electro-mechanical loadings was investigated. The phenomenological material model, which was implemented by means of a specialized radial return mapping algorithm into the open source finite element program PSU, was reduced to one algebraic equation for each case. This led to a vast reduction of computation time of simulations in opposite to the previous implementation by means of complex integration algorithms for the differential equations. Apart from simulations of the principal behaviour of the material model and its implementation, practical simulation examples are presented, which demonstrate the performance of the model and the implementation. The microscopically motivated material model was also implemented by means of a radial return mapping algorithm on the basis of the backward Euler method. For this, a set of nonlinear equations has to be solved which was successfully done by the discrete Newton method. Because of occasional convergence difficulties, several methods are presented, which were used in the implementation to improve the convergence of the local Newton iteration. After demonstration of the principal behaviour of the model by some simple examples, a simulation example of a cylinder with an infinite length is presented and compared to the results of the implementation of the phenomenological material model. For the global behaviour a good agreement of the two material models is shown. In local areas differences were investigated since the microscopically motivated material model is closer to the microscopic switching processes compared to the phenomenological material model.