Spectral Fabric of Stochastic Residual Stress Fields

We investigate the spectral fabric of heterogeneous residual stress fields that emerge in stochastic manufacturing processes, with shot peening as a motivating test case. Eshelby-like inclusions are used as a reduced-order basis for stress field predictions and compared with finite element predictions. Overlap at higher coverage introduces nonlinear interactions beyond uniform strain assumptions. To quantify and correct these effects, we introduce a power spectral density ratio (PSDR) filter that reconciles both local stress magnitudes and the spatial correlation structure. Beyond model correction, the PSDR serves as a statistical fabric descriptor, describing long-range coherence and local heterogeneity of residual stress fields. This framework provides a scalable route for predicting residual stress evolution while establishing fabric quantification as a transferable paradigm for manufacturing processes governed by stochastic, spatially variable stress states.