me338A - continuum mechanics 09

ellen kuhl, serdar goktepe, sudarsan acharya winter 2010 tue thu 11:00-12:15 530-127 syllabus and set of notes students comments

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. 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

grading

• 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

syllabus

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

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