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Course Criteria
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3.00 Credits
Prerequisite(s): Background equivalent to MEAM 519 and ENM 510. Linear elastic analysis of bodies with cracks. Energy balance criterion for crack growth and stability. Analysis of cracks in elastic-plastic and rate-dependent materials. J integral and applications to crack growth and stability. Large- scale yielding and dynamic fracture. Interface fracture.
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3.00 Credits
Prerequisite(s): First-year graduate-level applied mathematics for engineers (ENM 510 and 511) and a first course in continuum mechanics or elasticity or permission of instructor. This course is intended for 2nd year graduate students and introduces continuum mechanics theory of rods and shells with applications to structures and to biological systems as well as stability and buckling. The course begins with topics from differential geometry of curves and surfaces and the associated tensor analysis on Riemannian spaces. A brief introduction to variational calculus is included since variational methods are a powerful tool for formulating approximate structural mechanics theories and for numerical analysis. The structural mechanics theories of rods, plates and shells are introduced including both linear and nonlinear theories.
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3.00 Credits
Prerequisite(s): ENM 510. Corequisite(s): ENM 511. This course deals with the prediction of the average, or effective properties of composite materials. The emphasis will be on methods for determining effective behavior. The course will be concerned mostly with linear mechanical and physical properties, with particular emphasis on the effective conductivity and elastic moduli of multi-phase composites and polycrystals. However, time-dependent and non-linear properties will also be discussed.
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3.00 Credits
Fluid mechanics as a vector field theory; basic conservation laws, constitutive relations, boundary conditions, Bernoulli theorems, vorticity theorems, potential flow. Viscous flow; large Reynolds number limit; boundary layers.
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3.00 Credits
Waves, one-dimensional gas dynamics. Transition, turbulence. Small Reynolds number limit: Stokes' flow. Compressible potential flow. Method of characteristics. Rotating flows. Stratified flows. Jets.
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3.00 Credits
Role of transport processes in biological systems; Detailed review of Fluid Mechanics, Heat transfer and Mass transfer to enable a study of BioTransport; Cardiovascular system; Respiratory system; Rheology of Blood; Approximate methods for the analysis of complex physiological flows; Detailed treatment of blood flow in vessels; Mass transport in biological systems; Transport in porous media; Transport of gases between blood and tissues; Introduction to Bioheat transfer.
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3.00 Credits
Gas kinetic theory: Boltzmann equation. H-theorem, equilibrium solutions, transport coefficients. Rarified gas dynamics, methods of approximate solution to Boltzmann equation. Continuum limit: Navier-Stokes equations.
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3.00 Credits
Prerequisite(s): ENM 510, ENM 511, and one graduate level introductory course in mechanics. FORTRAN or C programming experience is necessary. The course is divided into two parts. The course first introduces general numerical techniques for elliptical partial differential equations - finite difference method, finite element method and spectral method. The second part of the course introduces finite volume method. SIMPLER formulation for the Navier-Stokes equations will be fully described in the class. Students will be given chances to modify a program specially written for this course to solve some practical problems in heat transfer and fluid flows.
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3.00 Credits
Prerequisite(s): ENM 510, MEAM 530 or MEAM 570, or permission of the instructor. Complex fluids are a broad class of materials. They are usually homogeneous at the macroscopic scale and disordered at the microscopic scale, but possess structure at an intermediate scale. The macroscopic behavior of these fluids is controlled by the fluid intermediate scale. This course will cover the basic concepts of structure, dynamics, and flow properties of polymers, colloids, liquid crystals, and other substances with both liquid and solid-like characteristics. Both the experimental and theoretical aspects of rheology will be discussed. The basic forces influencing complex fluid rheology will be outlined and discussed. These include van der Waals, electrostatic, excluded volume and other interactions. Methods for characterizing structure will be covered including scattering techniques, optical microscopy. Examples will focus on several types of complex fluids such as polymeric solutions and melts, emulsions & foams, gelling systems, suspensions and self-assembling fluids.
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3.00 Credits
Why and what to model: Complex lattice structures, structures of lattice defects, crystal surfaces, interfaces, liquids, linking structural studies with experimental observations, computer experiments. Methods: Molecular statics, molecular dynamics, Monte Carlo. Evaluation of physical quantities employing averages, fluctuations, correlations, autocorrelations, radial distribution function, etc. Total energy and interatomic forces: Local density functional theory and abinitio electronic structure calculations, tight-binding methods, empirical potentials for metals, semiconductors and ionic crystals.
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