living matter lab


me338A - continuum mechanics

me338A - continuum mechanics 09

ellen kuhl, serdar goktepe,
sudarsan acharya

winter 2010
tue thu 11:00-12:15

syllabus and set of notes
students comments


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. towards the end of the quarter, we will illustrate how the three sets of equations will change in nonlinear continuum mechanics. 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 and john for the hands on wet lab related to homework 02


  • 30 % homework - 3 homework assignments, 10% each
  • 40 % midterm - closed book, closed notes, one single page cheat sheet
  • 30 % final project - written evaluation of a manuscript and its discussion in class


day date topic notes slides hw
tue jan 05 tensor calculus I - vector algebra n01 s01
thu jan 07 tensor calculus II - tensor algebra n02 s02
tue jan 12 tensor calculus III - tensor analysis n03 s03
thu jan 14 tensor calculus IV - tensor analysis n04 s04 h01
tue jan 19 kinematics I - motion n05
thu jan 21 kinematics II - strain n06 s06
tue jan 26 balance equations I - contact fluxes n07
thu jan 28 balance equations II - concept of stress n08 s08 h02
tue feb 02 balance equations III - mass, momentum n09 s09
thu feb 04 balance equations IV - angular momentum, energy n10
tue feb 09 balance equations V - entropy, master balance law n11 s11
thu feb 11 constitutive equations I - linear equations n12 s12 h03
tue feb 16 constitutive equations II - hyperelasticity n13 s13
thu feb 18 constitutive equations III - isotropic elasticity n14 s14 project
tue feb 23 midterm prep n15
thu feb 25 midterm
tue mar 02 intro to nonlinear continuum mechanics I - finite strain kinematics n15
thu mar 04 intro to nonlinear continuum mechanics II - stress measures n16
tue mar 09 intro to nonlinear continuum mechanics III - constitutive equations n17
thu mar 11 journal club - final project discussion n18

final project

the final project of this class is the review of a recently published manuscript that introduces a new constitutive model for passive cardiac muscle tissue. if you would like to read more about it and learn how it can be applied to a realistic heart geometry, here is some additional reading material.

holzapfel ga, ogden rw: constitutive modelling of passive myocardium. a structurally-based framework for material characterization, philosophical transactions of the royal society a, 2009;367:3445-3475.

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