Study of Speed and Force in Biomanipulation

Ph.DDOCTOR OF PHILOSOPH

Regularized maxwell equations and nodal finite elements for electromagnetic field computations in frequency domain

In this work we present an alternative approach to the usual finite element formulation based on edge elements and double-curl Maxwell equations. This alternative approach is based on nodal elements and regularized Maxwell equations. The advantages are that, without adding extra unknowns (such as Lagrange multipliers), it provides spurious-free solutions and well-conditioned matrices. Besides, its integral representation involves a less singular kernel (order 1 instead of 3), which makes this approach best suited to hybridization with integral numerical techniques. On the other hand, a new set of difficulties arises that were not present in the classical formulation. The main drawback is that a globally wrong solution is obtained when the electromagnetic field has a singularity in the problem domain. Also, boundary conditions and field discontinuities are more laborious to implement. This work explains how to overcome these difficulties and demonstrates that accurate solutions can be obtained with nodal elements and the regularized formulation. We also present ERMES, the C++ implementation of the finite element approach depicted above and the main deliverable of this work. We compute with ERMES the scattering parameters of microwave filters and the specific absorption rate induced in a body when exposed to electromagnetic fields. ERMES is also the computational tool used in two novel numerical models introduced in this work. The first one characterizes electromagnetic metal forming processes and the second one the transfer impedance of cable shields. The electromagnetic metal forming model calculates the driving Lorentz force and estimates the optimum frequency at which it is attained the maximum workpiece deformation. The main advantage of the approach is that it provides an explicit relation between the capacitance of the capacitor bank and the frequency of the discharge, which is a key parameter in the design of an electromagnetic forming system. The successful application of the regularized formulation in this model reveals its excellent behavior in the low-frequency (quasi-static) regime. The second numerical model introduced in this work computes the transfer impedance of cable shields. The model reproduces the high frequency behavior of the transfer impedance more accurately than the approaches found in the literature and, moreover, it is able to analyze a wider variety of geometries and materials

Explicit finite-difference time-domain scheme for the simulation of 1-3 piezoelectric effect in axisymmetrical configurations

[EN] Numerical simulations are useful in the processes of design, development and optimization of transducers for non-destructive testing. In this work, a three-dimensional velocity-stress finite-difference model is presented for the elastic wave propagation in the piezoelectric substrate of a transducer excited by applying an impulsive voltage signal to the transducer electrodes. The allocation of the stress, velocity and electric field components on a staggered grid leads to a stable scheme. The different time scales of both mechanical and electromagnetic waves have leaded previous FDTD models to choose between significant physical simplifications or complicated implicit equations. The model presented here is explicit in all its time domain equations, contains only first order derivatives and is centered in time and space. The results of simulations show remarkable accuracy and stability for the different transducers studied. © 2012 Elsevier B.V.The authors want to thank Miquel Ardid, Víctor Sánchez and Bernardino Roig for their cooperation and fruitful discussions. This study was supported by the Programa de Apoyo a la Investigación y Desarrollo PAID-06-10-002-295 of Universidad Politécnica de Valencia.Ferri García, M.; Camarena Femenia, F.; Redondo, J.; Picó Vila, R.; Avis, MR. (2012). Explicit finite-difference time-domain scheme for the simulation of 1-3 piezoelectric effect in axisymmetrical configurations. Wave Motion. 49(6):569-584. https://doi.org/10.1016/j.wavemoti.2012.03.007S56958449

Tunable morphing of electroactive dielectric-elastomer balloons

Designing smart devices with tunable shapes has important applications in industrial manufacture. In this paper, we investigate the nonlinear deformation and the morphological transitions between buckling, necking, and snap-through instabilities of layered DE balloons in response to an applied radial voltage and an inner pressure. We propose a general mathematical theory of nonlinear electro-elasticity able to account for finite inhomogeneous strains provoked by the electro-mechanical coupling. We investigate the onsets of morphological transitions of the spherically symmetric balloons using the surface impedance matrix method. Moreover, we study the nonlinear evolution of the bifurcated branches through finite element numerical simulations. Our analysis demonstrates the possibility to design tunable DE spheres, where the onset of buckling and necking can be controlled by geometrical and mechanical properties of the passive elastic layers. Relevant applications include soft robotics and mechanical actuators

Mechanics and applications of stretchable serpentine structures

Stretchable structures have been developed for various applications, including expandable coronary stents, deployable sensor networks and stretchable bio-mimetic and bio-integrated electronics. High-performance, stretchable electronics have to utilize high-quality and long-lasting inorganic electronic materials such as silicon, oxide dielectrics and metals, which are intrinsically stiff and often brittle. It is therefore an interdisciplinary challenge to make inorganic electronics stretchable while retaining their electronic functionality. Patterning stiff materials into serpentine-shaped wavy ribbons has become a popular strategy for fabricating stretchable inorganic electronics. However due to a lack of mechanics understanding, design of serpentine structures is still largely empirical, whether for freestanding or substrate supported serpentines. This dissertation systematically investigates the mechanics of serpentine structures with emphasis on the effects of serpentine geometry and substrate stiffness, which involves theoretical analysis, numerical simulation, and experimental validation. Our theory has successfully predicted the stretchability and stiffness of various serpentine shapes and has been applied to the optimization of serpentine designs under practical constraints. We are also the first to point out that not all geometric effects are monotonic and serpentines are not always more stretchable than linear ribbons. To manufacture high quality serpentine ribbons with high throughput and low cost, we have invented a “cut-and-paste” method to fabricate both metallic and ceramic serpentines. As a demonstration of our method, a noninvasive, tattoo-like multifunctional epidermal sensor system has been built for the measurement of electrophysiological signals, skin temperature, skin hydration, and respiratory rate. Engineering of epidermal stretchable antenna for wireless communication is also detailed and rationalized.Mechanical Engineerin

Modeling Megathrust Earthquakes Across Scales: One‐way Coupling From Geodynamics and Seismic Cycles to Dynamic Rupture

Taking the full complexity of subduction zones into account is important for realistic modeling and hazard assessment of subduction zone seismicity and associated tsunamis. Studying seismicity requires numerical methods that span a large range of spatial and temporal scales. We present the first coupled framework that resolves subduction dynamics over millions of years and earthquake dynamics down to fractions of a second. Using a two‐dimensional geodynamic seismic cycle (SC) model, we model 4 million years of subduction followed by cycles of spontaneous megathrust events. At the initiation of one such SC event, we export the self‐consistent fault and surface geometry, fault stress and strength, and heterogeneous material properties to a dynamic rupture (DR) model. Coupling leads to spontaneous dynamic rupture nucleation, propagation, and arrest with the same spatial characteristics as in the SC model. It also results in a similar material‐dependent stress drop, although dynamic slip is significantly larger. The DR event shows a high degree of complexity, featuring various rupture styles and speeds, precursory phases, and fault reactivation. Compared to a coupled model with homogeneous material properties, accounting for realistic lithological contrasts doubles the amount of maximum slip, introduces local pulse‐like rupture episodes, and relocates the peak slip from near the downdip limit of the seismogenic zone to the updip limit. When an SC splay fault is included in the DR model, the rupture prefers the splay over the shallow megathrust, although wave reflections do activate the megathrust afterward

Finite element modeling of dielectric elastomer actuators for space applications

A special actuator device with passive sensing capability based on dielectric elastomer was studied and specialized to be used in space applications. The work illustrates the research project modeling procedure adopted to simulate the mechanical behavior of this material based on a finite element theory approach. The Mooney-Rivlin’s hyperelastic and Maxwell’s electrostatic models provide the theoretical basis to describe its electro-mechanic behavior. The validation of the procedure is performed through a numerical-experimental correlation between the response of a prototype of actuator developed by the Risø Danish research center and the 3D finite element model simulations. An investigation concerning a possible application in the space environment of dielectric elastomer actuators (DEA) is also presented

Continuum Mechanics

Continuum Mechanics is the foundation for Applied Mechanics. There are numerous books on Continuum Mechanics with the main focus on the macroscale mechanical behavior of materials. Unlike classical Continuum Mechanics books, this book summarizes the advances of Continuum Mechanics in several defined areas. Emphasis is placed on the application aspect. The applications described in the book cover energy materials and systems (fuel cell materials and electrodes), materials removal, and mechanical response/deformation of structural components including plates, pipelines etc. Researchers from different fields should be benefited from reading the mechanics approached to real engineering problems

Realistic tool-tissue interaction models for surgical simulation and planning

Surgical simulators present a safe and potentially effective method for surgical training, and can also be used in pre- and intra-operative surgical planning. Realistic modeling of medical interventions involving tool-tissue interactions has been considered to be a key requirement in the development of high-fidelity simulators and planners. The soft-tissue constitutive laws, organ geometry and boundary conditions imposed by the connective tissues surrounding the organ, and the shape of the surgical tool interacting with the organ are some of the factors that govern the accuracy of medical intervention planning.\ud \ud This thesis is divided into three parts. First, we compare the accuracy of linear and nonlinear constitutive laws for tissue. An important consequence of nonlinear models is the Poynting effect, in which shearing of tissue results in normal force; this effect is not seen in a linear elastic model. The magnitude of the normal force for myocardial tissue is shown to be larger than the human contact force discrimination threshold. Further, in order to investigate and quantify the role of the Poynting effect on material discrimination, we perform a multidimensional scaling study. Second, we consider the effects of organ geometry and boundary constraints in needle path planning. Using medical images and tissue mechanical properties, we develop a model of the prostate and surrounding organs. We show that, for needle procedures such as biopsy or brachytherapy, organ geometry and boundary constraints have more impact on target motion than tissue material parameters. Finally, we investigate the effects surgical tool shape on the accuracy of medical intervention planning. We consider the specific case of robotic needle steering, in which asymmetry of a bevel-tip needle results in the needle naturally bending when it is inserted into soft tissue. We present an analytical and finite element (FE) model for the loads developed at the bevel tip during needle-tissue interaction. The analytical model explains trends observed in the experiments. We incorporated physical parameters (rupture toughness and nonlinear material elasticity) into the FE model that included both contact and cohesive zone models to simulate tissue cleavage. The model shows that the tip forces are sensitive to the rupture toughness. In order to model the mechanics of deflection of the needle, we use an energy-based formulation that incorporates tissue-specific parameters such as rupture toughness, nonlinear material elasticity, and interaction stiffness, and needle geometric and material properties. Simulation results follow similar trends (deflection and radius of curvature) to those observed in macroscopic experimental studies of a robot-driven needle interacting with gels