# Multiscale Simulation of Concrete

## Jörg Unger

#### Federal Institute for Materials Research and Testing

Berlin, Germany

24. April 2013, 17.00

WW8, Room 2.018-2, Dr.-Mack-Str. 77, Fürth

In practical structural applications, materials are modelled on a macroscopic level assuming a homogeneous material. The constitutive formulation is described by a phenomenological approach and the complex models required to accurately simulate the material are often rather complex.

A different strategy is based on a simulation on ﬁner scales, thus allowing to accurately capture the real physical phenomena. By including the heterogenous description of the material, rather simple constitutive formulations with material parameters having a clear physical meaning can be used.

In this presentation, a multiscale strategy for the simulation of concrete is presented. At ﬁrst, a macroscopic formulation with a discrete crack concept using the eXtendend Finite Element Method (XFEM) to model adaptive crack propagation is presented. Afterwards, a mesoscale model for concrete with an explicit representation of particles, matrix material and the interface layer is introduced. Several examples will be given to show the importance of mesoscale modeling.

The problem of simulating large scale structures on ﬁne scales is the computational costs exceeding the capacities of current computers. As a consequence, multiscale strategies have to be developed to couple ﬁne and coarse scales in a single model. Two different multiscale strategies will be presented. The ﬁrst one uses an adaptive scheme. Starting from the macroscale, relevant parts are transformed to ﬁner scales. A discussion on coupling conditions is given, since the discretization on the ﬁne and on the coarse scale are substantially different. A second possibility is a multiscale strategy using the FE^{2}-concept, where the constitutive relation for each macroscopic integration point is deduced from the solution of a new boundary value problem of a corresponding ﬁne scale model. An extension is presented that is able to deal with localization within the FE^{2}-concept.