Prerequisites: IT graduate or upper division student, MATH 2243 or equiv., AEM 3031 or equiv.

Concepts that are common to all continuous media. Elements of tensor analysis. Motion, deformation, and vorticity. Material derivatives. Mass and the continuity equation. Balance of linear and angular momentum. Stress and its geometric characterization. Need for constitutive equations.

Textbook: Optional: Continuum Mechanics, Chadwick, Dover, 486401804; An Introduction to Continuum Mechanics, Reddy, Cambridge, 9780521870443; Nonlinear Solid Mechanics, Holzapfel, Wiley, 471823198; Introduction to the Mechanics, Malvern, Prentice, 134876032

Summary

This course is aimed at first year graduate students and undergraduates planning on continuing in graduate school in fluid or solid mechanics. This course relies heavily on linear algebra and differential calculus.

Continuum mechanics is the mathematical and physical foundation of all models of deformable materials. This includes both fluids and solids. This course starts with an introduction to Cartesian tensors and indicial notation. It then covers the three main parts of field theories in mechanics in turn: kinematics, conservation laws and constitutive theory. Kinematics is the study of deformations and the strains, stretches and rotations involved, in particular, the various non-linear stretch and strain measures are introduced. The conservation laws covered are mass, linear momentum, angular momentum and to a lesser extent, energy. These laws are introduced in their natural global forms and then are localized to differential equations. The concept of stress is introduced during this process for the conservation of linear momentum law. Constitutive equations for simple fluids and elastic solids are discussed along with the concepts of observer independence and material symmetry. Finally, simple boundary value problems are solved using these materials as examples.

Grading is based on homework assignments and two exams during the semester.