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There are empirical strategies for tuning the degree of strain localization in disordered solids, but they are system-specific and no theoretical framework explains their effectiveness or limitations. Here, we study three model disordered solids: a simulated atomic glass, an experimental granular packing, and a simulated polymer glass. We tune each system using a different strategy to exhibit two different degrees of strain localization. In tandem, we construct structuro-elastoplastic (StEP) models, which reduce descriptions of the systems to a few microscopic features that control strain localization, using a machine learning-based descriptor, softness, to represent the stability of the disordered local structure. The models are based on calculated correlations of softness and rearrangements. Without additional parameters, the models exhibit semiquantitative agreement with observed stress–strain curves and softness statistics for all systems studied. Moreover, the StEP models reveal that initial structure, the near-field effect of rearrangements on local structure, and rearrangement size, respectively, are responsible for the changes in ductility observed in the three systems. Thus, StEP models provide microscopic understanding of how strain localization depends on the interplay of structure, plasticity, and elasticity. 

Simulations are used to find the zero temperature jamming threshold, ϕ j , for soft, bidisperse disks in the presence of small fixed particles, or “pins”, arranged in a lattice. The presence of pins leads, as one expects, to a decrease in ϕ j . Structural properties of the system near the jamming threshold are calculated as a function of the pin density. While the correlation length exponent remains ν = 1/2 at low pin densities, the system is mechanically stable with more bonds, yet fewer contacts than the Maxwell criterion implies in the absence of pins. In addition, as pin density increases, novel bond orientational order and long-range spatial order appear, which are correlated with the square symmetry of the pin lattice.