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The stochastic modeling and calibration of an anisotropic elasto-plastic model for additive manufacturing materials are addressed in this work. We specifically focus on 316L stainless steel, produced by directed energy deposition. Tensile specimens machined from two additive manufactured (AM) box-structures were used to characterize material anisotropy and random spatial variations in elasticity and plasticity material parameters. Tensile specimens were cut parallel (horizontal) and perpendicular (vertical) to the AM deposition plane and were indexed by location. These results show substantial variability in both regimes, with fluctuation levels that differ between specimens loaded in the parallel and perpendicular build directions. Stochastic representations for the stiffness and Hill’s criterion coefficients random fields are presented next. Information-theoretic models are derived within the class of translation random fields, with the aim of promoting identifiability with limited data. The approach allows for the constitutive models to be generated on arbitrary geometries, using the so- called stochastic partial differential approach (to sampling). These representations are then partially calibrated using the aforementioned experimental results, hence enabling subsequent propagation analyses. Sampling is finally exemplified on the considered structure. 

Stochastic mesoscale inhomogeneity of material properties and material symmetries are investigated in a 3D-printed material. The analysis involves a spatially-dependent characterization of the microstructure in 316 L stainless steel, obtained through electron backscatter diffraction imaging. These data are subsequently fed into a Voigt–Reuss–Hill homogenization approxima- tion to produce maps of elasticity tensor coefficients along the path of experimental probing. Information-theoretic stochastic models corresponding to this stiffness random field are then introduced. The case of orthotropic fields is first defined as a high-fidelity model, the realizations of which are consistent with the elasticity maps. To investigate the role of material symmetries, an isotropic approximation is next introduced through ad-hoc projections (using various metrics). Both stochastic representations are identified using the dataset. In particular, the correlation length along the characterization path is identified using a maximum likelihood estimator. Uncertainty propagation is finally performed on a complex geometry, using a Monte Carlo analysis. It is shown that mechanical predictions in the linear elastic regime are mostly sensitive to material symmetry but weakly depend on the spatial correlation length in the considered propagation scenario.