Nichtlineare numerische Mehrfeldhomogenisierung der Inelastizität schmelzinfiltrierter Metall-Keramik-Verbundwerkstoffe
Zusammenfassung der Projektergebnisse
In this research, the extension of non-uniform transformation fields analysis (NTFA) to thermo-mechanical interaction and damage is presented, which generalize the results to anisotropic elastic constituents. A modification of the normalization condition is motivated and used in the subsequent steps. A finite element based implementation of the NTFA was developed. Two major differences with respect to the prior implementations are introduced: 1) three-dimensional problems are considered and 2) the FEM was used to approximate the solution of the full-field simulations on the microscale. The computational scheme used for the implicit time integration procedure of the constitutive equations of the homogenized material is provided. It allows for a fast numerical solution of the nonlinear equation using Newton method and it can be used to explicitly provide a formulation for the algorithmic stiffness operator of the non-linear effective material. Different numerical examples are presented for a two-phase composite material consisting of a ductile elasto-plastic matrix and linear elastic particles with complex three dimensional microstructure. Numerical experiments are used to compare the results of full-field simulations to the homogenized model under non-proportional loading conditions. Further, the model is used in three-dimensional structural problems, one including contact formulations. In both cases, integration point data were extracted and used to prescribe the observed strain history to unit cell simulations. The components of the macroscopic stress tensors showed a good agreement to full-field simulations. By using FEM, the NTFA becomes accessible for many researchers and for three-dimensional problems. This eased implementation of the method forms the basis for a series of further developments of the technique for a variety of physically non-linear multiscale problems. Interestingly, the model gives good predictions even in the case of load reversal, although only five inelastic modes were used. Moreover, these modes were identified in simulations with differently oriented and proportional loading paths. The reconstruction of the stress field showed a good agreement to the full-field simulation, i.e. the loci of the stress concentration are resolved and the quantitative values of equivalent stress are close to the full-field solution. The present results give rise to subsequent investigations dealing with the local distribution of the non-uniform fields.
