I am taking a class in continuum mechanics at the University of Alabama in Huntsville.

Here are some notes:

Derivation of the Epsilon-Delta Relationship: epsilon_delta.pdf

Continuum Mechanics Formulas (Kronecker delta, permutation symbol, dot product, cross-product, etc.) : cm_formulas.pdf

Del Operator Proofs (divergence, curl, cross-product, etc.): del_operator_proofs.pdf

Unit Vector Normal to an Inclined Plane: vector_normal_plane.pdf

Continuum Mechanics Formulas for Fluid Mechanics: cm_fluid_mechanics.pdf

Material Derivative: material_derivative.pdf

Displacement Gradient and the Lagrangian Strain Tensor: displacement_gradient.pdf

Laplace’s Equation: Laplacian_equation.pdf

Calculations with Position Vectors: position_vectors.pdf

Derivation of the Cayley-Hamiliton Equation: Cayley_Hamilton.pdf

Conservation of Mass: conservation_mass.pdf

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Homework_1.pdf

Homework_2.pdf

Homework_3.pdf

Homework_4a.pdf

Homework_5.pdf

Homework_6b.pdf

Homework_7.pdf

Homework_8.pdf

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Matlab script: continuum_mechanics_stress_strain.zip

Includes functions for calculating:

- Principal stresses or strain in either 2D or 3D
- Mohr’s circle and von Mises stress
- Stress on an arbitrary plane defined by a unit normal vector
- Thin-walled cylinder torsion with option for internal pressure
- Deviatoric Stress Tensor
- Octahedral Stress

* * *

References:

Continuum Mechanics – Solids

Constitutive Models Relations between Stress and Strain

NASA/TM–2011-217314, An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials

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See also: Linear Algebra

– Tom Irvine

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