ps_6 - Massachusetts Institute of Technology Biological...

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Massachusetts Institute of Technology Biological Engineering Division Department of Mechanical Engineering Department of Electrical Engineering and Computer Science BEH.410/2.798J/6.524J/10.539J Molecular, Cellular & Tissue Biomechanics, Spring 2003 Problem Set # 6 (Poroelastic materials) Issued: Mon., 4/7/03 Due: Wed., 4/16/03 READING ASSIGNMENT: Grodzinsky, Chapter 8 PROBLEMS: Do problems 1-2 attached.
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Problem 1: Linear, isotropic, homogeneous, poroelastic material Consider a Poroelastic tissue specimen subjected to confined compression. (a) Extending what was done in class, show that the displacement u 1 (x 1 ,t) is described by a partial differential equation having the form of a diffusion equation with equivalent “diffusivity” equal to Hk , the product of the confined compression modulus H = (2G + l ) and the hydraulic permeability k . (b) Derive an analogous diffusion equation that describes the spatial and temporal dependence of the fluid pressure p . What is the equivalent “diffusivity”? (c) A step in displacement is applied at
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ps_6 - Massachusetts Institute of Technology Biological...

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