Effect of connectivity on the elasticity of athermal network materials.

Network materials with stochastic structure are ubiquitous in biology and engineering, which drives the current interest in establishing relations between their structure and mechanical behavior. In this work we focus on the effect of connectivity defined by the number of fibers emerging from a crosslink, z, and compare networks with identical (z-homogeneous) and distinct (z-heterogeneous) z at the crosslinks. We observe that the functional form of strain stiffening is z-independent, and that the central z-dependent parameter is the small strain stiffness, E0. We confirm previous results indicating that the functional form of E0(z) is a power function with 3 regimes and observe that this applies to a broad range of z. However, the scaling exponents are different in the z-homogeneous and z-heterogeneous cases. We confirm that increasing z across the Maxwell's central force isostatic point leads to a transition from bending to axial energy storage. However, we observe that this does not necessarily imply that deformation becomes affine in the large z limit. In fact, networks of fibers with low bending stiffness retain a relaxation mode based on the rotational degree of freedom of the crosslinks which allows E0 in the large z limit to be smaller than the affine model prediction. We also conclude that in the z-heterogeneous case, the mean connectivity z̄ is sufficient to evaluate the effect of connectivity on E0 and that higher moments of the distribution of z are less important.

Investigation of Geometric Landscape and Structure-Property Relations for Colloidal Superstructures Using Genetic Algorithm.

Over the past two decades, colloidal particles with a variety of shapes, sizes, and compositions have been synthesized and characterized successfully. One of the most important applications for colloidal building blocks is to engineer functional structures as mechanical, electrical, and optical metamaterials. However, complex interaction dynamics between the building blocks as well as sophisticated structure-property relationships make it challenging to design structures with predictable target properties. In this paper, we implement an inverse material design framework using Genetic Algorithm (GA)-based techniques to streamline the design of colloidal structures based on target properties. We investigate spherical particles as well as colloidal molecules of different sizes and shapes and evaluate a Geometric Landscape Accessibility parameter that identifies the size of feasible domains within the geometric phase space of each structure. Considering target photonic properties, our GA-assisted framework is further utilized to identify sets of building blocks and structures that lead to various target values for the size of the photonic band gaps. The proposed framework in this study will provide new insight for predictive computational material design approaches and help establish more efficient ways of understanding structure-property relations in sub-micrometer-scale materials.