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Probabilistic Bayesian Approach for Delamination Localization in GFRP Composites Using Nonlinear Guided Waves

Abstract Nondestructive evaluation (NDE) techniques that use nonlinear wave–damage interactions have gained significant attention recently due to their improved sensitivity in detecting incipient damage. This study presents the use of finite element (FE) simulation with the experimental investigation to quantify the effects of guided waves’ propagation through multiple delaminations in unidirectional glass fiber-reinforced polymer (GFRP) composites. Further, it utilizes the outcomes of nonlinear interactions between guided waves and delaminations to locate the latter. This is achieved through probabilistic Bayesian updating with a structural reliability approach. Guided waves interacting with delaminations induce nonlinear acoustic signatures that can be quantified by the nonlinearity index (NLI). The study found that the NLI changes with the interrogation frequency, as confirmed by numerical and experimental observations. By using the numerical outcomes obtained from the nonlinear responses, a Bayesian model-based approach with subset simulation is proposed and subsequently used to locate multiple delaminations. The results indicate that both the log-likelihood and log-evidence are key factors in determining the localization phenomenon. The proposed method successfully localizes multiple delaminations and evaluates their number, interlaminar position, width, and type.

Thermomechanical Coupling in Polydomain Liquid Crystal Elastomers

Abstract Liquid crystal elastomers (LCEs) are made of liquid crystal molecules integrated with rubber-like polymer networks. An LCE exhibits both the thermotropic property of liquid crystals and the large deformation of elastomers. It can be monodomain or polydomain in the nematic phase and transforms to an isotropic phase at elevated temperature. These features have enabled various new applications of LCEs in robotics and other fields. However, despite substantial research and development in recent years, thermomechanical coupling in polydomain LCEs remains poorly studied, such as their temperature-dependent mechanical response and stretch-influenced isotropic-nematic phase transition. This knowledge gap severely limits the fundamental understanding of the structure-property relationship, as well as future developments of LCEs with precisely controlled material behaviors. Here, we construct a theoretical model to investigate the thermomechanical coupling in polydomain LCEs. The model includes a quasi-convex elastic energy of the polymer network and a free energy of mesogens. We study the working conditions where a polydomain LCE is subjected to various prescribed planar stretches and temperatures. The quasi-convex elastic energy enables a “mechanical phase diagram” that describes the macroscopic effective mechanical response of the material, and the free energy of mesogens governs their first-order nematic-isotropic phase transition. The evolution of the mechanical phase diagram and the order parameter with temperature is predicted and discussed. Unique temperature-dependent mechanical behaviors of the polydomain LCE that have never been reported before are shown in their stress-stretch curves. These results are hoped to motivate future fundamental studies and new applications of thermomechanical LCEs.

Creating Geometric Imperfections in Thin-Walled Structures Using Acoustic Excitation

Abstract Thermomechanical buckling of slender and thin-walled structural components happens without warning and can lead to catastrophic failure. Similar phenomena are observed during plasmolysis (contraction of a plant cell’s protoplast) and rupture of viral capsids. Analytical formulas derived from stability analyses of elastic plates and shells that do not account for the effects of random geometric imperfections introduced during the manufacturing process or biological growth may vastly over-estimate buckling capacity. To ensure structural safety, the formulas must therefore be combined with empirical data to define “knockdown factors” which are in turn used to establish safety factors. Towards improved understanding of the role of imperfections on mechanical response, ingenious methods have been used to fabricate and test near-perfectly hemispherical shells and those containing dimple-like defects. However, a method of inducing imperfections in the form of randomly shaped surfaces remains elusive. We introduce a protocol for realizing such imperfect shells and measuring the pressure required to buckle them. Silicone is poured onto an elastomeric mold under an acoustic excitation, which can be either random sound, or if desired the same as the modal frequency of the mold. Illustrative micro-computed-tomography images and buckling pressure experiments of a nearly perfect shell and an imperfect one show that the method is effective in introducing randomly shaped imperfections of significant magnitudes. This proof-of-concept study demonstrates that the experimental results when combined with computational simulations can lead to improved understanding of stochastic buckling phenomena.