A Dodecahedral Model for Alveoli. Part I. Theory and Numerical Methods
Abstract
The dodecahedron is introduced as a model for alveoli. Its geometric properties are derived in detail with regard to its three geometric features: 1D septal chords, 2D septal membranes, and the 3D alveolar sac. The kinematics are derived for us to model a deforming dodecahedron, including the shape functions needed for interpolating each geometry. Constitutive models are derived that are suitable for describing the thermomechanical response for the structural constituents of an alveolus: its septal chords, its permeable membranes, and its volume. Numerical methods are advanced for solving first- and second-order ordinary differential equations (ODEs) and spatial integrations along a bar, across a pentagon, and throughout a tetrahedron using Gaussian quadrature schemes designed for each geometry. A variational formulation is used to create our structural modeling of an alveolus. Constitutive equations suitable for modeling biological tissues are derived from thermodynamics using the theory of implicit elasticity, presented in an appendix.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 16, 2021
- Accession Number
- AD1123198
Entities
People
- Alan D. Freed
- John D. Clayton
- Sandipan Paul
- Shahla Zamani
Organizations
- Texas A&M University
- United States Army