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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.
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This content will become publicly available on July 1, 2026
Error propagation from microstructure changes to apparent stiffness in 2D biphase matrix-inclusion composites
The representation of material microstructure in most existing analytical homogenization models is condensed into a set of well-known ‘‘classical’’ microstructure descriptors, such as the volume fraction and morphology of the individual phases of a composite. This study considers an enriched set of micro descriptors, containing both those ‘‘classical’’ descriptors as well as ‘‘non-classical’’ descriptors which quantify the spatial correlations of any two given micro material points inside a random heterogeneous material. We focus on 2D composites consisting of a matrix with embedded inhomogeneities (or inclusions) of random spatial arrangement. Both phases are treated as homogeneous, linearly elastic and isotropic. Starting from a rich database of reference microstructures, new datasets of perturbed microstructures are created, by inducing changes emulating the physical processes of inclusion nucleation and growth. All microstructures are characterized using the enriched set of micro descriptors, while their apparent stiffness tensor is computed numerically with the finite element (FE) method. A sensitivity analysis between the changes of the micro descriptors and corresponding changes of the apparent stiffness tensor reveals that the ‘‘non-classical’’ descriptors are consistently highly important to the macroscopic behavior. This suggests that enhanced homogenization models, made dependent on the identified pertinent ‘‘non-classical’’ micro descriptors, could be of higher predictive capability than existing approaches.
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- PAR ID:
- 10657141
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- European Journal of Mechanics - A/Solids
- Volume:
- 112
- Issue:
- C
- ISSN:
- 0997-7538
- Page Range / eLocation ID:
- 105612
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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