ME 6201: Principles of Continuum Mechanics

ME 6201: Principles of Continuum Mechanics
Offered Every Fall

Credit Hours:	3-0-3
Prerequisites:	MATH 4581 or equivalent; or with the consent of the instructor
Catalog Description:	Introductory treatment of the fundamental, unifying concepts of the mechanics of continua.
Textbook:	Lawrence E. Malvern, Introduction to the Mechanics of a Continuous Medium, 1st Edition Prentice-Hall, 1997.
Instructors:	Iwona Jasiuk, Chris Lynch, David McDowell (Fall 2003), Richard Neu, Jianmin Qu (Fall 2004), Min Zhou

Goal:

To provide knowledge of the fundamental, unifying concepts of the mechanics of continua as a core course for graduate study in Mechanical Engineering.

Topics

Fundamentals of Tensors, Tensor Derivatives, Green-Gauss Theorem
Definition of Strain, Eulerian and Lagrangian Coordinate Systems, Stretch and Rotation, Rate of Deformation, Principal Strain, Compatibility.
Definition of Stress, Cauchy and Nominal Stresses, Balance of Linear and Angular Momentum, Principal Stresses, Deviatoric and Hydrostatic Stress.
First and Second Laws of Thermodynamics for a Continuum, Coupled Thermomechanics, Boundary Conditions, Fundamental Restrictions on Constitutive Laws.
Fundamentals of Elastic Behavior of Solids, Material Symmetries, Variational Principles. Linear and Nonlinear Elasticity.
Fundamentals of Fluids, Newtonian Fluids and Navier-Stokes Equations, Ideal and Rotational Flows, Laminar and Turbulent Flow.
Some Aspects of Inelastic Behavior of Solids and Non-Newtonian Fluids.

Audience: First year graduate students.

Prereq: Introduction to partial differential equations and vector mathematics desirable. Graduate standing or consent of instructor.

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Revised June 2004