A stochastic framework for multiscale strength prediction using adaptive discontinuity layout optimisation (ADLO)

The prediction of strength properties of matrix-inclusion materials, which in general are random in nature due to their spatial distribution and variation of pores, particles, and matrix-inclusion interfaces, plays an important role with regard to the reliability of materials and structures. The recently developed discontinuity layout optimisation (DLO) [18] and adaptive discontinuity layout optimisation (ADLO) [4], which can be used for determination of strength properties of materials [3, 4] and structures [9], are included in a stochastic framework, using random variables. Therefore different material properties, influencing the overall strength of the matrix-inclusion material (e.g. matrix and inclusion strength, number and distribution of pores/particles) in a considered RVE are assumed to follow certain probability distributions [12]. A sensitivity study for the identification of material parameters showing the largest influence on the strength of the considered matrix-inclusion materials is performed. The obtained results provide first insight into the nature of the reliability of strength properties of matrix-inclusion materials, paving the way to a better understanding and finally improvement of the effective strength properties of matrix-inclusion materials

Counting Zariski chambers on Del Pezzo surfaces

Zariski chambers provide a natural decomposition of the big cone of an algebraic surface into rational locally polyhedral subcones that are interesting from the point of view of linear series. In the present paper we present an algorithm that allows to effectively determine Zariski chambers when the negative curves on the surface are known. We show how the algorithm can be used to compute the number of chambers on Del Pezzo surfaces