Offered Every Fall

Credit Hours: 3-0-3
Prerequisites: Introduction to partial differential equations and vector mathematics desirable (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.
Textbooks: Lawrence E. Malvern, Introduction to the Mechanics of a Continuous Medium, 1st Edition Prentice-Hall, 1997.
Instructors: Chris Lynch, David McDowell, Richard Neu, Jianmin Qu, Min Zhou
References: IDEAS Masters Series, Student Guide.
Goals: To provide knowledge of the fundamental, unifying concepts of the mechanics of continua as a core course for graduate study in Mechanical Engineering.
  • 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.
Grading Scheme (%):



Midterm Examination


Final Examination