Modeling Ultrasonic NDE and Guided Wave based Structural Health Monitoring

Structural Health Monitoring (SHM) systems require integration of non-destructive technologies into structural design and operational processes. Modeling and simulation of complex NDE inspection processes are important aspects in the development and deployment of SHM technologies. Ray tracing techniques are vital simulation tools to visualize the wave path inside a material. These techniques also help in optimizing the location of transducers and their orientation with respect to the zone of interrogation. It helps in increasing the chances of detection and identification of a flaw in that zone. While current state-of-the-art techniques such as ray tracing based on geometric principle help in such visualization, other information such as signal losses due to spherical or cylindrical shape of wave front are rarely taken into consideration. The problem becomes a little more complicated in the case of dispersive guided wave propagation and near-field defect scattering. We review the existing models and tools to perform ultrasonic NDE simulation in structural components. As an initial step, we develop a ray-tracing approach, where phase and spectral information are preserved. This enables one to study wave scattering beyond simple time of flight calculation of rays. Challenges in terms of theory and modelling of defects of various kinds are discussed. Various additional considerations such as signal decay and physics of scattering are reviewed and challenges involved in realistic computational implementation are discussed. Potential application of this approach to SHM system design is highlighted and by applying this to complex structural components such as airframe structures, SHM is demonstrated to provide additional value in terms of lighter weight and/or longevity enhancement resulting from an extension of the damage tolerance design principle not compromising safety and reliability.

A simple method to simulate shrinkage-induced cracking in cement-based composites by lattice-type modeling

A new numerical procedure is proposed to investigate cracking behaviors induced by mismatch between the matrix phase and aggregates due to matrix shrinkage in cement-based composites. This kind of failure processes is simplified in this investigation as a purely spontaneous mechanical problem, therefore, one main difficulty during simulating the phenomenon lies that no explicit external load serves as the drive to propel development of this physical process. As a result, it is different from classical mechanical problems and seems hard to be solved by using directly the classical finite element method (FEM), a typical kind of "load -> medium -> response" procedures. As a solution, the actual mismatch deformation field is decomposed into two virtual fields, both of which can be obtained by the classical FEM. Then the actual response is obtained by adding together the two virtual displacement fields based on the principle of superposition. Then, critical elements are detected successively by the event-by-event technique. The micro-structure of composites is implemented by employing the generalized beam (GB) lattice model. Numerical examples are given to show the effectiveness of the method, and detailed discussions are conducted on influences of material properties.

Analog VLSI-based, neuromorphic sensorimotor systems: modeling the primate oculomotor system

Using neuromorphic analog VLSI techniques for modeling large neural systems has several advantages over software techniques. By designing massively-parallel analog circuit arrays which are ubiquitous in neural systems, analog VLSI models are extremely fast, particularly when local interactions are important in the computation. While analog VLSI circuits are not as flexible as software methods, the constraints posed by this approach are often very similar to the constraints faced by biological systems. As a result, these constraints can offer many insights into the solutions found by evolution. This dissertation describes a hardware modeling effort to mimic the primate oculomotor system which requires both fast sensory processing and fast motor control. A one-dimensional hardware model of the primate eye has been built which simulates the physical dynamics of the biological system. It is driven by analog VLSI circuits mimicking brainstem and cortical circuits that control eye movements. In this framework, a visually-triggered saccadic system is demonstrated which generates averaging saccades. In addition, an auditory localization system, based on the neural circuits of the barn owl, is used to trigger saccades to acoustic targets in parallel with visual targets. Two different types of learning are also demonstrated on the saccadic system using floating-gate technology allowing the non-volatile storage of analog parameters directly on the chip. Finally, a model of visual attention is used to select and track moving targets against textured backgrounds, driving both saccadic and smooth pursuit eye movements to maintain the image of the target in the center of the field of view. This system represents one of the few efforts in this field to integrate both neuromorphic sensory processing and motor control in a closed-loop fashion.

Discrete Modeling of Granular Media: A NURBS-based Approach

This dissertation is concerned with the development of a new discrete element method (DEM) based on Non-Uniform Rational Basis Splines (NURBS). With NURBS, the new DEM is able to capture sphericity and angularity, the two particle morphological measures used in characterizing real grain geometries. By taking advantage of the parametric nature of NURBS, the Lipschitzian dividing rectangle (DIRECT) global optimization procedure is employed as a solution procedure to the closest-point projection problem, which enables the contact treatment of non-convex particles. A contact dynamics (CD) approach to the NURBS-based discrete method is also formulated. By combining particle shape flexibility, properties of implicit time-integration, and non-penetrating constraints, we target applications in which the classical DEM either performs poorly or simply fails, i.e., in granular systems composed of rigid or highly stiff angular particles and subjected to quasistatic or dynamic flow conditions. The CD implementation is made simple by adopting a variational framework, which enables the resulting discrete problem to be readily solved using off-the-shelf mathematical programming solvers. The capabilities of the NURBS-based DEM are demonstrated through 2D numerical examples that highlight the effects of particle morphology on the macroscopic response of granular assemblies under quasistatic and dynamic flow conditions, and a 3D characterization of material response in the shear band of a real triaxial specimen.

First principles based multiparadigm modeling of electronic structures and dynamics

Electronic structures and dynamics are the key to linking the material composition and structure to functionality and performance.

An essential issue in developing semiconductor devices for photovoltaics is to design materials with optimal band gaps and relative positioning of band levels. Approximate DFT methods have been justified to predict band gaps from KS/GKS eigenvalues, but the accuracy is decisively dependent on the choice of XC functionals. We show here for CuInSe₂ and CuGaSe₂, the parent compounds of the promising CIGS solar cells, conventional LDA and GGA obtain gaps of 0.0-0.01 and 0.02-0.24 eV (versus experimental values of 1.04 and 1.67 eV), while the historically first global hybrid functional, B3PW91, is surprisingly the best, with band gaps of 1.07 and 1.58 eV. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a MAD of only 0.09 eV, which is substantially better than all modern hybrid functionals, including B3LYP (MAD of 0.19 eV) and screened hybrid functional HSE06 (MAD of 0.18 eV).

The laboratory performance of CIGS solar cells (> 20% efficiency) makes them promising candidate photovoltaic devices. However, there remains little understanding of how defects at the CIGS/CdS interface affect the band offsets and interfacial energies, and hence the performance of manufactured devices. To determine these relationships, we use the B3PW91 hybrid functional of DFT with the AEP method that we validate to provide very accurate descriptions of both band gaps and band offsets. This confirms the weak dependence of band offsets on surface orientation observed experimentally. We predict that the CBO of perfect CuInSe₂/CdS interface is large, 0.79 eV, which would dramatically degrade performance. Moreover we show that band gap widening induced by Ga adjusts only the VBO, and we find that Cd impurities do not significantly affect the CBO. Thus we show that Cu vacancies at the interface play the key role in enabling the tunability of CBO. We predict that Na further improves the CBO through electrostatically elevating the valence levels to decrease the CBO, explaining the observed essential role of Na for high performance. Moreover we find that K leads to a dramatic decrease in the CBO to 0.05 eV, much better than Na. We suggest that the efficiency of CIGS devices might be improved substantially by tuning the ratio of Na to K, with the improved phase stability of Na balancing phase instability from K. All these defects reduce interfacial stability slightly, but not significantly.

A number of exotic structures have been formed through high pressure chemistry, but applications have been hindered by difficulties in recovering the high pressure phase to ambient conditions (i.e., one atmosphere and room temperature). Here we use dispersion-corrected DFT (PBE-ulg flavor) to predict that above 60 GPa the most stable form of N₂O (the laughing gas in its molecular form) is a 1D polymer with an all-nitrogen backbone analogous to cis-polyacetylene in which alternate N are bonded (ionic covalent) to O. The analogous trans-polymer is only 0.03-0.10 eV/molecular unit less stable. Upon relaxation to ambient conditions both polymers relax below 14 GPa to the same stable non-planar trans-polymer, accompanied by possible electronic structure transitions. The predicted phonon spectrum and dissociation kinetics validate the stability of this trans-poly-NNO at ambient conditions, which has potential applications as a new type of conducting polymer with all-nitrogen chains and as a high-energy oxidizer for rocket propulsion. This work illustrates in silico materials discovery particularly in the realm of extreme conditions.

Modeling non-adiabatic electron dynamics has been a long-standing challenge for computational chemistry and materials science, and the eFF method presents a cost-efficient alternative. However, due to the deficiency of FSG representation, eFF is limited to low-Z elements with electrons of predominant s-character. To overcome this, we introduce a formal set of ECP extensions that enable accurate description of p-block elements. The extensions consist of a model representing the core electrons with the nucleus as a single pseudo particle represented by FSG, interacting with valence electrons through ECPs. We demonstrate and validate the ECP extensions for complex bonding structures, geometries, and energetics of systems with p-block character (C, O, Al, Si) and apply them to study materials under extreme mechanical loading conditions.

Despite its success, the eFF framework has some limitations, originated from both the design of Pauli potentials and the FSG representation. To overcome these, we develop a new framework of two-level hierarchy that is a more rigorous and accurate successor to the eFF method. The fundamental level, GHA-QM, is based on a new set of Pauli potentials that renders exact QM level of accuracy for any FSG represented electron systems. To achieve this, we start with using exactly derived energy expressions for the same spin electron pair, and fitting a simple functional form, inspired by DFT, against open singlet electron pair curves (H₂ systems). Symmetric and asymmetric scaling factors are then introduced at this level to recover the QM total energies of multiple electron pair systems from the sum of local interactions. To complement the imperfect FSG representation, the AMPERE extension is implemented, and aims at embedding the interactions associated with both the cusp condition and explicit nodal structures. The whole GHA-QM+AMPERE framework is tested on H element, and the preliminary results are promising.

Modeling Innovative Power Take-Off Based on Double-Acting Hydraulic Cylinders Array for Wave Energy Conversion

One of the key systems of a Wave Energy Converter for extraction of wave energy is the Power Take-Off (PTO) device. This device transforms the mechanical energy of a moving body into electrical energy. This paper describes the model of an innovative PTO based on independently activated double-acting hydraulic cylinders array. The model has been developed using a simulation tool, based on a port-based approach to model hydraulics systems. The components and subsystems used in the model have been parameterized as real components and their values experimentally obtained from an existing prototype. In fact, the model takes into account most of the hydraulic losses of each component. The simulations show the flexibility to apply different restraining torques to the input movement depending on the geometrical configuration and the hydraulic cylinders on duty, easily modified by a control law. The combination of these two actions allows suitable flexibility to adapt the device to different sea states whilst optimizing the energy extraction. The model has been validated using a real test bench showing good correlations between simulation and experimental tests.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model. © 2011 Elsevier Ltd.