Case studies in failure analysis of mechanical components. Basic concepts of stress and strain; Mohr's circle, principal stresses and strains, Elasticity (elastic deformation, generalized Hooke's law, basic equations of elasticity for plane elasticity problems; elastic constants and their relations; strain energy, membrane stresses in thin and thick cylinders and simple shells, thin walled pressure vessels), torsion (torsion of circular shaft, close coiled helical springs; torsion of thin walled open and closed sections and non-circular sections). Bending Moment and Shearing Force (definitions and conventions, shear and moment equations, bending moment and shearing force diagrams), classical beam theory (bending stresses in beams; various cross-sectional shapes of beams; shear stresses in beams; unsymmetrical bending and shear center; deflection of beams; double integration of governing differential equation), strain energy methods (Castigliano's theorem, applications). Introduction to failure in mechanical design and basic concepts of reliability; Structure of common engineering materials, their classification based on bonding, influence of structure on mechanical properties.Classes of failure: plasticity (stress-strain curve, mathematical descriptions of elasticity and plasticity, yield criteria, constitutive properties), visco-elasticity (stress-strain response of polymers, frequency and temperature dependence, Maxwell and Voigt models, storage and loss moduli, time-temperature superposition), fracture (Griffith analysis, stress intensity factor, energy release rate, leak-before-break, cyclic crack growth), Fatigue, creep, design for surface integrity (Engineering models for wear, design guidelines for wear). Laboratory consisting of experiments on solid mechanics and materials failure in ductile and brittle materials; impact; fracture and creep testing.
Case studies in thermal and fluid analysis. Fundamentals of Thermodynamics - System & Control volume, Property, State & Process, Exact & Inexact differentials; Work - Thermodynamic definition of work; examples, Displacement work, Path dependence of displacement work and illustrations for simple processes, Fully resisted, partially resisted and unresisted process, Definition of thermal equilibrium, Zeroth law, Definition of temperature and temperature scales, Heat - Definition; examples of heat/work interaction in systems. First Law - Cyclic & Non-cyclic processes, Enthalpy and internal energy; Second law - Definitions of direct and reverse heat engines - Definitions of thermal efficiency and COP, Kelvin-Planck and Clausius statements, Definition of reversible process, Internal and external irreversibilities, Carnot cycle, Absolute temperature scale; Entropy - Clausius inequality, Definition of entropy S Description of fluid motion: Kinematics. Conservation of mass, momentum and energy. Balance laws Constitutive equations; Navier -Stokes equations; Solutions in simple flows Hydrostatics Introduction and Classification of Fluid Machines. Analysis of Turbo machinery flows. Performance characteristics of turbo machines. Introduction to CFD. Heat Transfer: Conduction. General Conduction Equation. One dimensional Steady state conduction- Fins and Extended Surfaces. Transient conduction of lumped and distributed systems. Convection: Boundary Layers, dimensionless group for convection. Forced Convection. Laminar flow in a pipe. flow over cylinders, spheres. Elements of free convection. Turbulent flow in pipes. Introduction to the analysis of heat exchangers. Elements of Radiative Heat Transfer. Laboratory experiments to include aspects of flow control and measurement, material property measurement, pneumatics and hydraulics. CFD laboratory.
Types of microstructure and associated length scales. Microstructure sensitive material properties. Discussion of the experimental evidence of length scale effects. Evolution of microstructure. Driving forces for microstructure evolution. Continuum models and constitutive equations. Incorporation of length scales in continuum models through regularization. Strain gradient theories. Phase field models: variational formulation, continuum mechanical formulation, constitutive equations, multiphase field models, thermal, stress and diffusion effects. Monte Carlo-Potts models. Discrete lattice approaches. Molecular dynamics. Introduction to multiscale modeling. Concurrent multiscale models. Problems of handshaking. Simple one dimensional concurrent models. Sequential multiscale models. Homogenization. Transferring constitutive information across length scales.