living matter lab


me338 - continuum mechanics

me338 - continuum mechanics 12

ellen kuhl
manuel rausch, alex zollner

fall 2012
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 critical to understand the main three ingredients of continuum mechanics: the kinematic equations, the balance equations and the constitutive equations. after a brief summary of the relevant equations in tensor algebra and analysis, we will introduce the basic concepts of finite strain kinematics. we will then discuss the concept of stress, followed by 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. we will discuss constitutive equations for hyperelastic materials, both isotropic and anisotropic, and for inelastic materials with internal variables. last, we will address these considerations in the context of variational principles.

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
  • 50 % midterm - closed book, closed notes, one single page cheat sheet
  • 20 % final project - written evaluation of a manuscript and its discussion in class


... this is the book we will use in class...
holzapfel ga: nonlinear solid mechanics, a continuum approach for engineering, john wiley & sons, 2000

day date topic chapters pages notes
tue sep 25 why continuum mechanics? s01
thu sep 27 introduction to vectors and tensors 1.1-1.5 1-32 s02
tue oct 02 introduction to vectors and tensors 1.6-1.9 32-55 s03,h01
thu oct 04 kinematics 2.1-2.4 55-76 s04
tue oct 09 kinematics 2.5-2.8 76-109 s05
thu oct 11 concept of stress 3.1-3.4 109-131 s06
tue oct 16 balance principles 4.1-4.4 131-161 s07,h02
thu oct 18 balance principles 4.5-4.7 161-179 s08
tue oct 23 aspects of objectivity 5.1-5.4 179-205 s09
thu oct 25 hyperelastic materials 6.1-6.2 205-222 s10
tue oct 30 hyperelastic materials 6.3-6.5 222-252 s11,h03
thu nov 01 hyperelastic materials 6.6-6.8 252-278 s12
tue nov 06 hyperelastic materials 6.9-6.11 278-305 s13
thu nov 08 thermodynamics of materials 7.1-7.6 305-337 s14
tue nov 13 midterm prep s15
thu nov 15 midterm
tue nov 27 thermodynamics of materials 7.7-7.9 337-371 s17
thu nov 29 concept of internal variables 6.9-6.11 285-304 s18
tue dec 04 mixture theory s19
thu dec 06 no class h04

final project

the final project of later year's class was 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

... 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