living matter lab


spring 16 - me333c - mechanics/continuum mechanics

me333c - continuum mechanics 16

ellen kuhl
rijk de rooij
office hrs thu 2:00-3:00, 520-203

spring 2016
tue thu 10:30-11:50
hewlett 201


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 % final - 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 mar 29 why continuum mechanics? syllabus s01
thu mar 31 introduction to vectors and tensors - tensor algebra 1.1-1.5 1-32 s02
tue apr 05 introduction to vectors and tensors - tensor analysis 1.6-1.9 32-55 s03
thu apr 07 kinematics - motion 2.1-2.3 55-69 s04
tue apr 12 kinematics - deformation gradient 2.4,2.6 70-94 s05
thu apr 14 kinematics - strain 2.5,2.7,2.8 76-108 s05
tue apr 19 concept of stress 3.1-3.4 109-131 s06
thu apr 21 balance principles - mass and momentum 4.1-4.3 131-151 s07
tue apr 26 balance principles - energy and entropy 4.4-4.7 152-179 s08
thu apr 28 aspects of objectivity 5.1-5.4 179-205 s09
tue may 03 hyperelasticity - general remarks 6.1-6.6 205-264 s11
thu may 05 hyperelasticity - isotropy 6.2 212-221 s12
tue may 10 hyperelasticity - incompressibility 6.3,6.4 222-234 s13
thu may 12 hyperelasticity - transverse isotropy 6.7 265-277 s14
tue may 17 instabilities - 1d examples s15
thu may 19 instabilities - 3d examples s16
tue may 24 final prep 1.1-6.7 1-277 s17
thu may 26 final
tue may 31 inelasticity - damage s19
fri jun 03 written projects due

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