Browsing by Subject "Finite element analysis"

Biosensing is a critical area of research that involves detecting and measuring biological molecules. Among the various types of biosensors, acoustic biosensors are attractive for their simplicity, robustness, and low cost, particularly in point-of-care (POC) applications. However, the quality factor (Q-factor) of acoustic biosensors is often low, limiting their sensitivity and accuracy in terms of in-liquid gravimetric detection for biosensing applications. In this dissertation, we present a novel approach that eliminates nearly all dissipation and damping from sample liquids, rendering a significant improvement in Q-factor for in-liquid gravimetric detection. We constructed rigid microfluidic channels to confine liquids and the associated acoustic energy, thereby eliminating acoustic radiation damping. We also used the channels' side walls to create pressure waves, confining the liquids within and suppressing acoustic damping due to the viscous layer. The quartz crystal microbalance (QCM) was selected as the model system for implementing the new paradigm due to its widespread usage in various applications, simplicity, cost-effectiveness, and relevance of its principles to other types of acoustic biosensors. We hypothesized that the ratio of the wavelength of the pressure wave to the width of the channels is a crucial determining factor for optimal performance. We then tested the hypothesis by building the microfluidic QCM (the µ-QCM) to improve the Q-factor of conventional QCM. The combination of experiments, simulations, and theoretical studies demonstrated a 10-fold improvement in the Q-factor. The new system offers many other advantages, including direct data interpretation, minimized sample volume requirement, and easier temperature control for in-liquid gravimetric detection. Additionally, the same principles can be applied to other acoustic biosensors, benefiting the entire field.

Polymer-based nanocomposites (PNCs) are materials consisting of nanoparticles and polymers. The enhancement of the mechanical, thermal, electrical, and other properties of the PNCs brought by the nanoparticles makes it a useful material in various applications. The huge amount of surface area brought by the nanoparticles interacts with polymer chains to form an interphase, which drives the property change. The presence of the interphase adds to the complexity of the processing-structure-property (p-s-p) relationship of PNCs that guide material design. As conventional trial-and-error approaches in the laboratory prove time-consuming and resource-intensive, an alternative approach is to utilize data-driven methods for PNC design. However, data-driven material design suffers from data scarcity issues.To tackle the data scarcity issue on a cross-community level, there has been a growing emphasis on the adoption of the Findable, Accessible, Interoperable, and Reusable (FAIR) data principles. In 2016, the NanoMine data resource, later evolved into MaterialsMine with the inclusion of metamaterials, and its accompanying schema were introduced to handle PNC data, offering a user-friendly and FAIR approach to manage these complex PNC data, facilitating data-driven material design. To make this schema more accessible to curators and material scientists, an Excel-based customizable master template was designed for experimental data. In parallel to the long-lasting cumulative effort of curating experimental PNC data from literature, simulation data can be generated and curated much faster due to its computational nature. Thus, the NanoMine schema and template for experimental data were expanded to support popular simulation methods like Finite Element Analysis (FEA) with high utilization of existing fields, demonstrating the flexibility of the schema/template approach. With the schema and template in place for NanoMine to host FEA data, an efficient and highly automated end-to-end pipeline was developed for FEA data generation. A data management system was implemented to capture the FEA data and the associated metadata, which are critical for the data to be FAIR. A resource management system was implemented to address the system restrictions. Starting from microstructure generation, all the way to packaging the data into a curation-ready format, the pipeline lives in a standardized Jupyter notebook for easier usage and better bookkeeping. FEA simulations, while faster than laboratory experiments, remain resource-intensive and are often constrained by commercial software licenses. Thus, the last part of this research aims to develop an efficient, reliable, and lightweight surrogate model for FEA simulation of the viscoelastic response of PNCs, named ViscoNet, with machine learning (ML). Drawing inspiration from NLP models like GPT, ViscoNet utilizes pre-training and fine-tuning techniques to reproduce FEA simulations, achieving a mean absolute percentage error (MAPE) of < 5% for rubbery modulus, < 1% for glassy modulus, and 1.22% for tan delta peak, with as few as 500 FEA simulation data for fine-tuning. ViscoNet demonstrates impressive generalization capabilities from thermoplastics to thermosets. ViscoNet enables the generation of over 20k VE responses in under 2 minutes, making it a versatile tool for high-throughput PNC design and optimization. Notably, ViscoNet does not require a GPU for training, allowing anyone with Internet access to download 500 FEA data from NanoMine and fine-tune ViscoNet on a personal laptop, thereby making data-driven materials design accessible to a broader scientific community.

The surface of cell membranes can display a high degree of lateral heterogeneity. This non-uniform distribution of constituents is characterized by mobile nanodomain clusters called rafts. Enriched by saturated phospholipids, cholesterol and proteins, rafts are considered to be vital for several important cellular functions such as signalling and trafficking, morphological transformations associated with exocytosis and endocytosis and even as sites for the replication of viruses. Understanding the evolving distribution of these domains can provide significant insight into the regulation of cell function. Giant vesicles are simple prototypes of cell membranes. Microdomains on vesicles can be considered as simple analogues of rafts on cell membranes and offer a means to study various features of cellular processes in isolation.

In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles (GUVs). The interplay of species transport on the vesicle surface and the mechanics of vesicle shape change is captured using a chemo-mechanical model. Specifically, the approach focuses on the regime of vesicle dynamics where shape change occurs on a much faster time scale in comparison to species transport, as has been observed in several experimental studies on GUVs. In this study, shape changes are assumed to be instantaneous, while species transport, which is modeled by phase separation and domain coarsening, follows a natural time scale described by the Cahn--Hilliard dynamics.

The curvature energy of the vesicle membrane is defined by the classical Canham--Helfrich--Evans model. Dependence of flexural rigidity and spontaneous curvature on the lipid species is built into the energy functional. The chemical energy is characterized by a Cahn--Hilliard type density function that intrinsically captures the line energy of interfaces between two phases. Both curvature and chemical contributions to the vesicle energetics are consistently non-dimensionalized.

The coupled model is cast in a diffuse-interface form using the phase-field framework. The phase-field form of the governing equations describing shape equilibrium and species transport are both fourth-order and nonlinear. The system of equations is discretized using the finite element method with a uniform cubic-spline basis that satisfies global higher-order continuity. For shape equilibrium, geometric constraints of constant internal volume and constant surface area of the vesicle are imposed weakly using the penalty approach. A time-stepping scheme based on the unconditionally gradient-stable convexity-splitting technique is employed for explicit time integration of nonlocal integrals arising from the geometric constraints.

Numerical examples of axisymmetric stationary shapes of uniform vesicles are presented. Further, two- and three-dimensional numerical examples of domain formation and growth coupled to vesicle shape changes are discussed. Simulations qualitatively depicting curvature-dependent domain sorting and shape changes to minimize line tension are presented. The effect of capturing the difference in time scales is also brought out in a few numerical simulations that predict a starkly different pathway to equilibrium.

Spinal fusion is quickly becoming a common surgical operation in today's medical field. A major component of spinal fusion surgery is the use of metal rods. These rods, which are made of titanium or stainless steel, must be bent in such a way to hold the spine in the correct configuration. This part of the surgery is very time consuming and tiring for the surgeon, which increases the risk to the patient. A device is being designed that would automatically bend the rods to match a flexible pattern formed by the surgeon. A major consideration in the design of this device is predicting the amount of springback exhibited by the rod when bent. This thesis discusses a method of determining that springback. First, an experimental setup is designed and used to bend surrogate rods to certain angles. This experimental data is compared to a numerical simulation of the bending. The material model in the simulation uses a stress-strain curve derived from tensile test data. It was found that at bend angles less than 60 degrees, the simulation results are accurate enough to predict springback. Therefore, a curve was fit to the data, and the resulting polynomial equation was used to solve for the bend angle to which the rod would need to be bent in order to obtain a desired angle. However, the simulation became inaccurate at higher bend angles. It was found that a mesh finer than that which was used for the simulation resulted in better agreement with the experimental values. In conclusion, it was shown that a numerical simulation could be used to produce accurate springback values in order to develop a prediction algorithm for a rod bending device.

An advanced bulk constitutive model is used with a new cohesive zone model that is stress state and rate-dependent in order to simulate the ductile to brittle failure transition in polycarbonate. The cohesive zone model is motivated by experimental evidence that two different critical energies per unit area of crack growth exist in glassy polymers. A higher energy state is associated with ductile failure (slow crack growth), while a lower energy state is associated with brittle failure (fast crack growth). The model is formulated so that as rate or stress state changes within a simulation, the fracture energy and thus fracture mode may also change appropriately. The ductile to brittle transition occurs when the cohesive opening rate is over a threshold opening rate and when the stress state is close to plane strain in a fracture specimen. These effects are coupled. The principal contribution of this work is that this is the first time a single set of material input parameters can predict the transition from slow to fast crack growth as test loading rate and sample thickness are varied. This result enlisted the use of an advanced constitutive model and the new cohesive zone model with rate and stress-state dependencies in three-dimensional finite element analysis.