A Universal Continuum Theory and Shock Wave Analysis for Biologic Solids and Fluids

Author(s):

John D. Clayton

Abstract:

Soft biologic tissues comprise one or more solid and fluid phases and may exhibit nonlinear anisotropic elastic, viscoelastic, thermoelastic, and poroelastic behaviors. Tissues can tear or rupture when loading is severe. A mixture theory is formulated to account for finite deformations, thermal effects, phase interactions, and degradation of tissues. Physical mechanisms are encompassed in a universal, thermodynamically consistent formulation that combines the continuum theory of mixtures with phase-field mechanics of fracture. A metric tensor of generalized Finsler geometry provides insight on rearrangements of microstructure; for example, degrading collagen fibers and remnant strains. Energy potentials capture isotropic and anisotropic behaviors pertinent to fibrous-tissue microstructures. Kinetic equations consistent with derived conservation laws and the dissipation inequality describe viscoelasticity, fracture, and exchanges of mass, momentum, and energy among coexisting phases. Shock waves are modeled as surfaces of singularity. Hugoniot states and shock decay are quantified, the latter by a new analytical solution encompassing dissipation from viscoelasticity, damage, and phase interactions that reduce shock amplitudes over time. Agreement of calculations and experimental data is respectable, validating theory and parameters. Materials studied include water, extracellular fluid, blood, skeletal muscle, liver, lung, and skin.