Continuum Phenomena in Biomedical Engineering

Syllabus – Intro_Continuum_Course_Outline_F18_v5

Reading – Coefficient of Variation and Sensitivity in Modeling (Cook et al., 2014) – Cook_sensitivity_analysis_review_2014_with_highlights

Handout – What is a continuum? – Definition_of_a_Continuum

Lecture 1: Pressure, temperature, candy, and bone

Lecture 2: Sensitivity analysis and introduction to vectors

Homework 1 – Due 11:59 pm 8/31/2018 – HW1

Homework 1 Solution – F18_HW1_Solution

Lecture 3: Vectors and one particular differential operator (“Del” as opposed to “Del the Funky Homosapien”)

Some important vector papers – Hui_Sher_Bone_Fluid_Conductance_1996Kang_FRAP_Coefficients_small_2012,

Lecture 4: Introduction to Tensors. Just enough to get us going.

Homework 2 – F18_HW02

Homework 2 Solution – HW02_Solution_Updated

Lecture 5: Introduction to Motion and Mappings

Lecture 6: The Deformation Gradient and Balance of Mass

Solution to Homework 6!!: F18_HW06_Solutions

Homework 3: This one will take a little time F18_HW03

Homework 3 Solution – F18_HW03_Solution

Lecture 7: Stress

Lecture 8: Balance of Linear Momentum and a little angular momentum too.

Homework 4: Lots of stress – F18_HW04

Homework 4: Solution – F18_HW04_Solution

Lecture 9: Introduction to Fluid Flow

Fluids Handout – Biofluids_Worksheets_v2

Lecture 10: Classic Fluid Problems in Cartesian Coordinates

Homework 5: Fluids – F18_HW05

Homework 5: Solution – F18_HW05_Solution

Lecture 11: Fluids in Polar Coordinates

Lecture 12: Fluids, constitutive laws, and non-dimensionalization

Homework 6: F18_HW06

Homework 6 Solution (part 1): F18_HW06_Solutions_part_1

Homework 6 Solution (part 2): F18_HW06_Solutions_part_2

Lecture 13: Dimensional Analysis vs. Non-Dimensionalization

Lecture 14: Introduction to Solid Mechanics

Lecture 15: Solid Mechanics and the Archetypal Motions

Lecture 16: Constitutive Laws

Homework 7: F18_HW07

Data for homework 7: bc_mcl_data

Lecture 17: Solid Mechanics – Error measures, determining material constants, and the difference between the stress tensor, traction vector, and resultant force. Pretty good day!

Great resource for solid mechanics. One of the best thesis theory sections ever: Galle_chapter_3_scanned

Designing a sensor to measure compression and shear and high strains!!

Lecture 18: Intro to the sensor

Lecture 19: Working out the math

Lecture 20: Introduction to viscoelasticity

Lecture 21: Applying viscoelastic models correctly! 

The Pioletti paper: Pioletti_strain_rate_effect_1999

Solution to the Spherical Tensor Problem: Spherical_Tensor_Solution

Homework 8: F18_HW08

Homework 9: F18_HW09

Partial Solution to Homework 9: F18_HW09_Problems_1_3_Solution

Lecture 22 – Constitutive Laws

Lecture 23 – Diffusion Equation

Lecture 24 – Wave Equation

Lecture 25 – Laplace Equation

Exam 3 covers all the strain energy work – up through lecture 22. Lecture 25 was just a review of the concepts we’ve talked about and the homeworks. There aren’t any posted solutions to homeworks 7 and 8 because we did all that in class or it was in the handouts (Galle’s paper and her Chapter 3 masterpiece).

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