living matter lab


me338A - continuum mechanics

me338A - continuum mechanics 09

ellen kuhl, serdar goktepe,
fawad muzaffar, olivier lacroix

winter 2009
tue thu 11:00-12:15

syllabus and set of notes


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. 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. throughout this class, we will discuss the mechanics of the heart with its strains, fiber stretches, stresses, forces, and constitutive equations, to illustrate how continuum mechanics can be applied to relevant clinical problems.

continuum mechanics of the heart

special thanks to wolf, john, and neil for the hands on wet lab as introduction to homework 02


  • 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


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
tue feb 03 balance equations III - mass, momentum n09 h02
thu feb 05 balance equations IV - angular momentum, energy n10
tue feb 10 balance equations V - entropy, master balance law n11
thu feb 12 constitutive equations I - linear equations n12
tue feb 17 constitutive equations II - hyperelasticity n13 h03
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 n15
thu mar 05 intro nonlinear continuum mechanics - stress measures n16
tue mar 10 intro nonlinear continuum mechanics - constitutive equations n17
thu mar 12 journal club - final project discussion n18

final project

the final project of this class is the review of a recently submitted manuscript that introduces a new constitutive model for passive cardiac muscle tissue

holzapfel ga, ogden rw: constitutive modelling of passive myocardium. a structurally-based framework for material characterization, philosophical transactions of the royal society a, accepted for publication, 2009

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