Multiscale modeling of composite materials with DECM approach: Shape effect of inclusions

This paper addresses the study of the stress field in composites continua with the multiscale approach of the DECM (Discrete Element modeling with the Cell Method). The analysis focuses on composites consisting of a matrix with inclusions of various shapes, to investigate whether and how the shape of the inclusions changes the stress field. The purpose is to provide a numerical explanation for some of the main failure mechanisms of concrete, which is precisely a composite consisting of a cement-based matrix and aggregates of various shapes. Actually, while extensive experimental campaigns detailed the shape effect of concrete aggregates in the past, so far it has not been possible to model the stress field within the inclusions and on the interfaces accurately. The reason for this lies in the limits of the differential formulation, which is the basis of the most commonly used numerical methods. The Cell Method (CM), on the contrary, is an algebraic method that provides descriptions up to the micro-scale, independently of the presence of rheological discontinuities or concentrated sources. This makes the CM useful for describing the shape effect of the inclusions, on the micro-scale. When used together with a multiscale approach, it also models the macro-scale behavior of periodic composite continua, without losing accuracy on the micro-scale. The DECM uses discrete elements precisely to provide the CM with a multiscale approach.