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Generalized Finsler geometry and the anisotropic tearing of skin
Soft Condensed Matter · Submitted 17 Sep 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. | contribution 0.90 | 0.69 | 0.31 | asserted 1.00 |
| s1 | A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with microstructure. | method 0.90 | 0.64 | 0.05 | asserted 1.00 |
| s2 | An internal state vector is introduced on each configuration, describing subscale physics. | method 0.83 | 0.84 | 0.03 | asserted 1.00 |
| s3 | 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. | method 0.88 | 0.69 | 0.06 | asserted 1.00 |
| s4 | Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. | method 0.89 | 0.88 | 0.07 | asserted 1.00 |
| s5 | 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). | method 0.87 | 0.64 | 0.11 | asserted 1.00 |
| s6 | Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. | method 0.95 | 0.80 | 0.05 | asserted 1.00 |
| s7 | Governing equations are derived for one- and two-dimensional base manifolds. | method 0.80 | 0.91 | 0.03 | asserted 1.00 |
| s8 | 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. | result 0.96 | 0.88 | 0.67 | asserted 1.00 |
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Original 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.
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Cites as background 2 papers
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Finsler geometry and its generalizations have also been used for describing anisotropic space-time, general relativity, quantum fields, gravitation, electromagnetism, and diffusion [ref] .
Geometrical Models of the Locally Anisotropic Space-Time · Introduction · 0.95
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Finsler geometry and its generalizations have also been used for describing anisotropic space-time, general relativity, quantum fields, gravitation, electromagnetism, and diffusion [ref] .
Lorentz-Finsler metrics on symplectic and contact transformation groups · Introduction · 0.95
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