It is important from a fundamental standpoint and for practical applications to understand how the mechanical properties of graphene are influenced by defects. Here we report that the two-dimensional elastic modulus of graphene is maintained even at a high density of sp³-type defects. Moreover, the breaking strength of defective graphene is only ~14% smaller than its pristine counterpart in the sp³-defect regime. By contrast, we report a significant drop in the mechanical properties of graphene in the vacancy-defect regime. We also provide a mapping between the Raman spectra of defective graphene and its mechanical properties. This provides a simple, yet non-destructive methodology to identify graphene samples that are still mechanically functional. By establishing a relationship between the type and density of defects and the mechanical properties of graphene, this work provides important basic information for the rational design of composites and other systems utilizing the high modulus and strength of graphene.

We study a unique biomaterial developed from fungal mycelium, the vegetative part and the root structure of fungi. Mycelium has a filamentous network structure with mechanics largely controlled by filament elasticity and branching, and network density. We report the morphological and mechanical characterization of mycelium through an integrated experimental and computational approach. The monotonic mechanical behavior of the mycelium is non-linear both in tension and compression. The material exhibits considerable strain hardening before rupture under tension, it mimics the open cell foam behavior under compression and exhibits hysteresis and the Mullins effect when subjected to cyclic loading. Based on our morphological characterization and experimental observations, we develop and validate a multiscale fiber network-based model for the mycelium which reproduces the tensile and compressive behavior of the material.

This article presents a review of the current understanding of the mechanics of random fiber networks. The discussion refers to athermal fiber networks, for which the governing functional is the system enthalpy, as well as to molecular networks, in which thermal fluctuations are important. Fiber networks are broadly encountered in everyday life as paper, insulation and damping materials, and as the essential component of some consumer products, while molecular networks form the structure of biological and non-biological materials such as the cytoskeleton, connective tissue, gels and rubber. The mechanics of these materials is defined by the structure of the network and by the mechanical behavior of individual filaments. The structure is characterized by a number of parameters, such as the density, filament orientation, fiber waviness, density and nature of cross-links, which are discussed in the first part of the article. The constitutive behavior of individual filaments is defined by their bending and axial stiffness, and by the response to thermal fluctuations. The constitutive response of the cross-links plays a central role in defining the system-scale mechanical behavior. The analysis of the network mechanics is divided into two parts addressing cross-linked and entangled (non-cross-linked) networks. Both molecular and athermal cross-linked networks are discussed, while only the literature on athermal entangled networks is included. Flexible and semi-flexible fibers are considered, with special attention given to the second category. The constitutive behavior under small and large deformations, including attempts to define continuum representations of the discrete system, is reviewed. A number of open issues are discussed in closure.