Original Paper

Biomechanics and Modeling in Mechanobiology

, Volume 11, Issue 3, pp 557-573

First online:

Hypo-elastic model for lung parenchyma

  • Alan D. FreedAffiliated withDepartment of Mechanical Engineering, Saginaw Valley State University Email author 
  • , Daniel R. EinsteinAffiliated withBiological Monitoring and Modeling, Pacific Northwest National Laboratory

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A simple, isotropic, elastic constitutive model for the spongy tissue in lung is formulated from the theory of hypo-elasticity. The model is shown to exhibit a pressure dependent behavior that has been interpreted in the literature as indicating extensional anisotropy. In contrast, we show that this behavior arises naturally from an analysis of isotropic hypo-elastic invariants and is a result of non-linearity, not anisotropy. The response of the model is determined analytically for several boundary value problems used for material characterization. These responses give insight into both the material behavior as well as admissible bounds on parameters. The model predictions are compared with published experimental data for dog lung.


Biomechanics Elastic moduli Finite deformation Soft solids Thermodynamics