Lecture04 - ME 382 Lecture 04 12/ix/07 1 M ULTIAXIAL STRAIN...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ME 382 Lecture 04 12/ix/07 1 M ULTIAXIAL STRAIN & STIFFNESS Isotropic linear elasticity • Normal stresses and strains are related by: i) Young’s modulus: E ii) Poisson’s ratio: ν ! 1 " # " 0.5 For most materials 0.2 ! " ! 0.5 • Shear stresses and strains related by: " xx = # xx / E ! zz = " zz / E " yy = " zz = # $" xx = # $% xx / E " xx = " yy = # $" zz = # $% zz / E (no cross terms for shear) ! yy = " yy / E ¡ xy = ¢ xy / G ! xx = ! zz = " #! yy = " #$ yy / E ¡ xz = ¢ xz / G ¡ yz = ¢ yz / G ME 382 Lecture 04 12/ix/07 2 In general : 3-D Hooke’s Law ! xx = " xx # $" yy # $" zz ( ) / E ! yy = " #$ xx + $ yy " #$ zz ( ) / E ! zz = " #$ xx " #$ yy + $ zz ( ) / E ! xy = " xy / G ! xz = " xz / G ! yz = " yz / G Special cases: (i) Plane stress: One stress = 0; e.g. , σ zz = 0 (such as at free surface) (ii) Plane strain: One strain = 0; e.g. , ε zz = 0 (constraint in rigid die) Volumetric strain: Original volume: V o = l 3 New volume: V = l + u ( ) l + v ( ) l + w ( ) ∴ V...
View Full Document

This note was uploaded on 10/12/2008 for the course MECHENG 382 taught by Professor Thouless during the Spring '08 term at University of Michigan.

Page1 / 5

Lecture04 - ME 382 Lecture 04 12/ix/07 1 M ULTIAXIAL STRAIN...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online