Modelling & Simulation


Multiscale simulation of micro-heterogeneous materials

Dominik Brands, Insitute of Mechanics, University of Duisburg-Essen, Essen, Germany
Lisa Scheunemann, Insitute of Mechanics, University of Duisburg-Essen, Essen, Germany
Matthias Labusch, Insitute of Mechanics, University of Duisburg-Essen, Essen, Germany
Jörg Schröder, Insitute of Mechanics, University of Duisburg-Essen, Essen, Germany

In almost all fields of engineering the application of micro-heterogeneous, advanced materials has become a reliable method to improve the properties of components and devices. Mostly the overall (effective) properties of these materials are mainly governed by the underlying composition at lower scales, the micro-heterogeneity.

For example, in the last three decades several new steels types, the group of advanced high strength steels, have been developed to enable lightweight, safe and more stable constructions. The dual-phase steel is one prominent type of these steels, as it is mainly characterized by a two-phase microstructural composition, i.e. martensitic inclusion in a ferritic matrix. This microscopic composition leads to enhanced macroscopic (effective) mechanical properties, e.g. higher ultimate tensile strength and better ductility, compared to conventional steels like single phase ferritic steels.

Another example are the multiferroic materials, which exhibit magneto-electric (ME) coupling and are applied in sensor technology and data storage. Since natural materials have no ME coupling at room temperature, synthetic (composite) materials consisting of electro- and magneto-active phases become relevant. In such composites, the ME coupling arises as a strain-induced product property.

Both these materials exhibit material behaviours which result from the micro-heterogeneous composition and the phenomena occurring at this scale. A suitable numerical tool for the prediction of the macroscopic (effective) behaviour of micro-heterogeneous materials is the computational direct micro-macro transition approach, the FE2-method. Instead of applying a constitutive material law at each integration point (standard finite element method), the macroscopic quantities are computed based on the solution of a microscopic boundary value problem (bvp). This microscopic bvp based on a representative volume element (RVE) reflects the real microstructure.

In this contribution, we will present methods to increase the efficiency of the FE2-method by the application of statistically similar RVEs and the multiscale modeling of multiferroic composites with strain-induced magneto-electric coupling.

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