A nonlinear thermoelastic-viscoelastic continuum model of lung mechanics for shock wave analysis

Abstract

A finite deformation constitutive model for lung parenchyma—including stiffness contributions from dense soft tissue, surface tension, and internal air pressure—is constructed for dynamic loading protocols and eventual injury assessments. The material is approximated as a homogeneous isotropic, nonlinear viscoelastic solid. Internal energy depends on finite strain measures, entropy, and internal state variables. The equilibrium response in the hyperelastic limit follows from a strain energy function depending on strain attributes stemming from a Gram-Schmidt decomposition of deformation. For rapid loading, a composite closed-cell model is invoked to estimate an isentropic bulk modulus of the effective continuum that depends strongly on initial airway pressure and stress-free mass density. Viscoelasticity is addressed by internal state variables in a thermodynamically consistent manner. Stiffness degradation and injury mechanisms can be tracked by additional internal variables. Solutions for planar shock compression are reported, verifying wave speed predictions in the low amplitude limit, exhibiting moderate nonlinearity in shock velocity versus particle velocity profiles, and demonstrating strong influence of initial air pressure on Hugoniot responses.