University of Pennsylvania
School of Engineering and Applied Science
BE & MEAM 455
Continuum Biomechanics
Dr. Dennis Discher / Dr. Susan Margulies
8-4809 / 8-0882
discher@eniac / margulie@eniac
 
Fall  2000
                                                   Lectures:    Tu Th 12 - 1:30,  321 Towne Bldg
                                         Recitation:  Fri  2 - 3,  309 Towne Bldg
                                                                                        Off Hrs:      Margulies TuW 3-4;   Discher (open door 112 Towne)
                                                                    Laboratory:  to begin in Nov and held in LRSM Rm. 13A

Announcements

FRIDAY RECITATIONS require attendance.
Please keep up with regular  Problem Sets  and  Numerical Problem Sets!
Midterm Exam is  Thurs., OCT.19.
 

Handouts

Homework

Course Description  -  Lecture, Experiments, Computation

    Biological and non-biological systems are both subject to several basic physical balance laws of broad engineering importance.
Fundamental conservation laws are introduced and illustrated using examples from animate as well as inanimate systems.  Topics
include kinematics of deformation, the concept of stress, conservation of mass, momentum, and energy. Mechanical constitutive
equations for fluids, solids, and intermediate types of media are described and complemented by hands-on experimental and
computational laboratory experiences.  Practical problem-solving using numerical methods will be introduced.
    A lecture and topics course for senior and exceptional junior undergraduate students in Bioengineering and Mechanical Engineering.
Course enrollment is limited to 30 students.

Prerequisite coursework:  Statics, linear algebra, and differential equations.

Required Texts:
   YC Fung, A First Course in Continuum Mechanics, 3rd Ed.Prentice Hall, 1994.
   YC Fung, Biomechanics: Mechanical Properties of Living Tissues  2nd Ed.Springer- Verlag, 1993.

Supplemental Texts (on reserve in Towne Library):
   YC Fung, Biomechanics: Motion, Flow Stress and Growth
   YC Fung, Foundations in Solid Mechanics
   Atkins and Fox, An Introduction to the Theory of Elasticity

Course Schedule

week 1 - Continuum Notions & Boundary Value Problems;  Tensors

week 2 -  Coordinate Systems and Transformations;  Stress;  Equations of Motion

week 3 - Plane stress & Principal Stress;  Thick-walled cylinder (aorta) & Boundary Stress;  Failure criteria

week 4 - Deformation & Strain;  Strain Measurement;  Principal Strain

week 5 - Examples of Strain;  Constitutive Descriptions: Elasticity via Microscopic Models

EXAM   -  Stress, Strain, and Tensors

week 6 - More Linear Elasticity;  Intro. to Inelastic Phenomena

week 7 - Viscoelasticity, Dissipative Models, Pre-conditioning, Poroelasticity

week 8 - Fluids, Biofluids, & Molecular Ideas;  Conservation of mass, momentum and energy

week 9 - Laboratory:  Uniaxial tests chicken skin & muscle, and synthetic elastomers

week 10 - Differential Eqn. forms of conservation laws;  a simple example with body force integration

week 11 - Practical Intro. to Finite Differences, Methods I, II;  Computational Module I - Elastic Solid

week 12 - Practical Intro. to Finite Elements & Minimiz'n., Method III;  Module II - Soap Film

THANKSGIVING

week 13 - Module III - Fluid Flow;  Heart / Thick-walled Sphere under Pressure

week 14 - Problems in Fluid Mechanics;  Remodeling, Growth, & Active Materials

FINAL
 

Grading
Problem Sets         20%
Laboratory             20%
Single Midterm      30%
Final Paper/Exam  30%

Instructors Office Hours:

Handouts

• Notes on CARTESIAN TENSORS:
 
Page 1
Page 5
Page 9
Page 13
Page 2
Page 6
Page 10
Page 14
Page 3
Page 7
Page 11
 
Page 4
Page 8
Page 12
 
 
• Transformation of Stress Components from Rectangular Cartersian Coordinates to Cylindrical Coordinates

• Deformation of a unit square

• Data for pre-lab PS#7

• Numerical Methods and Modules
Introduction
Methods I & II
Method IIIA
Method IIIB
Module I
Module II
Module III
 
HOMEWORK:  NumPS#1 - 7  as  indicated in Numerical Methods Introduction.
 
A complete listing of the campus public (meaning open to all Penn students) labs is at
http://www.upenn.edu/computing/view/labs/lablist.html
Note the link on that page to College House Computing Labs, which are located in the residences across campus.

Homework

Homework: [generally assigned Tuesdays and due Thursday of the next week (9 days)]

Problem Set #1             due Thursday Sept. 14
 
Problem Set #2             due Thursday, Sept. 21

Problem Set #3             due Thursday, Sept. 28

Problem Set #4             not to be turned in!!

Problem Set #5            due Thursday, Oct. 5

Problem Set #6            due Tuesday, Oct. 17
 
Extra Credit Problem Supplement    due Friday, Dec. 11

Problem Set #7            see Lab Manual;   due Thursday, Oct. 27
 
Problem Set #8            due Thursday, Nov. 9

Problem Set #9            due Wednesday, Nov. 22
 

+ NumPS#1 - 7  as  indicated in Numerical Methods Handout.
 
 

Homework Solutions:

Can only be found in Towne Library.
They are copyrighted material and cannot be posted on the web.
 

Exams and Quizzes

 
Exam Dates:
Exam 1 is tentatively scheduled Oct. 19  to cover Tensors, Stress, Eqns of Motion, & Strain
 
 

Links

Newsgroup
CETS
Course Laboratory
SEAS
University of Pennsylvania Library System
 

Created: Sept. 1, 1998
Last Update: Nov. 5,1998

All rights reserved; 1998 University of Pennsylvania