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Brittle solids are often toughened by adding a second-phase material. Thispractice often results in composites with material heterogeneities on the mesoscale: large compared to the scale of the process zone but small compared tothat of the application. The specific configuration (both geometrical andmechanical) of this mesoscale heterogeneity is generally recognized asimportant in determining crack propagation and, subsequently, the (effective)toughness of the composite. Here, we systematically investigate how dynamiccrack propagation is affected by mesoscale heterogeneities taking the form ofan array of inclusions. Using a variational phase-field approach, we computethe apparent crack speed and fracture energy dissipation rate to compare crackpropagation under Mode-I loading across different configurations of theseinclusions. If fixing the volume fraction of inclusions, matching the inclusionsize to the K-dominance zone size gives rise to the best toughening outcome.Conversely, if varying the volume fraction of inclusions, a lower volumefraction configuration can lead to a better toughening outcome if and only ifthe inclusion size approaches from above the size of the K-dominance zone.Since the size of the K-dominance zone can be estimated \textit{a priori} givenan understanding of the application scenario and material availability, we can,in principle, exploit this estimation to design a material's mesoscaleheterogeneity that optimally balances the tradeoff between strength andtoughness. This paves the way for realizing functional (meta-)materials againstcrack propagation in extreme environments.

Meso-scale size effects of material heterogeneities on crack propagation in brittle solids: Perspectives from phase-field simulations