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Elastoplastic lattice models for the response of solids to deformation typically incorporate structure only implicitly via a local yield strain that is assigned to each site. However, the local yield strain can change in response to a nearby or even distant plastic event in the system. This interplay is key to understanding phenomena such as avalanches in which one plastic event can trigger another, leading to a cascade of events, but typically is neglected in elastoplastic models. To include the interplay one could calculate the local yield strain for a given particulate system and follow its evolution, but this is expensive and requires knowledge of particle interactions, which is often hard to extract from experiments. Instead, we introduce a structural quantity, "softness," obtained using machine learning to correlate with imminent plastic rearrangements. We show that softness also correlates with local yield strain. We incorporate softness to construct a "structuro-elasto-plasticity" model that reproduces particle simulation results quantitatively for several observable quantities, confirming that we capture the influence of the interplay of local structure, plasticity, and elasticity on material response.