exam2_review2

# exam2_review2 - Poroelasticity in 1D Confined Compression...

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Unformatted text preview: Poroelasticity in 1D Confined Compression ( ε 22 = ε 33 = 0) Assumptions: Solid: Hookean (linear elastic, or viscoelastic), homogeneous, isotropic, incompressible Liquid: Inviscid (fluid friction negligible or μ =0, but there is solid-liquid friction), incompressible Constitutive relation Conservation of mass Conservation of momentum Fluid-structure interaction: Darcy’s law ( ) p H p G tot − = − + = 11 11 11 2 ε ε λ σ with 1 1 11 x u ∂ ∂ = ε (1) ( ) ( s f tot f s f v v A A v v U t u U − = − = + ∂ ∂ − = φ 1 1 ) (2) 1 11 = ∂ ∂ x σ (3) 1 1 x p k U ∂ ∂ − = (4) Diffusion equation For stress relaxation 2 1 1 2 1 x u Hk t u ∂ ∂ = ∂ ∂ ( ) ∑ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = n t L Hk n L x n n u L x u t x u 2 2 2 1 1 1 1 exp sin 2 1 , π π π Cell-Membrane Mechanics • Stretching • Bending • Shear • Composite Equation ( ) ( ) ν ν ε ν σ σ − = Δ = Δ − = − = = = ∫ −...
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## This note was uploaded on 11/11/2011 for the course BIO 2.797j taught by Professor Matthewlang during the Fall '06 term at MIT.

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exam2_review2 - Poroelasticity in 1D Confined Compression...

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