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We devise reduced-dimension metrics for effectively measuring the distance between two points (i.e., microstructures) in the microstructure space and quantifying the pathway associated with microstructural evolution, based on a recently introduced set of hierarchical $n$-point polytope functions $P_n$. The $P_n$ functions provide the probability of finding particular $n$-point configurations associated with regular $n$-polytopes in the material system, and a special sub-set of the standard $n$-point correlation functions $S_n$ that effectively decomposes the structural features in the systems into regular polyhedral basis with different symmetry. The $n$-th order metric $\Omega_n$ is defined as the $\mathbb{L}_1$ norm associated with the $P_n$ functions of two distinct microstructures. By choosing a reference initial state (i.e., a microstructure associated with $t_0 = 0$), the $\Omega_n(t)$ set quantifies the evolution of distinct polyhedral symmetries and can in principle capture emerging polyhedral symmetries that are not apparent in the initial state. To demonstrate their utility, we apply the $\Omega_n$ metrics to a 2D binary system undergoing spinodal decomposition to extract the phase separation dynamics via the temporal scaling behavior of the corresponding $\Omega_n(t)$, which reveals mechanisms governing the evolution. Moreover, we employ $\Omega_n(t)$ to analyze pattern evolution during vapor-deposition of phase-separating alloy films with different surface contact angles, which exhibit rich evolution dynamics including both unstable and oscillating patterns. The $\Omega_n$ metrics have potential applications in establishing quantitative processing-structure-property relationships, as well as real-time processing control and optimization of complex heterogeneous material systems., Comment: 11 pages 9 figures

Disordered systems are ubiquitous in physical, biological and material sciences. Examples include liquid and glassy states of condensed matter, colloids, granular materials, porous media, composites, alloys, packings of cells in avian retina and tumor spheroids, to name but a few. A comprehensive understanding of such disordered systems requires, as the first step, systematic quantification, modeling and representation of the underlying complex configurations and microstructure, which is generally very challenging to achieve. Recently, we introduce a set of hierarchical statistical microstructural descriptors, i.e., the n-point polytope functions Pn, which are derived from the standard n-point correlation functions Sn, and successively include higher-order n-point statistics of the morphological features of interest in a concise, explainable, and expressive manner. Here we investigate the information content of the Pn functions via optimization-based realization rendering. This is achieved by successively incorporating higher order Pn functions up to n = 8 and quantitatively assessing the accuracy of the reconstructed systems via un-constrained statistical morphological descriptors (e.g., the lineal-path function). We examine a wide spectrum of representative random systems with distinct geometrical and topological features. We find that generally, successively incorporating higher order Pn functions, and thus, the higher-order morphological information encoded in these descriptors, leads to superior accuracy of the reconstructions. However, incorporating more Pn functions into the reconstruction also significantly increases the complexity and roughness of the associated energy landscape for the underlying stochastic optimization, making it difficult to convergence numerically., Comment: 23 pages, 17 figures. arXiv admin note: substantial text overlap with arXiv:1905.06979

Tunable dry adhesion is a crucial mechanism in compliant manipulation. The gripping force, mainly originated from the van der Waals force between the adhesive composite and the object to be gripped, can be controlled by reversibly varying the physical properties (e.g., stiffness) of the composite via external stimuli. The maximal gripping force Fmax and its tunability depend on, among other factors, the stress distribution on the gripping interface and its fracture dynamics (during detaching), which in turn are determined by the composite microstructure. Here, we present a computational framework for the modeling and design of a class of binary smart composites containing a porous low-melting-point alloy (LMPA) phase and a polymer phase, in order to achieve desirable dynamically tunable dry adhesion. In particular, we employ spatial correlation functions to quantify, model and represent the complex bi-continuous microstructure of the composites, from which a wide spectrum of realistic virtual 3D composite microstructures can be generated using stochastic optimization. A recently developed volume-compensated lattice-particle (VCLP) method is then employed to model the dynamic interfacial fracture process to compute Fmax for different composite microstructures. We focus on the interface defect tuning (IDT) mechanism for dry adhesion tuning enabled by the composite, in which the thermal expansion of the LMPA phase due to Joule heating initializes small cracks on the adhesion interface, subsequently causing the detachment of the gripper from the object due to interfacial fracture. We find that for an optimal microstructure among the ones studied here, a 10-fold dynamic tuning of Fmax before and after the thermal expansion of the LMPA phase can be achieved. Our computational results can provide valuable guidance for experimental fabrication of the LMPA-polymer composites., Comment: 23 pages, 9 figures

Effective and accurate characterization and quantification of complex microstructure of a heterogeneous material and its evolution under external stimuli are very challenging, yet crucial to achieving reliable material performance prediction, processing optimization and advanced material design. Here, we address this challenge by developing a set of novel hierarchical statistical microstructural descriptors, which we call the "n-point polytope functions" Pn, for quantitative characterization, representation and modeling of complex material microstructure and its evolution. These novel polytope functions successively include higher-order n-point statistics of the features of interest in the microstructure in a concise, expressive, explainable, and universal manner; and can be directly computed from multi-modal imaging data. We develop highly efficient computational tools to directly extract the Pn functions up to n = 8 from multi-modal imaging data. Using simple model microstructures, we show that these novel statistical descriptors effectively "decompose" the structural features of interest into a set of "polytope basis", allowing one to easily detect any underlying symmetry or emerging features during the structural evolution. We apply these novel Pn functions to quantify and model a variety of heterogeneous material systems, including particle-reinforced composites, metal-ceramic composites, concretes, porous materials; as well as the microstructural evolution in an aged lead-tin alloy. Our results indicate that the Pn functions can offer a practically complete and compact set of basis for quantitative microstructure representation (QMR), for both static 3D complex microstructure and 4D microstructural evolution of a wide spectrum of heterogeneous material systems., Comment: 23 pages, 11 figures