Lecture14Extras

Lecture14Extras - Maxwell Model (better for stress...

Info iconThis preview shows pages 1–4. 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

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: Maxwell Model (better for stress relaxation) dσ dε Hookeʼs law when applied stress =E dt dt varies in time: dε σ assumes viscous = forces are dt η newtonian; plug in to Hookeʼs law equation above. rearrange to get: 1 ∂σ σ ∂ε( t ) += E ∂t η ∂t if stress is constant, this predicts no creep! 29 Maxwell Model 1 ∂σ σ ∂ε( t ) += E ∂t η ∂t impose a condition of constant strain, integrate σ E ln = − t σ0 η rearrange: ⎡E⎤ ⎢− t ⎥ ⎣η⎦ ⎡ t⎤ ⎢− ⎥ ⎣ τt ⎦ σ = σ 0e = σ 0e 30 Maxwell Model ln σ E =− t σ0 η σ = σ 0e ⎡E⎤ ⎢− t ⎥ ⎣η⎦ = σ 0e ⎡ t⎤ ⎢− ⎥ ⎣ τt ⎦ 31 Voigt Model (better for creep) dε( t ) σ ( t ) = Eε( t ) + η d (t ) apply constant stress: dε( t ) ε( t ) σ 0 + '= d( t ) τt η ⎛ t ⎞⎤ ⎡ ⎜− ' ⎟ ⎜ ⎟ σ0 ⎢ ⎝ τ t ⎠⎥ ε( t ) = 1− e ⎥ E⎢ ⎣ ⎦ solution to linear differential equation: 32 ...
View Full Document

This note was uploaded on 11/29/2010 for the course BME 104 taught by Professor Kasko during the Fall '10 term at UCLA.

Page1 / 4

Lecture14Extras - Maxwell Model (better for stress...

This preview shows document pages 1 - 4. Sign up to view the full document.

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