Infinite periodic model of human lung

Abstract

As described in a companion abstract, an investigation is underway to develop a bioacoustic model of human lung. In parallel with the numerical model described in the companion abstract, a semianalytic model is being developed. The basic unit cell, a truncated octahedron, is the same. In contrast here, the medium is assumed to be infinite in extent. The resulting lattice possesses cubic symmetry, and, for homogeneous deformation, all material properties are determined by a single unit cell. Deformation of the unit cell is determined by the 24 vertices of the polyhedron, only 6 of which are independent. In this presentation we discuss quasistatic deformation of the discretized medium, and thus ignore inertia and energy dissipation. An analytic model for the nonlinear elasticity of collagen and elastin is used to determine the stiffnesses of the springs connecting vertices of the polyhedra. Minimization of the potential energy for a given macroscopic deformation permits calculation of microscopic deformation within the unit cell, which in turn determines the stresses and therefore the elastic constants. Sample calculations will be presented, including the longitudinal and transverse wave speeds in the medium as functions of direction and orientation. [Work supported by ONR and ARL IR&D.]