me338A - continuum mechanics 09

ellen kuhl, serdar goktepe, fawad muzaffar, olivier lacroix winter 2009 tue thu 11:00-12:15 530-127 syllabus and set of notes

goals

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

grading

• 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

syllabus

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

...