Prerequisites: IT upper division or graduate student, MATH 2373 or equiv., MATH 2374 or equiv., AEM 3031

Modern topics in solid and continuum mechanics. Continuum mechanics in one dimension: kinematics, balances of mass, momentum and energy, constitutive theory. Applications to linear and nonlinear wave propagation, and heat conduction in bars. Strings. Euler-Bernoulli theory of bending in beams. Elementary kinematics of three-dimensional deformations and stress: principle strains and stresses. Various topics in solid mechanics typically chosen from: fracture mechanics, structural stability, vibrations, mechanical behavior of thin films and layered media, behavior of smart materials, mechanics of phase transformations, three-dimensional elastic wave propagation, introductory elasticity, viscoelasticity, plasticity.

Summary

This course is aimed at seniors who may be interested in graduate school and first year graduate students. This course math intensive.

Continuum mechanics provides a mathematical framework for studying the behavior of materials. We start with a description of the kinematics of a material, i.e., deformations, strains and velocities. We then introduce the balances of mass, momentum and energy, including stress, internal energy and heat flux. Finally constitutive behavior describing the connection betweeen these quantities and the kinematics are introduced.

The focus in this class is on the physical basis of continuum mechanics without introducing some advanced mathematical concepts, and so much of the work is done in one spatial dimension. Applications in one-dimension include linear and nonlinear wave propagation, heat conduction in bars and Euler-Bernoulli theory of bending in beams. Some elementary topics in three-dimensional continuum mechanics are then discussed. Examples of the successes of continuum mechanics, including smart materials, liquid crystals, phase transformations, elasticity and plasticity, are presented.

The grade is based on homework assignments and exams.