Instabilities in liquid crystal elastomers

Stability is an important and fruitful avenue of research for liquid crystal elastomers. At constant temperature, upon stretching, the homogeneous state of a nematic body becomes unstable, and alternating shear stripes develop at very low stress. Moreover, these materials can experience classical mechanical effects, such as necking, void nucleation and cavitation, and inflation instability, which are inherited from their polymeric network. We investigate the following two problems: First, how do instabilities in nematic bodies change from those found in purely elastic solids? Second, how are these phenomena modified if the material constants fluctuate? To answer these questions, we present a systematic study of instabilities occurring in nematic liquid crystal elastomers, and examine the contribution of the nematic component and of fluctuating model parameters that follow probability laws. This combined analysis may lead to more realistic estimations of subsequent mechanical damage in nematic solid materials. Because of their complex material responses in the presence of external stimuli, liquid crystal elastomers have many potential applications in science, manufacturing, and medical research. The modeling of these materials requires a multiphysics approach, linking traditional continuum mechanics with liquid crystal theory, and has led to the discovery of intriguing mechanical effects. An important problem for both applications and our fundamental understanding of nematic elastomers is their instability under large strains, as this can be harnessed for actuation, sensing, or patterning. The goal is then to identify parameter values at which a bifurcation emerges, and how these values change with external stimuli, such as temperature or loads. However, constitutive parameters of real manufactured materials have an inherent variation that should also be taken into account, thus the need to quantify uncertainties in physical responses, which can be done by combining the classical field theories with stochastic methods that enable the propagation of uncertainties from input data to output quantities of interest. The present study demonstrates how to characterize instabilities found in nematic liquid crystal elastomers with probabilistic material parameters at the macroscopic scale, and paves the way for a systematic theoretical and experimental study of these fascinating materials.

The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta

A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

Micromechanics of Void Nucleation and Early Growth at Incoherent Precipitates: Lattice-Trapped and Dislocation-Mediated Delamination Modes

The initial stages of debonding at hard-particle interfaces during rupture is relevant to the fracture of most structural alloys, yet details of the mechanistic process for rupture at the atomic scale are poorly understood. In this study, we employ molecular dynamics simulation of a spherical Al2Cu θ precipitate in an aluminum matrix to examine the earliest stages of void formation and nanocrack growth at the particle-matrix interface, at temperatures ranging from 200–400 K and stresses ranging from 5.7–7.2 GPa. The simulations revealed a three-stage process involving (1) stochastic instantaneous or delayed nucleation of excess free volume at the particle-matrix interface involving only tens of atoms, followed by (2) steady time-dependent crack growth in the absence of dislocation activity, followed by (3) dramatically accelerated crack growth facilitated by crack-tip dislocation emission. While not all three stages were present for all stresses and temperatures, the second stage, termed lattice-trapped delamination, was consistently the rate-limiting process. This lattice-trapped delamination process was determined to be a thermally activated brittle fracture mode with an unambiguous Arrhenius activation energy of 1.37 eV and an activation area of 1.17 Å2. The role of lattice-trapped delamination in the early stages of particle delamination is not only relevant at the high strain-rates and stresses associated with shock spallation, but Arrhenius extrapolation suggests that the mechanism also operates during quasi-static rupture at micrometer-scale particles.