Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, 2018 Nanjing University of Science and Technology

#### Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

*SIUE Faculty Research, Scholarship, and Creative Activity*

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between local strong ...

Development Of A Neural Network Simulator For Studying The Constitutive Behavior Of Structural Composite Materials, 2017 Iowa State University

#### Development Of A Neural Network Simulator For Studying The Constitutive Behavior Of Structural Composite Materials, Hyuntae Na, Seung-Yub Lee, Ersan Ustundag, Sarah L. Ross, Halil Ceylan, Kasthurirangan Gopalakrishnan

*Halil Ceylan*

This paper introduces a recent development and application of a noncommercial artificial neural network (ANN) simulator with graphical user interface (GUI) to assist in rapid data modeling and analysis in the engineering diffraction field. The real-time network training/simulation monitoring tool has been customized for the study of constitutive behavior of engineering materials, and it has improved data mining and forecasting capabilities of neural networks. This software has been used to train and simulate the finite element modeling (FEM) data for a fiber composite system, both forward and inverse. The forward neural network simulation precisely reduplicates FEM results several orders ...

Virtual Melting As A New Mechanism Of Stress Relaxation Under High Strain Rate Loading, 2017 Iowa State University

#### Virtual Melting As A New Mechanism Of Stress Relaxation Under High Strain Rate Loading, Valery I. Levitas, Ramon Ravelo

*Valery I. Levitas*

Generation and motion of dislocations and twinning are the main mechanisms of plastic deformation. A new mechanism of plastic deformation and stress relaxation at high strain rates (109–1012 s-1) is proposed, under which virtual melting occurs at temperatures much below the melting temperature. Virtual melting is predicted using a developed, advanced thermodynamic approach and confirmed by large-scale molecular dynamics simulations of shockwave propagation and quasi-isentropic compression in both single and defective crystals. The work and energy of nonhydrostatic stresses at the shock front drastically increase the driving force for melting from the uniaxially compressed solid state, reducing the melting ...

Pre-Stressing Micron-Scale Aluminum Core-Shell Particles To Improve Reactivity, 2017 Iowa State University

#### Pre-Stressing Micron-Scale Aluminum Core-Shell Particles To Improve Reactivity, Valery I. Levitas, Jena Mccollum, Michelle Pantoya

*Valery I. Levitas*

The main direction in increasing reactivity of aluminum (Al) particles for energetic applications is reduction in their size down to nanoscale. However, Al nanoparticles are 30–50 times more expensive than micron scale particles and possess safety and environmental issues. Here, we improved reactivity of Al micron scale particles by synthesizing pre-stressed core-shell structures. Al particles were annealed and quenched to induce compressive stresses in the alumina passivation shell surrounding Al core. This thermal treatment was designed based on predictions of the melt-dispersion mechanism (MDM); a theory describing Al particle reaction under high heating rate. For all anneal treatment temperatures ...

Thermodynamically Consistent Phase Field Theory Of Phase Transformations With Anisotropic Interface Energies And Stresses, 2017 Iowa State University

#### Thermodynamically Consistent Phase Field Theory Of Phase Transformations With Anisotropic Interface Energies And Stresses, Valery I. Levitas, James A. Warren

*Valery I. Levitas*

The main focus of this paper is to introduce, in a thermodynamically consistent manner, an anisotropic interface energy into a phase field theory for phase transformations. Here we use a small strain formulation for simplicity, but we retain some geometric nonlinearities, which are necessary for introducing correct interface stresses. Previous theories have assumed the free energy density (i.e., gradient energy) is an anisotropic function of the gradient of the order parameters in the current (deformed) state, which yields a nonsymmetric Cauchy stress tensor. This violates two fundamental principles: the angular momentum equation and the principle of material objectivity. Here ...

Shear-Induced Phase Transition Of Nanocrystalline Hexagonal Boron Nitride To Wurtzitic Structure At Room Temperature And Lower Pressure, 2017 Texas Tech University

#### Shear-Induced Phase Transition Of Nanocrystalline Hexagonal Boron Nitride To Wurtzitic Structure At Room Temperature And Lower Pressure, Cheng Ji, Valery I. Levitas, Hongyang Zhu, Jharna Chaudhuri, Archis Marathe, Yanzhang Ma

*Valery I. Levitas*

Disordered structures of boron nitride (BN), graphite, boron carbide (BC), and boron carbon nitride (BCN) systems are considered important precursor materials for synthesis of superhard phases in these systems. However, phase transformation of such materials can be achieved only at extreme pressure–temperature conditions, which is irrelevant to industrial applications. Here, the phase transition from disordered nanocrystalline hexagonal (h)BN to superhard wurtzitic (w)BN was found at room temperature under a pressure of 6.7 GPa after applying large plastic shear in a rotational diamond anvil cell (RDAC) monitored by in situ synchrotron X-ray diffraction (XRD) measurements. However, under ...

Multiphase Phase Field Theory For Temperature- And Stress-Induced Phase Transformations, 2017 Iowa State University

#### Multiphase Phase Field Theory For Temperature- And Stress-Induced Phase Transformations, Valery I. Levitas, Arunabhas M. Roy

*Valery I. Levitas*

Thermodynamic Ginzburg-Landau potential for temperature- and stress-induced phase transformations (PTs) between n phases is developed. It describes each of the PTs with a single order parameter without an explicit constraint equation, which allows one to use an analytical solution to calibrate each interface energy, width, and mobility; reproduces the desired PT criteria via instability conditions; introduces interface stresses; and allows for a controlling presence of the third phase at the interface between the two other phases. A finite-element approach is developed and utilized to solve the problem of nanostructure formation for multivariant martensitic PTs. Results are in a quantitative agreement ...

Internal Stresses In Pre-Stressed Micron-Scale Aluminum Core-Shell Particles And Their Improved Reactivity, 2017 Iowa State University

#### Internal Stresses In Pre-Stressed Micron-Scale Aluminum Core-Shell Particles And Their Improved Reactivity, Valery I. Levitas, Jena Mccollum, Michelle L. Pantoya, Nobumichi Tamura

*Valery I. Levitas*

Dilatation of aluminum (Al) core for micron-scale particles covered by alumina (Al_{2}O_{3}) shell was measured utilizing x-ray diffraction with synchrotron radiation for untreated particles and particles after annealing at 573 K and fast quenching at 0.46 K/s. Such a treatment led to the increase in flame rate for Al + CuO composite by 32% and is consistent with theoretical predictions based on the melt-dispersion mechanism of reaction for Al particles. Experimental results confirmed theoretical estimates and proved that the improvement of Al reactivity is due to internal stresses. This opens new ways of controlling particle reactivity ...

Leaky Lamb Waves In An Anisotropic Plate. Ii: Nondestructive Evaluation Of Matrix Cracks In Fiber-Reinforced Composites, 2017 Iowa State University

#### Leaky Lamb Waves In An Anisotropic Plate. Ii: Nondestructive Evaluation Of Matrix Cracks In Fiber-Reinforced Composites, Vinay Dayal, Vikram K. Kinra

*Vinay Dayal*

This paper is concerned with the use of leaky Lamb waves for the nondestructive evaluation (NDE) of damage in anisotropic materials such as fiber-reinforced composites. Two fundamental acoustic properties of the material, namely, the wave speed and attenuation have been measured. Stiffness is deduced from the wave speed. The damage mode selected for this study is matrix cracking. As expected, the in-plane stiffness decreases and the attenuation increases with an increase in the linear crack density.

Modeling Rotation And Curvature Effects Within Scalar Eddy Viscosity Model Framework, 2017 Iowa State University

#### Modeling Rotation And Curvature Effects Within Scalar Eddy Viscosity Model Framework, Paul A. Durbin, Sunil K. Arolla

*Paul A. Durbin*

Two approaches to incorporate the effects of rotation and curvature in scalar eddy viscosity models are explored. One is the “Modified coefficients approach” – to parameterize the model coefficients such that the growth rate of turbulent kinetic energy is suppressed or enhanced. The other is the “Bifurcation approach” – to parameterize the eddy viscosity coefficient such that the equilibrium solution bifurcates from healthy to decaying solution branches. Simple, yet, predictive models in each of these two approaches are proposed and validated on some benchmark test cases characterized by profound effects of system rotation and/or streamline curvature. The results obtained with both ...

Les Of Spatially Developing Turbulent Boundary Layer Over A Concave Surface, 2017 Cornell University

#### Les Of Spatially Developing Turbulent Boundary Layer Over A Concave Surface, Sunil K. Arolla, Paul A. Durbin

*Paul A. Durbin*

We revisit the problem of a spatially developing turbulent boundary layer over a concave surface. Unlike previous investigations, we simulate the combined effects of streamline curvature as well as curvature-induced pressure gradients on the turbulence. Our focus is on investigating the response of the turbulent boundary layer to the sudden onset of curvature and the destabilising influence of concave surface in the presence of pressure gradients. This is of interest for evaluating the turbulence closure models. At the beginning of the curve, the momentum thickness Reynolds number is 1520 and the ratio of the boundary layer thickness to the radius ...

Helical Modes In Boundary Layer Transition, 2017 Iowa State University

#### Helical Modes In Boundary Layer Transition, Rikhi Bose, Paul A. Durbin

*Paul A. Durbin*

Observations are presented to show that in an adverse pressure gradient boundary layer, beneath free-stream turbulence, the interaction between Klebanoff streaks and naturally arising instability waves leads to helical disturbances which break down to form turbulent spots. This occurs under low to moderate levels, 1%–2%, of free-stream turbulence. At high levels of free-stream turbulence, conventional bypass mechanisms are seen. The helical structures are clearly identifiable in visualizations of isosurfaces of streamwise perturbation velocity. A direct numerical simulation also was performed in zero pressure gradient, with a time-periodic Tollmien-Schlichting wave eigenfunction at the inlet. Again, under a moderate level of ...

Aerodynamic Noise Prediction For A Rod-Airfoil Configuration Using Large Eddy Simulations, 2017 Iowa State University

#### Aerodynamic Noise Prediction For A Rod-Airfoil Configuration Using Large Eddy Simulations, Bharat R. Agrawal, Anupam Sharma

*Anupam Sharma*

Aerodynamic noise produced by aerodynamic interaction between a cylinder (rod) and an airfoil in tandem arrangement is investigated using large eddy simulations. Wake from the rod convects with the flow, impinges of the airfoil to produce unsteady force which acts as a sound source. This rod-airfoil interaction problem is a model problem for noise generation due to inflow or upstream-generated turbulence interacting with a turbomachine bladerow or a wind turbine rotor. The OpenFoam and Charles (developed by Cascade Technologies) solvers are chosen to carry out the numerical simulations. The airfoil is set at zero angle of attack for the simulations ...

Numerical Investigations Of Bio-Inspired Blade Designs To Reduce Broadband Noise In Aircraft Engines And Wind Turbines, 2017 Iowa State University

#### Numerical Investigations Of Bio-Inspired Blade Designs To Reduce Broadband Noise In Aircraft Engines And Wind Turbines, Bharat R. Agrawal, Anupam Sharma

*Anupam Sharma*

Simplified representations of the leading edge serrations in owl feathers are modeled numerically to investigate their effectiveness in reducing inflow turbulence noise. The rod wake-airfoil interaction problem is selected for this investigation. Two numerical methods utilizing compressible- and incompressible large eddy simulation techniques are used for the analyses. The methods are first validated against experimental results for the baseline airfoil (no serrations). Good agreement is observed between measurement and predictions for mean surface pressure, near-field velocity spectra, and far-field sound spectra. Two serrated leading edge blade designs are then analyzed for noise. The leading edge serrations are found to give ...

On Predicting The Phenomenon Of Surface Flow Convergence In Wind Farms, 2017 Iowa State University

#### On Predicting The Phenomenon Of Surface Flow Convergence In Wind Farms, Suganthi Selvaraj, Anupam Sharma

*Anupam Sharma*

A systematic analysis of a single-rotor horizontal axis wind turbine aerodynamics is performed to obtain a realistic potential maximum efficiency. It is noted that by including the effects of swirl, viscosity and finite number of blades, the maximum aerodynamic efficiency of a HAWT is within a few percentage points of the efficiency of commercially-available turbines. The need for investigating windfarm (as a unit) aerodynamics is thus highlighted.

An actuator disk model is developed and implemented in the OpenFOAM software suite. The model is validated against 1-D momentum theory, blade element momentum theory, as well as against experimental data. The validated ...

Towards Identifying Contribution Of Wake Turbulence To Inflow Noise From Wind Turbines, 2017 Iowa State University

#### Towards Identifying Contribution Of Wake Turbulence To Inflow Noise From Wind Turbines, Bharat R. Agrawal, Aaron Rosenberg, Anupam Sharma

*Anupam Sharma*

Downstream turbines in a wind farm often operate under the influence of wakes from upstream turbines. Aerodynamic losses and aeromechanical issues (stochastic loads) associated with such wake-turbine interactions have been investigated before. However, the role such interactions play in the generation of aerodynamic noise has not been evaluated. This paper presents a two-step approach for predicting noise due to wake-turbine interaction. The first step involves an aerodynamic analysis of a wind farm using large eddy simulations. Time accurate data and turbulence statistics in the turbine wakes are obtained from this simulation just ahead of the downstream wind turbines. The second ...

Inverse Design Of Horizontal Axis Wind Turbine Blades, 2017 Iowa State University

#### Inverse Design Of Horizontal Axis Wind Turbine Blades, Behnam Moghadassian, Anupam Sharma

*Anupam Sharma*

A method for inverse design of horizontal axis wind turbine (HAWT) is presented in this paper. The direct solver for aerodynamic analysis solves the Reynolds Averaged Navier Stokes (RANS) equations, where the effect of the turbine rotor is modeled as momentum sources using the actuator disk model (ADM).The inverse problem is posed as follows: for a given selection of airfoils, the objective is to find the blade geometry (described as blade twist and chord distributions) which realizes the desired turbine aerodynamic performance at the design point; the desired performance is prescribed as angle of attack (α) and axial induction ...

Pressure Self-Focusing Effect And Novel Methods For Increasing The Maximum Pressure In Traditional And Rotational Diamond Anvil Cells, 2017 Iowa State University

#### Pressure Self-Focusing Effect And Novel Methods For Increasing The Maximum Pressure In Traditional And Rotational Diamond Anvil Cells, Biao Feng, Valery I. Levitas

*Valery I. Levitas*

The main principles of producing a region near the center of a sample, compressed in a diamond anvil cell (DAC), with a very high pressure gradient and, consequently, with high pressure are predicted theoretically. The revealed phenomenon of generating extremely high pressure gradient is called the pressure self-focusing effect. Initial analytical predictions utilized generalization of a simplified equilibrium equation. Then, the results are refined using our recent advanced model for elastoplastic material under high pressures in finite element method (FEM) simulations. The main points in producing the pressure self-focusing effect are to use beveled anvils and reach a very thin ...

Phase Field Approach With Anisotropic Interface Energy And Interface Stresses: Large Strain Formulation, 2017 Iowa State University

#### Phase Field Approach With Anisotropic Interface Energy And Interface Stresses: Large Strain Formulation, Valery I. Levitas, James A. Warren

*Valery I. Levitas*

A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the *deformed* configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the ...

Effects Of Gasket On Coupled Plastic Flow And Strain-Induced Phase Transformations Under High Pressure And Large Torsion In A Rotational Diamond Anvil Cell, 2017 Iowa State University

#### Effects Of Gasket On Coupled Plastic Flow And Strain-Induced Phase Transformations Under High Pressure And Large Torsion In A Rotational Diamond Anvil Cell, Biao Feng, Valery I. Levitas

*Valery I. Levitas*

Combined plastic flow and strain-induced phase transformations (PTs) under high pressure in a sample within a gasket subjected to three dimensional compression and torsion in a rotational diamond anvil cell (RDAC) are studied using a finite element approach. The results are obtained for the weaker, equal-strength, and stronger high-pressure phases in comparison with low-pressure phases. It is found that, due to the strong gasket, the pressure in the sample is relatively homogenous and the geometry of the transformed zones is mostly determined by heterogeneity in plastic flow. For the equal-strength phases, the PT rate is higher than for the weaker ...