Modeling dynamic impact, shock waves, and injury in liver tissue with a constrained mixture theory

A nonlinear continuum theory is advanced for high-rate mechanics and thermodynamics of liver parenchyma. The homogenized continuum is idealized as a solid-fluid mixture of dense viscoelastic tissue and liquid blood. The solid consists of a matrix material comprising the liver lobules and a collagenous fiber network. Under high loading rates pertinent to impact and blast, the velocity difference between solid and fluid is assumed negligible, leading to a constrained mixture theory. The model captures nonlinear isotropic elasticity, viscoelasticity, temperature changes from thermoelasticity and dissipation, and tissue damage, the latter via a scale-free phase-field representation. Effects of blood volume and initial constituent pressures are included. The model is implemented in 3-D finite element software. Analytical and numerical solutions for planar shock loading are compared with observations of liver trauma from shock-tube experiments. Finite-element simulations of dynamic impact are compared with cylinder drop-weight experiments. Model results, including matrix damage exceeding fiber damage at high rates and reduced mechanical stiffness with higher perfused blood volume, agree with experimental trends. Viscoelasticity is important at modest impact speeds.