Influence of anisotropy on the expansion performance of auxetic skin meshing geometries: a finite element study

Denis O'Mahoney; Kevin Moerman; Masoumeh Razaghi Pey Ghaleh

arxiv: 2606.04893 · v1 · pith:W5J5TCLGnew · submitted 2026-06-03 · ⚛️ physics.med-ph · cond-mat.mtrl-sci

Influence of anisotropy on the expansion performance of auxetic skin meshing geometries: a finite element study

Masoumeh Razaghi Pey Ghaleh , Denis O'Mahoney , Kevin Moerman This is my paper

Pith reviewed 2026-06-28 02:49 UTC · model grok-4.3

classification ⚛️ physics.med-ph cond-mat.mtrl-sci

keywords auxetic meshesskin anisotropyfinite element analysisskin graft expansionLanger's linesanisotropic constitutive modelauxetic structures

0 comments

The pith

Anisotropy strongly influences expansion in auxetic skin graft meshes, with effects varying by mesh type and fiber orientation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines the interaction between skin's natural anisotropy and auxetic mesh designs for skin grafts through finite element simulations. Models apply 25 percent strain to slit-based auxetic geometries while rotating the direction of anisotropy relative to the loading axis. Anisotropy affects expansion in a mesh-specific manner, either boosting or reducing the auxetic response, with poorest performance when fibers align transversely and best when aligned with load. Isotropic versions of the models consistently predict higher stresses than their anisotropic counterparts. The work shows that realistic tissue anisotropy must be included to accurately forecast how these meshes will expand in practice.

Core claim

Anisotropy strongly influenced expansion behaviour. The effect was observed to be complex and highly dependent on mesh type. Anisotropy was observed to enhance or inhibit the auxetic expansion behaviour. In all mesh types studied, the expansion performance is lowest when Langer's lines align with the transverse direction. Greatest expansion was typically observed when Langer's lines were close to the loading direction. Isotropic models overpredicted stress relative to the anisotropic models. These findings support the use of auxetic structures for skin mesh expansion applications and show that anisotropy is an important factor in both deformation and stress prediction.

What carries the argument

Finite element models of auxetic slit-based geometries using an anisotropic constitutive formulation for skin, with Langer's line orientations varied relative to the load direction.

If this is right

Expansion performance is lowest in all mesh types when Langer's lines align with the transverse direction.
Greatest expansion is typically observed when Langer's lines are close to the loading direction.
Anisotropy can enhance or inhibit auxetic expansion behaviour depending on the mesh type.
Isotropic models overpredict stress relative to anisotropic models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Designers of skin graft meshes may benefit from tailoring patterns to typical anisotropy directions in target body areas.
The complex interaction suggests that certain auxetic geometries are more robust to variations in skin orientation than others.
Incorporating anisotropy could lead to better predictions of required graft sizes or tension in clinical applications.

Load-bearing premise

Skin tissue can be adequately represented by the chosen anisotropic constitutive formulation under 25% strain, and the specific auxetic slit geometries studied are representative of practical skin graft meshes.

What would settle it

Direct experimental measurement of expansion ratios and stresses in real skin tissue samples meshed with the studied auxetic patterns under 25% strain, checking if transverse Langer's line alignment indeed yields lowest expansion.

read the original abstract

This study investigates the combined effects of anisotropy and auxetic mesh geometry on the performance of skin graft expansion. Finite element models of auxetic slit-based geometries were developed and subjected to 25 percent tensile strain. Skin was modelled using an anisotropic constitutive formulation. Langer's line orientations were varied relative to the load direction. Results showed anisotropy strongly influenced expansion behaviour. The effect was observed to be complex and highly dependent on mesh type. Anisotropy was observed to enhance or inhibit the auxetic expansion behaviour. In all mesh types studied, the expansion performance is lowest when Langer's lines align with the transverse direction. Greatest expansion was typically observed when Langer's lines were close to the loading direction. Isotropic models overpredicted stress relative to the anisotropic models. These findings support the use of auxetic structures for skin mesh expansion applications and show that anisotropy is an important factor in both deformation and stress prediction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Anisotropy produces mesh-dependent effects on auxetic skin graft expansion with isotropic models overpredicting stress, but the lack of validation for the constitutive model at 25% strain limits how much weight the differences can carry.

read the letter

The main takeaway is that this finite element study finds anisotropy interacts with auxetic slit geometries in complex, orientation-specific ways during 25% tensile strain on skin graft meshes. Langer's line alignment with the transverse direction gives the lowest expansion across all types studied, while alignment near the load direction tends to give the highest, and isotropic runs overestimate stress relative to the anisotropic ones.

The work applies established auxetic patterns and an anisotropic constitutive model to this biomedical setting in a systematic way. Varying the fiber angle relative to load for multiple mesh types and reporting the resulting expansion and stress differences is a straightforward extension that adds some practical detail for device design.

The soft spot is exactly the one flagged in the stress-test note. The abstract gives no indication that the chosen anisotropic formulation was checked against experimental skin data at the 25% strain level used. Skin mechanics are nonlinear, and if the parameters or fiber implementation do not match real tissue behavior, the reported enhancements, inhibitions, and stress gaps are tied to this specific model rather than general results. That makes the central claims harder to rely on without further checks.

The paper is aimed at engineers working on skin expansion devices or similar soft-tissue simulations. Someone already modeling auxetic structures for grafts would get value from the orientation sweeps as a prompt for their own runs. It deserves peer review because the application is relevant and the comparisons are clear, even if referees will likely ask for model validation or sensitivity checks on the constitutive parameters.

Referee Report

1 major / 1 minor

Summary. The manuscript uses finite element analysis to examine how skin anisotropy (via Langer's line orientations relative to loading) affects the expansion performance of several auxetic slit-based mesh geometries under 25% tensile strain. Anisotropic models are compared to isotropic baselines; results indicate that anisotropy produces complex, mesh-dependent changes in expansion (enhancing or inhibiting auxetic behavior), with lowest performance when Langer's lines align transversely and highest when aligned near the load direction, while isotropic models overpredict stress.

Significance. If the chosen anisotropic constitutive model accurately captures skin mechanics at 25% strain, the work would demonstrate that anisotropy must be included in skin-graft mesh simulations to avoid erroneous stress and expansion predictions, potentially guiding more physiologically realistic mesh designs. The study provides no machine-checked proofs, reproducible code, or experimental validation data.

major comments (1)

[Methods (constitutive model description)] The central claims (anisotropy produces mesh-dependent enhancement/inhibition of expansion, isotropic models overpredict stress) rest on the adequacy of the anisotropic constitutive formulation for skin at 25% strain. No experimental calibration or validation data for this model (or its fiber-orientation implementation) under the applied loading are presented, making the reported orientation-specific trends and differences versus isotropic cases potentially formulation-dependent rather than general.

minor comments (1)

[Abstract] The abstract states results for 'all mesh types studied' but does not enumerate the specific geometries or provide quantitative metrics (e.g., expansion ratios, stress values) that would allow direct assessment of effect sizes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and the opportunity to clarify aspects of our finite element study. The major comment concerns the constitutive model; we respond point-by-point below and propose revisions to improve transparency.

read point-by-point responses

Referee: The central claims (anisotropy produces mesh-dependent enhancement/inhibition of expansion, isotropic models overpredict stress) rest on the adequacy of the anisotropic constitutive formulation for skin at 25% strain. No experimental calibration or validation data for this model (or its fiber-orientation implementation) under the applied loading are presented, making the reported orientation-specific trends and differences versus isotropic cases potentially formulation-dependent rather than general.

Authors: We agree that the manuscript is a purely computational study and does not include new experimental calibration or validation of the anisotropic constitutive model at 25% strain. The formulation and fiber-orientation implementation are taken from established literature on skin mechanics. The central comparison is between anisotropic and isotropic realizations of the same framework to isolate the effect of anisotropy on the auxetic geometries. We acknowledge that the specific quantitative trends and the magnitude of stress overprediction are therefore dependent on the chosen model parameters and may not be universal. In the revised manuscript we will add a new subsection (Methods or Discussion) that explicitly states the model source, its assumptions and limitations at the applied strain level, and notes the absence of direct experimental validation in this work. This will allow readers to interpret the orientation-specific results within the appropriate modeling context. revision: yes

Circularity Check

0 steps flagged

No circularity: simulation outputs are independent of inputs

full rationale

The paper reports results from finite element simulations of auxetic slit geometries under 25% strain using an anisotropic constitutive model for skin with varied Langer's line orientations. These outputs (expansion performance, stress predictions, orientation-dependent effects) are direct numerical results from the FE models and do not reduce by construction to fitted parameters, self-definitions, or self-citation chains. Comparisons to isotropic baselines are external and falsifiable via the simulation setup itself. No load-bearing step equates a claimed prediction to its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on standard finite-element assumptions and an anisotropic constitutive model for skin; no new entities are introduced.

free parameters (1)

Anisotropic constitutive parameters
Material constants in the skin model are required to run the simulations and are not derived within the study.

axioms (1)

domain assumption Skin tissue behaves as a transversely isotropic or orthotropic hyperelastic material under tensile loading
Invoked to justify the constitutive formulation used in all models.

pith-pipeline@v0.9.1-grok · 5697 in / 1173 out tokens · 43342 ms · 2026-06-28T02:49:56.674750+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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[1] [1]

Development of Hierarchical Auxetic Skin Graft Simulants with High Expansion Potential

Gupta, V .; Singh, G.; Chanda, A. Development of Hierarchical Auxetic Skin Graft Simulants with High Expansion Potential. Biomedical Engineering Advances 2 23, 5, 100087, doi:10.1016/j.bea.2023.100087

work page doi:10.1016/j.bea.2023.100087 2023

[2] [2]

A Comprehensive Review of Computational and Experimental Studies on Skin Mechanics and Meshing: Discrepancies, Challenges, and Optimization Strategies

Ghaleh, M.R.P.; Marques, D.; O’Mahoney, D. A Comprehensive Review of Computational and Experimental Studies on Skin Mechanics and Meshing: Discrepancies, Challenges, and Optimization Strategies. Biomimetics 2026, Vol. 11, 2 25, 11, 4, doi:10.3390/biomimetics11010004

work page doi:10.3390/biomimetics11010004 2026

[3] [3]

The True Meshing Ratio of Skin Graft Meshers

Lyons, J.L.; Kagan, R.J. The True Meshing Ratio of Skin Graft Meshers. Journal of Burn Care & Research 2 14, 35, 257–260, doi:10.1097/BCR.0b013e3182a3692e

work page doi:10.1097/bcr.0b013e3182a3692e

[4] [4]

Biomechanical Modeling of Novel High Expansion Auxetic Skin Grafts

Gupta, S.; Gupta, V .; Chanda, A. Biomechanical Modeling of Novel High Expansion Auxetic Skin Grafts. Int. J. Numer. Method. Biomed. Eng. 2 22, 38, 1–18, doi:10.1002/cnm.3586

work page doi:10.1002/cnm.3586

[5] [5]

Development and Testing of Skin Grafts Models with Varying Slit Orientations

Gupta, V .; Singh, G.; Chanda, A. Development and Testing of Skin Grafts Models with Varying Slit Orientations. Mater. Today Proc. 2 22, 62, 3462–3467, doi:10.1016/j.matpr.2022.04.282

work page doi:10.1016/j.matpr.2022.04.282 2022

[6] [6]

Biomechanical Properties of Dermis

Daly, C.H. Biomechanical Properties of Dermis. Journal of Investigative Dermatology 1982, 79, 17–20

1982

[7] [7]

Mechanical Properties and Microstructure of the Superficial Musculoaponeurotic System

Har-Shai, Y .; Bodner, S.R.; Egozy-Golan, D.; Lindenbaum, E.S.; Ben-Izhak, O.; Mitz, V .; Hirshowitz, B. Mechanical Properties and Microstructure of the Superficial Musculoaponeurotic System. Plast. Reconstr. Surg. 1996, 98, 59–70

1996

[8] [8]

Graft Orientation Influences Meshing Ratio

Capek, L.; Flynn, C.; Molitor, M.; Chong, S.; Henys, P. Graft Orientation Influences Meshing Ratio. Burns 2 18, 44, 1439–1445, doi:10.1016/j.burns.2018.05.001

work page doi:10.1016/j.burns.2018.05.001 2018

[9] [9]

Automated Estimation of Collagen Fibre Dispersion in the Dermis and Its Contribution to the Anisotropic Behaviour of Skin

Ní Annaidh, A.; Bruyère, K.; Destrade, M.; Gilchrist, M.D.; Maurini, C.; Otténio, M.; Saccomandi, G. Automated Estimation of Collagen Fibre Dispersion in the Dermis and Its Contribution to the Anisotropic Behaviour of Skin. Ann. Biomed. Eng. 2 12, 40, 1666–1678, doi:10.1007/s10439-012-0542-3

work page doi:10.1007/s10439-012-0542-3

[10] [10]

Computational and Experimental Characterization of Skin Mechanics: Identifying Current Challenges and Future Directions

Jor, J.W.Y .; Parker, M.D.; Taberner, A.J.; Nash, M.P.; Nielsen, P.M.F. Computational and Experimental Characterization of Skin Mechanics: Identifying Current Challenges and Future Directions. WIREs Systems Biology and Medicine 2 13, 5, 539–556, doi:10.1002/wsbm.1228

work page doi:10.1002/wsbm.1228

[11] [11]

Biomechanics of Skin Grafts: Effect of Pattern Size, Spacing and Orientation

Gupta, V .; Chanda, A. Biomechanics of Skin Grafts: Effect of Pattern Size, Spacing and Orientation. Engineering Research Express 2 22, 4, 015006, doi:10.1088/2631-8695/ac48cb

work page doi:10.1088/2631-8695/ac48cb

[12] [12]

Finite Element Analysis of Hierarchical Metamaterial -Based Patterns for Generating High Expansion in Skin Grafting

Gupta, V .; Chanda, A. Finite Element Analysis of Hierarchical Metamaterial -Based Patterns for Generating High Expansion in Skin Grafting. Mathematical and Computational Applications 2 23, 28, 89, doi:10.3390/mca28040089

work page doi:10.3390/mca28040089

[13] [13]

Optimal Geometrical Selection of Skin Mesh: Experimental Analysis and Numerical Optimization

Khayami, M.; Rassoli, A.; Feizkhah, A. Optimal Geometrical Selection of Skin Mesh: Experimental Analysis and Numerical Optimization. Scientific Reports 2025 15:1 2 25, 15, 21263-, doi:10.1038/s41598-025-04829-0

work page doi:10.1038/s41598-025-04829-0 2025

[14] [14]

Parametric Study and Inverse Design of Perforated Silicone Auxetic Structures

Vargovics, T.; Kossa, A. Parametric Study and Inverse Design of Perforated Silicone Auxetic Structures. Forschung im Ingenieurwesen 2025 89:1 2 25, 89, 62-, doi:10.1007/S10010-025-00828-9

work page doi:10.1007/s10010-025-00828-9 2025

[15] [15]

Optimization of the Cut Configuration for Skin Grafts

Harbrecht, H.; Karnaev, V . Optimization of the Cut Configuration for Skin Grafts. Biomechanics and Modeling in Mechanobiology 2025 25:1 2 26, 25, 12-, doi:10.1007/S10237-025-02035-5

work page doi:10.1007/s10237-025-02035-5 2025

[16] [16]

Numerical Optimization for Selecting the Optimal Geometrical Configuration of Polymeric Skin Mesh

Khayami, M.; Rassoli, A. Numerical Optimization for Selecting the Optimal Geometrical Configuration of Polymeric Skin Mesh. Journal of Artificial Organs 2026 29:1 2 26, 29, 20-, doi:10.1007/S10047-026-01549-8

work page doi:10.1007/s10047-026-01549-8 2026

[17] [17]

Expansion Limits of Meshed Split -Thickness Skin Grafts

Yu, H.; Jafari, M.; Mujahid, A.; Garcia, C.F.; Shah, J.; Sinha, R.; Huang, Y .; Shakiba, D.; Hong, Y .; Cheraghali, D.; et al. Expansion Limits of Meshed Split -Thickness Skin Grafts. Acta Biomater. 2 25, 191, 325 –335, doi:10.1016/J.ACTBIO.2024.11.038

work page doi:10.1016/j.actbio.2024.11.038 2024

[18] [18]

Implementation and Validation of Constitutive Relations for Human Dermis Mechanical Response

Aldieri, A.; Terzini, M.; Bignardi, C.; Zanetti, E.M.; Audenino, A.L. Implementation and Validation of Constitutive Relations for Human Dermis Mechanical Response. Med. Biol. Eng. Comput. 2 18, 56, 2083 –2093, doi:10.1007/S11517-018-1843-Y/FIGURES/6

work page doi:10.1007/s11517-018-1843-y/figures/6 2083

[19] [19]

Auxetic Incisions with Alternating Slit Shapes: A Promising Technique for Enhancing Synthetic Skin Grafts Expansion

Gupta, V .; Chanda, A. Auxetic Incisions with Alternating Slit Shapes: A Promising Technique for Enhancing Synthetic Skin Grafts Expansion. Mater. Res. Express 2 23, 10, 075802, doi:10.1088/2053-1591/ace611

work page doi:10.1088/2053-1591/ace611 2053

[20] [20]

Expansion Potential of Skin Grafts with Novel I-Shaped Auxetic Incisions

Gupta, V .; Chanda, A. Expansion Potential of Skin Grafts with Novel I-Shaped Auxetic Incisions. Biomed. Phys. Eng. Express 2 22, 8, 015016, doi:10.1088/2057-1976/ac3b72

work page doi:10.1088/2057-1976/ac3b72 2057

[21] [21]

GIBBON: The Geometry and Image -Based Bioengineering Add-On

M Moerman, K. GIBBON: The Geometry and Image -Based Bioengineering Add-On. The Journal of Open Source Software 2 18, 3, 506, doi:10.21105/JOSS.00506

work page doi:10.21105/joss.00506

[22] [22]

FEBio: Finite Elements for Biomechanics

Maas, S.A.; Ellis, B.J.; Ateshian, G.A.; Weiss, J.A. FEBio: Finite Elements for Biomechanics. J. Biomech. Eng. 2 12, 134, doi:10.1115/1.4005694/455684

work page doi:10.1115/1.4005694/455684

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