Reduced order homogenization for viscoplastic composite materials including dissipative imperfect interfaces

The computational effort of homogenization schemes based on full-field simulations is prohibitively high for many applications and motivates the use of model order reduction techniques. A reduced order homogenization scheme is presented which allows for a coupled treatment of dissipative mechanisms both in the bulk and on imperfect interfaces within the microstructure. Extending the key idea of the nonuniform transformation field analysis (NTFA), reduced bases are introduced for all fields of internal variables and also for the displacement discontinuities at the interfaces. In the online phase, an initial value problem is solved, which is derived from a mixed incremental variational principle. The variational formulation requires that the underlying constitutive models are given by two potentials, as known from the framework of generalized standard materials. As an example, a unidirectional fiber composite with a viscoplastic matrix and a viscoelastic interface is studied. It is demonstrated that the reduced order model can be used to analyze the rate-dependence of the overall behavior as well as the interface-induced size effect and the impact of varying interface parameters. At a significantly reduced computational effort, good quantitative agreement with finite element reference solutions is found for predictions of global quantities such as the effective stress and the effective mechanical work. For this is a rather simple training strategy sufficient. It is found that the reduced model provides good approximations of the local stress field and of the internal variables within the microstructure, which can benefit from a more comprehensive training.