Cauchy's Stress Theorem

Materials Science · 1822

Equation: t = σ·n
Field: Materials Science
Named After: Augustin-Louis Cauchy
Year: 1822

Symbols

t the traction — force per unit area on an imaginary cut through the material · n the unit normal to that cut · σ the stress tensor, a 3×3 array holding the whole state of stress at a point

Significance

The force on any surface inside a solid follows from one object — the stress tensor — by a single multiplication, whatever the surface's orientation. Cauchy's insight made 'stress' a proper mathematical quantity and founded continuum mechanics: Young's modulus, Griffith's cracks, and the elastic waves of seismology all live downstream of this line.