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A well-posed CDM model and an adequate representation of deterministic and random inhornogeneity factors, combined with an efficient numerical algorithm of modified lattices, yield a realistic simulation of the rupture properties of alumina ceramic specimens at tensile tests. Effects of energy dissipation and acoustic emission, the load-carrying capacity and the post-critical response are analysed in dependence of the heterogeneity realisations, which are related to the initial damage distribution within the specimen. This distribution is shown to be a crucial factor determining the response of brittle damaging ceramics at rupture.