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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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:
Constitutive Models Relations between Stress and Strain
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See also: Linear Algebra
– Tom Irvine
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