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We develop a physically-motivated mechanical theory for predicting the behavior of nematic elastomers – a subset of liquid crystal elastomers (LCEs). We begin with a statistical description of network geometry that naturally incorporates independent descriptors for the mesogens, which create the nematic phase, and the polymer chains, which are assumed to not deform affinely with global deformations. From here, we develop thermodynamically consistent constitutive laws based on classical continuum mechanics principles and ultimately provide simple governing equations that have a transparent physical interpretation. We found that our framework converges identically to two previously developed mechanical theories, including the well-known neo-classical theory when considering the extreme ends of our parametric space. We then explore the new predictive capabilities of our model inside these two extremes and illustrate its unique predictions at finite strains, which are distinct in form from other theories. We validate our model using published experimental data from four monodomain nematic liquid crystal elastomers. 

We present a statistically-based theoretical framework to describe the mechanical response of dynamically crosslinked semi-flexible polymer networks undergoing finite deformation. The theory starts from a statistical description, via a distribution function, of the chain conformation and orientation. Assuming a so-called tangent affine deformation of the chains, this distribution is then allowed to evolve in time due to a combination of elastic network distortion and a permanent chain reconfiguration enabled by dynamic crosslinks. After presenting the evolution law for the chain distribution function, we reduce the theory to the evolution of the network conformation tensor in both its natural and current state. With this model, we use classical thermodynamics to determine how the stored elastic energy, energy dissipation, and true stress evolve in terms of the network conformation. We show that the model degenerates to classical anisotropic hyperelastic models when crosslinks are permanent, while we recover the classical form of the transient network theory (that describes hyper-viscoelasticity) when chains are fully flexible. Theoretical predictions are then illustrated and compared to the literature for both basic model problems and biomechanically relevant situations 

Dynamic networks composed of constituents that break and reform bonds reversibly are ubiquitous in nature owing to their modular architectures that enable functions like energy dissipation, self-healing, and even activity. While bond breaking depends only on the current configuration of attachment in these networks, reattachment depends also on the proximity of constituents. Therefore, dynamic networks composed of macroscale constituents (not benefited by the secondary interactions cohering analogous networks composed of molecular-scale constituents) must rely on primary bonds for cohesion and self-repair. Toward understanding how such macroscale networks might adaptively achieve this, we explore the uniaxial tensile response of 2D rafts composed of interlinked fire ants (S. invicta). Through experiments and discrete numerical modeling, we find that ant rafts adaptively stabilize their bonded ant-to-ant interactions in response to tensile strains, indicating catch bond dynamics. Consequently, low-strain rates that should theoretically induce creep mechanics of these rafts instead induce elastic-like response. Our results suggest that this force-stabilization delays dissolution of the rafts and improves toughness. Nevertheless, above 35 $\%$strain low cohesion and stress localization cause nucleation and growth of voids whose coalescence patterns result from force-stabilization. These voids mitigate structural repair until initial raft densities are restored and ants can reconnect across defects. However mechanical recovery of ant rafts during cyclic loading suggests that—even upon reinstatement of initial densities—ants exhibit slower repair kinetics if they were recently loaded at faster strain rates. These results exemplify fire ants’ status as active agents capable of memory-driven, stimuli-response for potential inspiration of adaptive structural materials. 

Abstract Viscoelastic material behavior in polymer systems largely arises from dynamic topological rearrangement at the network level. In this paper, we present a physically motivated microsphere formulation for modeling the mechanics of transient polymer networks. By following the directional statistics of chain alignment and local chain stretch, the transient microsphere model (TMM) is fully anisotropic and micro-mechanically based. Network evolution is tracked throughout deformation using a Fokker–Planck equation that incorporates the effects of bond creation and deletion at rates that are sensitive to the chain-level environment. Using published data, we demonstrate the model to capture various material responses observed in physical polymers.