living matter lab


me338A - continuum mechanics

me338A - continuum mechanics

ellen kuhl, serdar goktepe, gilwoo choi

spring 2008
tue thu 11:00-12:15, 530-127
office hours tue 1:00-2:00, durand 203


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 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.


  • 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


day date topic notes hw
tue apr 01 introduction - why potatos? n01
thu apr 03 vectors & tensors - vector algebra n02
tue apr 08 vectors & tensors - tensor algebra n03 h01
thu apr 10 vectors & tensors - tensor analysis n04
tue apr 15 kinematics - configurations, deformation n05
thu apr 17 kinematics - temporal derivatives n06 h01 solution
tue apr 22 kinematics - spatial derivatives n07 h02
thu apr 24 kinematics - strain measures n08
tue apr 29 kinematics - examples, midterm evaluation n09 evaluation
thu may 01 balance equations - concept of stress n10 h02 due
tue may 06 balance equations - mass, momentum n11 h03
thu may 08 balance equations - energy, entropy, master balance law n12
tue may 13 constitutive equations - 2nd law, objectivity, symmetry n13
thu may 15 constitutive equations - isotropic elasticity n14 h03 solution
tue may 20 midterm project
thu may 22 constitutive equations - iterative computation of stress-stretch response n15
tue may 27 constitutive equations - nearly and strictly incompressible elasticity n16
thu may 29 constitutive equations - transversely isotropic elasticity n17
tue jun 03 journal club - final project discussion

final project

the final project is 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