Fundamentals of Continuum Mechanics

Problem 3.9

Given the motion

$x_1=2X_2,x_2=5X_3,x_3=X_1,$

(a) calculate the principal stretches $\stackrel{1}{\lambda }$, $\stackrel{2}{\lambda }$, and $\stackrel{3}{\lambda }$ (common to both U and V);

(b) calculate the principal directions $\stackrel{1}{\mathbf{N}}$, $\stackrel{2}{\mathbf{N}}$, $\stackrel{3}{\mathbf{N}}$ of U;

(c) calculate the principal directions of $\stackrel{1}{\mathbf{n}}$, $\stackrel{2}{\mathbf{n}}$, $\stackrel{3}{\mathbf{n}}$ of V;

(d) ...