Connections between inhomogeneities and the failure behavior of brittle material may be investigated by finite element simulations of representative volume elements. Representative volume elements are typically subjected to periodic boundary conditions. Moreover, representative volume elements are often chosen as planar, i.e., two dimensional in order to reach reasonable statistics with regard to random distributions of inhomogeneities. The significance of such strongly simplified simulations needs to be validated, especially if the matrix failure is potentially dominated by defects, as is the case, e. g., in macro-porous ceramics. We propose a quasi-periodic concept to design specimens with cylindrical pores, which reproduce the stress state in a two dimensional representative volume element. This is achieved by a partial periodic replication of the region of interest. We suggest that material models used in simulations can be assessed by comparison between simulated and experimentally observed failure.
Prediction of the breaking strength of macro-porous materialsThe breaking strength of macro-porous materials shows large variations also at constant material porosity in experiments. These variation can be ascribed to randomly distributed defects. We divide defects into matrix defects (defects) and macro pores (pores). With reference to empiric and semi-empiric approaches and geometric models [1-4] the breaking strength of a macro-porous brittle material is potentially dominated by interactions between pores, defects, pores and defects.In recent years approaches based on Finite Element simulations of so-called representative volume elements (RVE) are used to develop a deeper understanding of correlations between pore distribution and mechanical characteristics of porous materials [5]. Influences of defects are usually not taken into account in these works. Representative volume elements are typically subjected to periodic boundary conditions. Moreover, representative volume elements are often chosen as planar, i.e., two dimensional in order to reach reasonable statistics and the matrix is taken as homogeneous. The significance of such strongly simplified simulations needs to be validated, especially if the matrix failure is potentially dominated by defects, as is the case for many brittle materials, e.g. macro-porous ceramics.We aim at a separation of pore and defect influences on the macroscopic failure by comparisons of the mechanical failure behavior in simulations of periodic RVEs under compression and in experimental compression tests. The aim is to design specimens, which well reproduce the stress state of the periodic simulations. This approach is similar to the work by Song et al. (2008) [6]. In the current paper we treat planar macro-porous ceramics characterized by distributions of closed spherical pores under uniaxial compression, but the idea is in principle also applicable to three-dimensional RVEs.
Concept of almost periodic boundary conditionsPeriodic boundary conditions regard the RVE geometry ...