Key Equations

First Equilibrium Condition	$\sum_{k} {\vec{F}}_{k} = \vec{0}$
Second Equilibrium Condition	$\sum_{k} {\vec{τ}}_{k} = \vec{0}$
Linear relation between stress and strain	$stress = (elastic modulus) \times strain$
Young’s modulus	$Y = \frac{tensile stress}{tensile strain} = \frac{F_{⊥}}{A} \frac{L_{0}}{Δ L}$
Bulk modulus	$B = \frac{bulk stress}{bulk strain} = − Δ p \frac{V_{0}}{Δ V}$
Shear modulus	$S = \frac{shear stress}{shear strain} = \frac{F_{∥}}{A} \frac{L_{0}}{Δ x}$