Contents |
me338A - continuum mechanics
goals
although the basic concepts of continuum mechanics have been established more than five decades ago, the 21 century faces many new and exciting potential applications of continuum mechanics theories that go way beyond the standard classical theory. when applying continuum mechanics to these challenging new phenomena, it is important to understand the main three ingredients of continuum mechanics: the kinematic equations, the balance equations and the constitutive equations. after a brief repetition of the relevant equations in tensor algebra and analysis, this class will introduce the basic concepts of finite deformation kinematics. within the framework of large deformations, we will then discuss the balance equations for mass, momentum, moment of momentum, energy and entropy. while all these equations are general and valid for any kind of material, the last set of equations, the constitutive equations, specifies particular subclasses of materials. in particular, we will focus on isotropic and anisotropic hyperelasticity and on viscoelasticity and elastodamage. finally, we will briefly address variational principles that characterize the governing equations.
grading
- 50 % homework - 3 homework assignments, 16.7% each
- 30 % midterm - open book, open notes
- 20 % final project - written evaluation of a manuscript and its discussion in class
syllabus
| day | date | topic | notes | hw | |
|---|---|---|---|---|---|
| tue | apr | 01 | introduction - why potatoes? | ||
| thu | apr | 03 | vectors & tensors - vector algebra | ||
| tue | apr | 08 | vectors & tensors - tensor algebra | ||
| thu | apr | 10 | vectors & tensors - tensor analysis | h01 | |
| tue | apr | 15 | kinematics - configurations, deformation | ||
| thu | apr | 17 | kinematics - temporal derivatives | ||
| tue | apr | 22 | kinematics - spatial derivatives | ||
| thu | apr | 24 | kinematics - strain measures | h02 | |
| tue | apr | 29 | balance equations - mass, reynolds' transport theorem | ||
| thu | may | 01 | balance equations - momentum, concept of stress | ||
| tue | may | 06 | balance equations - moment of momentum, energy | ||
| thu | may | 08 | balance equations - entropy, master balance law | h03 | |
| tue | may | 13 | constitutive equations - hyperelasticity, isotropic | ||
| thu | may | 15 | constitutive equations - hyperelasticity, anisotropic | ||
| tue | may | 20 | midterm | ||
| thu | may | 22 | constitutive equations - viscoelasticity | ||
| tue | may | 27 | constitutive equations - elastodamage | ||
| thu | may | 29 | variational principles - virtual work | ||
| tue | jun | 03 | journal club - final project discussion |
suggested reading
holzapfel ga: nonlinear solid mechanics, a continuum approach for engineering, john wiley & sons, 2000
murnaghan fd: finite deformation of an elastic solid, john wiley & sons, 1951
eringen ac: nonlinear theory of continuous media, mc graw-hill, 1962
truesdell c, noll, w: the non-linear field theories of mechaics, springer, 1965
eringen ac: mechanics of continua, john wiley & sons, 1967
chadwick p: continuum mechanics - concise theory and problems, dover, 1976
maugin ga: the thermodynamics of plasticity and fracture, cambridge university press, 1992
robers aj: one-dimensional introduction to continuum mechanics, world scientific, 1994
bonet j, wood rd: nonlinear continuum mechanics for finite element analysis, cambridge university press, 1997
silhavy m: the mechanics and thermodynamics of continuous media, springer, 1997
haupt p: continuum mechanics and theory of materials, springer, 2000
podio-guidugli p: a primer in elasticity, kluwer academic pres, 200
liu is: continuum mechanics, springer, 2002