多孔介质中强度和降解的形态学描述
Morphometric description of strength and degradation in porous media
摘要：
多孔介质的微观结构对材料性能的影响已被广泛认识，特别是在岩土材料，但也在生物材料和工程材料。成像技术，如X射线显微计算机断层扫描，并在建模的最新进展，使人们有可能捕捉到精确的微观结构的高精度的形态。然而，大多数现有的连续统理论只能部分地解释形态学。我们在这里提出了一个统一的方法来连接多孔材料的强度与必要和足够的微观结构信息，使用闵可夫斯基泛函，根据Hadwiger定理。一个形态强度法推断合成微观结构具有广泛的孔隙度和异质性，通过定性的二维相场模拟。也就是说，通过跟踪机械载荷下的固体-孔隙界面，在微观结构水平上对损伤进行建模。强度被认为是最好的描述由指数函数的形态计，从而概括了早期的金属和陶瓷的作品。然后，我们表明，这种关系的预测性延伸到真正的多孔介质，包括岩石和骨骼。
英文摘要：
The influence of the microstructural geometry on the behavior of porous media is widely recognized, particularly in geomaterials, but also in biomaterials and engineered materials. Recent advances in imaging techniques, such as X-ray microcomputed tomography, and in modeling make it possible to capture the exact morphometry of the microstructure with high precision. However, most existing continuum theories only partially account for the morphometry. We propose here a unifying approach to link the strength of porous materials with the necessary and sufficient microstructural information, using Minkowski functionals, as per Hadwiger's theorem. A morphometric strength law is inferred from synthetic microstructures with a wide range of porosities and heterogeneities, through qualitative 2D phase-field simulations. Namely, the damage is modeled at the microstructural level by tracking the solid-pore interfaces under mechanical loading. The strength is found to be best described by an exponential function of the morphometers, thus generalizing early works on metals and ceramics. We then show that the predictiveness of this relationship extends to real porous media, including rocks and bones.
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