Browsing by Author "Bonito, Andrea"

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Finite Element Approximations of Bending Actuated Devices
Mathematics; TAMU; https://hdl.handle.net/20.500.14641/630; National Science Foundation
The ability to generate complex deformations from relatively small energies has tremendous applications in micro-engineering and biomedical science. This research focuses on developing and implementing mathematical algorithms able to predict and optimize the deformation of elastic films, chosen for their potential in the production of robust and light-weight micro-scale devices. The deformations considered are triggered by exposing to external stimuli either polymers with different expansion characteristics or manufactured gels with residual stresses. Devices based on these technologies are, for instance, employed as drug delivery vesicles, cell encapsulation devices, sensors, bio-muscles and as proxies for tissue growth. In addition to these applications in biomedical science, the development of autonomous foldable structures such as self-deployable sun sails in spacecraft or deployable aircrafts, photovoltaic devices, actuators, micromotors, microgrippers, microvalves, microswimmers are very popular interests in the engineering community this research is likely to have impact on. The proposed study focuses on thin devices where bending is the principal mechanism for, possibly large, deformations. The mathematical models are derived as the two dimensional limit of thin three dimensional hyper-elastic solids. They are characterized by energy densities dominated by bending, expressed geometrically as the film's second fundamental form. In addition to the difficulties inherent in the non-divergence form of this fourth order system, fully non-linear geometrical constraints must be taken into account in the context of large deformations. The aim of this research is to derive mathematical models when not available for the targeted application, and to design, analyze and implement finite element based algorithms for their approximations. The entire process from the mathematical analysis to the actual highly parallel implementation of finite element algorithms is covered. Hence, analytical tools borrowed from differential geometry and calculus of variation are blended with numerical analysis and delicate computational efforts to achieve efficient and practical algorithms. The ability to generate complex deformations from relatively small energies has tremendous application in micro-engineering and biomedical science. The algorithms resulting from the proposed research - and in particular their relatively effortless implementations - are likely to have impact in these areas. To mention a few applications, devices based on bilayers of polymers or prestrained films are employed as drug delivery vesicles, cell encapsulation devices, sensors, bio-muscles and as proxies for tissue growth. In addition to these applications in biomedical science, the development of autonomous foldable structures such as self-deployable sun sails in spacecraft or deployable aircrafts, photovoltaic devices, engineered scaffolds, actuators, micromotors, microgrippers, microvalves, microswimmers are very popular research interests in the engineering community. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
Finite Element Approximations of Developable Surfaces with Curved Folds
Mathematics; https://hdl.handle.net/20.500.14641/1119; National Science Foundation
The ability to generate complex and robust deformations from relatively small energies has a tremendous number of applications in many areas including the strategic areas of aerospace, nanotechnology and biotechnology. This research project explores the potential benefits of folding devices where folding does not necessarily occur on straight lines. Compared to more traditional origami-type deformations, curved creases greatly expand the range and rigidity of achievable configurations. The design of deployable surfaces such as solar panels, solar sails, space telescopes, airbags, flapping devices, and ingestible robots are few examples benefiting from this technology. This project encompasses the mathematical modeling of folding devices, the design of numerical algorithms predicting their deformations, and a mathematical analysis guaranteeing the efficiency of the predictions. The PI will consider thin materials resisting shear and stretch but allowing for bending away from non-necessarily straight creases. In recent years, these curved origamis received significant attention from the scientific community in view of the fascinating variety of shapes they can exhibit, their ability to produce rigid configurations and flapping mechanisms, their capacity to undergo large deformations using a small amount of energy, and their applicability at small and large scales alike. The outcomes of this research program include the derivation of a reduced plate model for thin materials resisting bending and allowing for folding along curved locations, the design and analysis of finite element algorithms approximating the dynamics and equilibriums of the corresponding plate deformations, and a parallel implementation of the proposed algorithms illustrating their efficiency on benchmarks as well as on configurations relevant to practitioners. Central in this study, the concept of gamma convergence is used to justify the reduced model but also developed for the analysis of the associated numerical methods.