living matter lab


spring 17 - me333c - mechanics/continuum mechanics

me333c - continuum mechanics 17

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

spring 2017
tue thu 10:30-11:50


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 apr 04 why continuum mechanics? syllabus s01
thu apr 06 introduction to vectors and tensors - tensor algebra 1.1-1.5 1-32 s02
tue apr 11 introduction to vectors and tensors - tensor analysis 1.6-1.9 32-55 s03
thu apr 13 kinematics - motion 2.1-2.3 55-69 s04
tue apr 18 kinematics - deformation gradient 2.4,2.6 70-94 s05
thu apr 20 kinematics - strain 2.5,2.7,2.8 76-108 s05
tue apr 25 concept of stress 3.1-3.4 109-131 s06
thu apr 27 balance principles - mass and momentum 4.1-4.3 131-151 s07
tue may 02 balance principles - energy and entropy 4.4-4.7 152-179 s08
thu may 04 aspects of objectivity 5.1-5.4 179-205 s09
tue may 09 hyperelasticity - general remarks 6.1-6.6 205-264 s11
thu may 11 hyperelasticity - isotropy 6.2 212-221 s12
tue may 16 hyperelasticity - incompressibility 6.3,6.4 222-234 s13
thu may 18 hyperelasticity - examples 6.5 235-251 s14
tue may 23 hyperelasticity - transverse isotropy 6.7 265-277 s15
thu may 25 final prep 1.1-6.11 1-304 s16
tue may 30 inelasticity - viscoelasticity 6.9, 6.11 282-294 s17
thu jun 01 final
tue jun 06 inelasticity - damage 6.9, 6.11 278-304 s19
fri jun 09 written projects due

final project

the final project of later year's class was the review of a recently published manuscript that discusses constitutive models for ultrasoft materials. if you would like to read more about it, here is some additional reading material.

mihai la, chin l, janmey pa, goriely a. a comparison of hyperelastic constitutive models applicable to brain and fat tissues. journal of the royal society interface, 2015;12:20150486.

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