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12.005 Applications of Continuum Mechanics to Earth, Atmospheric, and Planetary Sciences

Spring 2006

Strain ellipses and their axes.Strain ellipses and their axes. (Image by MIT OCW.)

Course Highlights

This course features a full set of lecture notes, assignments and solutions.

Course Description

This course focuses on the practical applications of the continuum concept for deformation of solids and fluids, emphasizing force balance. Topics include stress tensor, infinitesimal and finite strain, and rotation tensors. Constitutive relations applicable to geological materials, including elastic, viscous, brittle, and plastic deformation are studied.



Syllabus

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Overview

This course talks about practical applications of the continuum concept for deformation of solids and fluids, emphasizing force balance. Topics include stress tensor, infinitesimal and finite strain, and rotation tensors. Constitutive relations applicable to geological materials, including elastic, viscous, brittle, and plastic deformation are studied along with solutions to classical problems in geodynamics.

You are encouraged to discuss the homework, exams, lecture, or the class in general. Problem sets will be given out approximately weekly.



Prerequisites

Electricity and Magnetism (8.02), Calculus (18.02), Differential Equations (18.03).



Supplementary Texts

Amazon logo Schubert, G., D. L. Turcotte, and J. Schubert. Geodynamics. Cambridge, MA; New York, NY: Cambridge University Press, 2001. ISBN: 9780521666244.

Amazon logo Middleton, G. V., and P. R. Wilcock. Mechanics in the Earth and Environmental Sciences. Cambridge, MA; New York, NY: Cambridge University Press, 1994. ISBN: 9780521446693.



Grading

The grading criteria for the course is: 1/3 for homework; 1/6 for each of 2 in-class 1-hour open-notes mid-term exams; and 1/3 for the in-class 3-hour open-notes final exam held during final exam week.

In a nutshell:


ACTIVITIESPERCENTAGES
Homework33.3%
Two In-class 1-hour Open-notes Mid-term Exams33.3%
In-class 3-hour Open-notes Final Exam33.3%




Calendar

Lec #TOPICSKEY DATES
1Course Overview
2Tractions
3Stress Tensor
4Stress Tensor (cont.)
5Stress Tensor in Different Coordinate Systems
6Pore Fluid Pressure
7Newton's Second LawProblem set 1 due
8Stress in the Earth
9Stress Rotation
10Sandbox Tectonics
11Sandbox Tectonics - Simple TheoryProblem set 2 due
12Displacement Gradients
13Measurement of Displacement Gradient Tensor
14Finite Strain
15ElasticityProblem set 3 due
16Simple Example: Uniaxial Strain
17Special Cases
18Dislocation in Elastic Halfspace Model of the Earthquake Cycle
19Stress and Strain from a Screw DislocationProblem set 4 due
20Plates
21Plates (cont.)
22Plates (cont.)Problem set 5 due
23Plates Summary and Fluids
24Fluids (cont.)
25Navier Stokes EquationProblem set 6 due
26Growth and Decay of Boundary Undulations
27Flow in Porous Media
28Time Dependent Porous FlowProblem set 7 due




Lecture Notes

Lec #TOPICS
1Course Overview (PDF)
2Tractions (PDF)
3Stress Tensor (PDF)
4Stress Tensor (cont.) (PDF)
5Stress Tensor in Different Coordinate Systems (PDF)
6Pore Fluid Pressure (PDF)
7Newton's Second Law (PDF)
8Stress in the Earth (PDF)
9Stress Rotation (PDF)
10Sandbox Tectonics (PDF)
11Sandbox Tectonics - Simple Theory (PDF)
12Displacement Gradients (PDF)
13Measurement of Displacement Gradient Tensor (PDF)
14Finite Strain (PDF)
15Elasticity (PDF)
16Simple Example: Uniaxial Strain (PDF)
17Special Cases (PDF)
18Dislocation in Elastic Halfspace Model of the Earthquake Cycle (PDF)
19Stress and Strain from a Screw Dislocation (PDF)
20Plates (PDF)
21Plates (cont.) (PDF)
22Plates (cont.) (PDF)
23Plates Summary and Fluids (PDF)
24Fluids (cont.) (PDF)
25Navier Stokes Equation (PDF)
26Growth and Decay of Boundary Undulations (PDF)
27Flow in Porous Media (PDF)
28Time Dependent Porous Flow (PDF)




Assignments

Problem Set 1 (PDF)

Problem Set 2 (PDF)

Problem Set 3 (PDF)

Problem Set 4 (PDF)

Problem Set 5 (PDF)

Problem Set 6 (PDF)

Problem Set 7 (PDF)




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