# Continuum Mechanics

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

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

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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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