Two-scale Modelling of Reactive Powder Concrete by the Method of Numerical Homogenization

Abstract

The paper is concerned with the modeling of reactive powder concrete (RPC) by using the method of numerical homogenization. More specifically, we use a two-scale modeling approach and the finite element method. The behaviour of a concrete model of RPC on the macro scale is described on the basis of the phenomena occurring in the microstructure of the material. The applied approach makes it possible to design an optimal composition of the reactive powder concrete and provides the possibility to take into account the phenomena occurring in the microstructure as concerns the physical and mechanical properties of the material. The method does not require any knowledge of the constitutive equations at the macro level, which are determined implicitly for each load increment by solving a boundary value problem for the numerical model of RPC on the micro level as a representative volume element (RVE). Thus, to determine the constitutive equations on the macro scale it is necessary to know the geometry of the microstructure, the constitutive equations at the micro level and their parameters. In this contribution the material response of each material constituents (cement matrix, sand, crushed quartz) is assumed to be elastic. The microstructure of RPC concrete (RVE) is generated by a stochastic way. A computer program for two-scale homogenization has been developed and numerical results for two test problems are presented. The aim of the first two-scale test was to check the program in the case of homogeneous material. The second example present the results obtained for another micro-scale problem. Further studies of the considered problem, including also laboratory experiments, are under way.