Dwuskalowy model betonu z proszków reaktywnych. Część I: reprezentatywny element objętościowy (RVE) i rozwiązanie zagadnienia brzegowego na RVE

Arkadiusz Denisiewicz

The article is the first part of a series concerned with the modelling of reactive powder concrete by using a numerical homogenization technique. This technique is a multi-scale modelling approach. Specifically, in this paper a two scale modelling concept was applied. A model of reactive powder concrete (RPC) is considered whose behaviour on the macro scale is described on the basis of the phenomena occurring in the microstructure of the material. This approach provides the ability to take into account some complex phenomena occurring in the microstructure and their influence on the macroscopic physical and mechanical properties of the material. The method does not require knowledge of the constitutive equation parameters at the macro level. These are determined implicitly for each load increment on the basis of numerical model of a representative volume element (RVE), which reflects the geometrical layout of particular material phases, their constitutive relations and mutual interactions. In this paper the linearly elastic behaviour of each constituent material is assumed within the small strain range. In solving the boundary value problems formulated on the RVE for RPC, the finite element method was utilized. A number of numerical test examples were solved which illustrate the influence of inhomogeneities on the overall response.