A Multiphase Continuum Mechanics Model for Shock Loading of Lung Parenchyma

A large deformation, coupled finite-element (FE) model is developed to simulate the multi-
phase response of soft porous materials subjected to high strain-rate (shock) loading, herein for particular application to lung parenchyma. The approach is based on the theory of porous media (TPM) at large deformations. The theoretical model developed herein is general and thermodynamically consistent to allow for a range of applications. Simplifications to the one-dimensional regime studied in the numerical simulations follow.
Numerical examples are presented for (i) verification against closed-form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain-rate, and (iii) showing differences in deformations between a single-phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain-rate. The multiphase model shows that the relative motion of the pore fluid (air) significantly dampens the deformation response of the solid skeleton (lung parenchyma) as compared to the single-phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton.
The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain-rate loading of soft porous materials. Therein, it was discovered that (i) explicit, adaptive time-stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit (or explicit central difference) schemes, (ii) shock viscosity is necessary to regularize the shock front, and (iii) additional stabilization parameters and non-standard mixed-element types improve both computational cost and accuracy compared to traditional implementations.