me338 - continuum mechanics 12

ellen kuhl manuel rausch, alex zollner fall 2012 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 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

grading

• 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

syllabus

... 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

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