Generalized Finsler geometry and the anisotropic tearing of skin

TL;DR

This paper develops a generalized Finsler geometric framework to model the complex anisotropic tearing behavior of skin, incorporating microstructural damage and evolving configurations for improved predictive capability.

Contribution

It introduces a fiber bundle-based continuum mechanics model with a generalized Finsler metric that accounts for microstructural damage and anisotropy in skin tearing.

Findings

Analytical solutions match experimental force-stretch data.

Model captures microstructural evolution during tearing.

Framework extends prior phenomenological models with geometric rigor.

Abstract

A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on position and the state vector, where the latter dependence allows for both direction (i.e., as in Finsler geometry) as well as magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber rearrangements and ruptures) in different directions with respect to intrinsic orientations (e.g., parallel or perpendicular to Langer's lines). Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. Governing equations are derived for one- and two-dimensional base manifolds. Analytical solutions capture experimental force-stretch data, toughness, and observations on evolving microstructure, in a more geometrically and physically descriptive way than prior phenomenological models.