Prediction Of Macroscopic Properties Research Articles

A data-driven framework for structure-property correlation in ordered and disordered cellular metamaterials.

Extracting the relation between microstructural features and resulting material properties is essential for advancing our fundamental knowledge on the mechanics of cellular metamaterials and to enable the design of novel material systems. Here, we present a unified framework that not only allows the prediction of macroscopic properties but, more importantly, also reveals their connection to key morphological characteristics, as identified by the integration of machine-learning models and interpretability algorithms. We establish the complex manner in which strut orientation can be critical in determining effective stiffness for certain microstructures and highlight cellular metamaterials with counterintuitive material behavior. We further provide a refined version of Maxwell's criteria regarding the rigidity of frame structures and their connection to cellular metamaterials. By examining the shear moduli of these metamaterials, the mean cell compactness emerges as a key morphological feature. The generality of the proposed framework allows its extension to broader classes of architected materials as well as different properties of interest.

On the Homogenization Concepts and Macroscopic Properties of Orthotropic Composites with Non-Symmetrically Shaped Inclusions

Homogenization is an important analysis approach of composite materials with structural hierarchy and can give the prediction of macroscopic properties of the composites. There are many homogenization theories and methods. The present paper discusses applications of some homogenization approaches including both direct and mathematical homogenizations for the analysis of anisotropic composites with periodic microstructures. The macroscopic properties of the composite are predicted by the direct homogenization and the mathematical homogenisation method. The periodic boundary conditions of a representative volume element are implemented by a transformation method of the degrees of freedom. The numerical results are demonstrated for two model composites. The study shows that these two homogenization methods gave the same results for the macroscopic elastic stiffness of the composites although they are of different mathematical forms and different operation procedures.

Permeability and electrical conductivity of porous media from 3D stochastic replicas of the microstructure

In this paper we report on the application of low-order statistical information (porosity, two-point correlation function), obtained from 2D micrographs of real porous media, to derive stochastic replicas of their 3D pore networks. The main focus is on assessing the usefulness of stochastic reconstruction as a means of relating macroscopic transport coefficients (intrinsic permeability and effective electrical conductivity) to the geometry and topology of the pore space. To this end we employ newly developed algorithms, based on morphological skeletonization, to obtain a comprehensive geometric and topological description of each simulated pore network. Using the skeleton or graph of the pore space as a basis, detailed geometrical measurements are performed to estimate the effective hydraulic and electrical conductance of individual flow paths, identified with skeleton links. In combination with exact knowledge of the network topology, these measurements enable the specification of equivalent resistor-type network models for the calculation of intrinsic permeability and formation factor. Consistently successful predictions of permeability over a wide range of values are obtained for five reservoir rock samples of diverse origin and lithology. Predictions of formation factor are within a factor of three of the experimental values. These predictions are, however, inconsistent, a fact attributed to the inability of the reconstruction method to accurately reflect the contributions of smaller pores and throats to electrical conductivity. Additionally, it is shown that the hydraulic conductance of pore space channels in stochastically simulated pore networks is spatially correlated over distances equal to the characteristic length scale of the two-point correlation function. The effect of spatial resolution and sample size on the prediction of macroscopic properties is also investigated. Finally, the physical meaning of various length scales relating flow permeability to effective electrical conductivity is elucidated.