Boundary shape controls the stress distribution in two-component elastic materials

Abstract

We investigate how the shape and arrangement of high-stiffness regions govern stress redistribution in two-component triangular elastic spring networks subjected to spatially correlated and uncorrelated random prestress. We compare boundary roughness, partitioning into disconnected regions, and graded transitions between regions of different stiffness. Our simulations identify interface bonds as channels for energy transfer: increasing their number provides additional transfer paths and reduces stress concentration in mechanically rigid regimes, while offering little benefit in compliant subnetworks. This is analogous to defects in naturally occurring crystal structures, where the defects themselves isolate stress. At a fixed fraction of high-stiffness material, partitioning reduces stress concentration for both correlated and uncorrelated prestress. The benefit diminishes with further subdivision as the number of interface bonds becomes comparable to the number of interior nodes. Stress reduction, however, depends on the spatial correlations of the imposed prestress: random prestress generally yields a stronger effect, though the difference diminishes in some regimes. Graded interfaces further reduce peak stress by distributing the stiffness transition over a broader region. Together, these results suggest design strategies based on increasing interface area, matching subdivision scale to prestress correlations, and grading stiffness transitions. This minimal framework identifies how internal structure controls energy transfer and stress redistribution, suggesting design principles for mechanical robustness under both internal and external loading.