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TECHNICAL PAPERS

Wrinkling of Plane Isotropic Biological Membranes

[+] Author and Article Information
Roberta Massabò1

Department of Civil, Environmental and Architectural Engineering, University of Genova, Genova, 16145 ItalyRoberta.massabo@unige.it

Luigi Gambarotta

Department of Civil, Environmental and Architectural Engineering, University of Genova, Genova, 16145 Italy

A flap of skin is a domain of the skin that has been detached (undermined) from the subcutaneous attachments.

1

Corresponding author.

J. Appl. Mech 74(3), 550-559 (Jun 26, 2006) (10 pages) doi:10.1115/1.2424240 History: Received June 29, 2005; Revised June 26, 2006

The problem of the wrinkling of plane isotropic membranes characterized by a Fung type constitutive model in biaxial tension has been formulated and solved within the framework of finite strain hyperelasticity. The formulation follows the approach of Pipkin [Pipkin, A.C., 1986, IMA J. Appl. Math., 36, pp. 85–99; 1994, ibid., 52, pp. 297–308], and the out of plane geometric nonlinearities are treated as constitutive nonlinearities through a modification of the elastic potential. The wrinkling criteria are based on the natural contraction of a membrane in simple tension. Both the natural contraction and the modified elastic potential are defined in closed form. The model has been implemented in a finite element code and the numerical solution validated using study cases with analytical solution. Applications are presented that simulate the response of stretched membranes, where distinct regions of behavior (taut, wrinkled, and slack or inactive) develop during loading, and a simple procedure of reconstructive surgery, characterized by the excision of a circular portion of the skin and the suture of the wound edges, where the wrinkling of the skin causes the extrusion of the edges (dog-ear formation).

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Experimental test on a clamped rectangular polyethylene membrane, after Barsotti (1). (b) Experimental test on a clamped rectangular polyethylene membrane loaded in axial tension, after Cerda See Ref. 2. (c) Drawings after Ref. 3: (1) Spindle shape excision of a skin cancer; (2) dog-ear formation following the suture of the wound edges; (3) procedures used to eliminate the extrusion (postsuture) or to avoid it (while suturing).

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Figure 2

Reference (dotted line) and current (solid line) configurations of a plane membrane

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Figure 3

Principal membrane force fields (PKII, in kPa cm) plotted onto the deformed configuration of a stretched membrane. The figure highlights regions where the membrane is in biaxial tension (T), where it has wrinkled (W) and where it is slack and inactive (S). The principal direction 1 of the Cauchy membrane force tensor indicates the direction of the wrinkles in the W regions (shown on half of the domain).

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Figure 4

Principal membrane force fields (PKII, in kPa cm) plotted onto the deformed configuration of a stretched membrane subject to axial tension. The figure highlights regions where the membrane is in biaxial tension (T) and where it has wrinkled (W). The principal direction 1 of the Cauchy membrane force tensor indicates the direction of the wrinkles in the W regions (shown on half of the domain).

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Figure 5

Principal membrane force field (PKII, in kPa cm) obtained using the model of Eq. 2 plotted onto the deformed configuration of a stretched membrane subject to axial tension. The figure highlights the region where the membrane forces are compressive (up to −1.49E–03kPacm).

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Figure 6

(a)–(d) Steps of a procedure of reconstructive surgery on a skin flap. (a) Natural configuration of the skin; (b) incision and skin partial relaxation; (c) excision of a spindle shape portion of the skin; (d) closure and suture. (e) Excision of a circular portion of a skin flap (membrane forces diagrams after closure are shown in Fig. 7).

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Figure 7

Principal membrane force fields (PKII, in kPa cm) in a skin flap after the excision of a circular portion of the skin (dashed line) and the closure of the wound edges. The figure compares solutions obtained using the constitutive model 2, diagrams (a), which allows compressive stresses in the skin, and the constitutive model (Table 1), diagrams (b), which accounts for the wrinkling of the skin. The diagrams highlight the phenomenon of the extrusion of the edges of the wound after suture that occurs in the regions identified as slack and wrinkled.

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