Contents |
me338A - continuum mechanics
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ellen kuhl,
serdar goktepe, winter 2009 syllabus and set of notes |
goals
although the basic concepts of continuum mechanics have been established more than five decades ago, the 21st century faces many new and exciting potential applications of continuum mechanics 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 small strain 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. finally, we will briefly address variational principles that characterize the governing equations.
kinematics of the human heart
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grading
- 30 % homework - 3 homework assignments, 10% each
- 40 % midterm - closed book, closed notes, one single letter format page of notes
- 30 % final project - written evaluation of a manuscript and its discussion in class
syllabus
| day | date | topic | notes | hw | |
|---|---|---|---|---|---|
| tue | jan | 06 | tensor calculus I - vector algebra | n01 | |
| thu | jan | 08 | tensor calculus II - tensor algebra | n02 | |
| tue | jan | 13 | tensor calculus III - tensor analysis | n03 | |
| thu | jan | 15 | tensor calculus IV - tensor analysis | n04 | |
| tue | jan | 20 | kinematics I - motion | n05 | h01 |
| thu | jan | 22 | kinematics II - strain | n06 | |
| tue | jan | 27 | balance equations I - contact fluxes | n07 | |
| thu | jan | 29 | balance equations II - concept of stress | n08 | h02 |
| tue | feb | 03 | balance equations III - mass, momentum | n09 | |
| thu | feb | 05 | balance equations IV - angular momentum, energy | n10 | |
| tue | feb | 10 | balance equations V - entropy, master balance law | n11 | h03 |
| thu | feb | 12 | constitutive equations I - linear equations | n12 | |
| tue | feb | 17 | constitutive equations II - hyperelasticity | n13 | |
| thu | feb | 19 | constitutive equations III - isotropic elasticity | n14 | project |
| tue | feb | 24 | midterm prep | ||
| thu | feb | 26 | midterm | ||
| tue | mar | 03 | intro nonlinear continuum mechanics - finite strain kinematics | ||
| thu | mar | 05 | intro nonlinear continuum mechanics - stress measures | ||
| tue | mar | 10 | intro nonlinear continuum mechanics - constitutive equations | ||
| thu | mar | 12 | journal club - final project discussion |
final project
here's last year's final project, a paper review of your choice, you can choose between rubber mechanics, biomechanics, geomechanics and growth mechanics
(1) boyce mc, arruda em: constitutive models of rubber elasticity: a review, rubber chemistry and technology 73, 504-533, 2000
(2) holzapfel ga: biomechanics of soft tissues, in: handbook of material behavior, academic press, 2000
(3) jeremic b, runesson k, sture s: finite deformation analysis of geomaterials, international journal for numerical and analytical methods in geomechanics 25, 809-840, 2001
(4) rodriguez ek, hoger a, mc culloch ad: stress-dependent finite growth in soft elastic tissues, journal of biomechanics 27, 455-467, 1994
suggested reading
... this is the book we will use in class...
holzapfel ga: nonlinear solid mechanics, a continuum approach for engineering, john wiley & sons, 2000
... and here are some other cool books for additional reading...
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 mechanics, springer, 1965
eringen ac: mechanics of continua, john wiley & sons, 1967
malvern le: introduction to the mechanics of a continuous medium, prentice hall, 1969
oden jt: finite elements of nonlinear continua, dover reprint, 1972
chadwick p: continuum mechanics - concise theory and problems, dover reprint, 1976
ogden, rw: non-linear elastic deformations, dover reprint, 1984
maugin ga: the thermodynamics of plasticity and fracture, cambridge university press, 1992
spencer ajm: continuum mechanics, dover reprint, 1992
robers aj: one-dimensional introduction to continuum mechanics, world scientific, 1994
bonet j, wood rd: nonlinear continuum mechanics for fe 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 press, 2000
liu is: continuum mechanics, springer, 2002
reddy jn: an introduction to continuum mechanics, cambridge university press, 2007