TAM 445: Continuum Mechanics

Class Description:

Tensor algebra and analysis; kinematics of continua; mass, force, stress, and the general balance laws of continuum mechanics; introduction to constitutive equations. Theoretical and Applied Mechanics students will not receive graduate credit for this course, except by petition to the Graduate Program Committee. Prerequisite: TAM 251. 4 undergraduate or 4 graduate hours.

Topics:

Tensor algebra and analysis (26 hr)
Indicial notation, determinants, matrices; vectors, change of coordinate frame, scalar products; second-order tensors; higher-order tensors, vector products; principal directions of symmetric second-order tensors; positive-definite tensors, tensor square roots, polar decompositions; tensor fields; theorems from advanced calculus.

Kinematics (12 hr)
Bodies, deformations, displacements; rigid deformations; volume-preserving deformations; the geometry of general deformations, strain; motions; rate of deformation and vorticity; the transport and localization theorems

Balance laws (12 hr)
Conservation of mass; Cauchy|#39;s stress principle and Euler|#39;s laws; virtual power; the stress tensor; Cauchy|#39;s stress equations of motion; some properties of the stress tensor

Introduction to constitutive equations (8 hr)
Inviscid fluids, Newtonian fluids, elastic solids

Examinations and review (2 hr)
TOTAL HOURS: 60

 

ME:  MechSE or technical elective.

EM:  Required.

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ME

TAM