A universal phase-field mixture representation of thermodynamics and shock wave mechanics in porous soft biologic continua

Abstract

A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues. Such tissues consist of one or more solid and fluid phases and can demonstrate nonlinear anisotropic elastic, viscoelastic, thermoelastic, and poroelastic physics. Under extremely large or rapid deformations, for example impact or shock loading, tissues may fracture, tear, or rupture. 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 space supplies geometric insight on effects rearrangements of microstructure, for example degrading collagen fibers. Governing equations are derived, and energy potentials and kinetic laws posited, for generic soft porous tissues with solid and liquid or gas phases. Shock waves are modeled as singular surfaces; Hugoniot states and shock decay are studied analytically. Suitability of the framework for representing blood, skeletal muscle, and liver is demonstrated. Insight into physics presently unresolved by experiments is obtained.

arXiv comment29 pages, 6 figures

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Cited by in corpus (5)

• Analysis of shear localization in viscoplastic solids with pressure-sensitive structural transformations
• Accretion and Ablation in Deformable Solids using an Eulerian Formulation: A Finite Deformation Numerical Method
• Analysis of adiabatic shear coupled to ductile fracture and melting in viscoplastic metals
• Nonlinear soft-tissue elasticity, remodeling, and degradation described by an extended Finsler geometry
• Modeling dynamic impact, shock waves, and injury in liver tissue with a constrained mixture theory