Predicting the Yield Stress of Geomaterials from Their Microstructure

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The seminal work of Gurson (J Eng Mater Technol 99:2–5, 1977) on a simplified pore structure, a single spherical pore, first provided a theoretical relationship between the yield stress and the porosity. This contribution extends the approach to determine the macroscopic yield of a porous material by taking explicitly into account its internal structure. As the yielding of a porous material is controlled by the geometry of its internal structure, we postulate that it is nearly independent of the constitutive plastic behaviour of the material. Here, we show that the influence of that internal structure on the yield could be retrieved from a finite element computation with just an elastoplastic ideal (J2) material equivalent of the skeleton’s. With some basic knowledge about the skeleton’s mechanical properties, this process allows the determination of the yield stress without requiring the experimental compression of the material. We showcase the predictive power of the method against experimental testing, initially for a unit cell following Gurson, i.e., unique cylindrical void in a 3D printed cylinder sample. Eventually, the applicability of the method is demonstrated on a complex 3D printed rock microstructure, reconstructed from a sandpack’s CT-scan.