An Invariant-Based Damage Model for Human and Animal Skins

Abstract

Constitutive modelling of skins that account for damage effects is important to provide insight for various clinical applications, such as skin trauma and injury, artificial skin design, skin aging, disease diagnosis, surgery, as well as comparative studies of skin biomechanics between species. In this study, a new damage model for human and animal skins is proposed for the first time. The model is nonlinear, anisotropic, invariant-based, and is based on the Gasser-Ogden-Holzapfel constitutive law initially developed for arteries. Taking account of the mean collagen fibre orientation and its dispersion, the new model can describe a wide range of skins with damage. The model is first tested on the uniaxial test data of human skin and then applied to nine groups of uniaxial test data for the human, swine, rabbit, bovine and rhino skins. The material parameters can be inversely estimated based on uniaxial tests using the optimization method in MATLAB with a root mean square error ranged between 2.15% and 12.18%. A sensitivity study confirms that the fibre orientation dispersion and the mean fibre angle are among the most important factors that influence the behaviour of the damage model. In addition, these two parameters can only be reliably estimated if some histological information is provided. We also found that depending on the location of skins, the tissue damage may be brittle controlled by the fibre breaking limit (i.e., when the fibre stretch is greater than 1.13-1.32, depending on the species), or ductile (due to both the fibre and the matrix damages). The brittle damages seem to occur mostly in the back, and the ductile damages are seen from samples taken from the belly. The proposed constitutive model may be applied to various clinical applications that require knowledge of the mechanical response of human and animal skins.

Keywords: Constitutive model; Damage; Fibre orientation; Fibre orientation dispersion; Inverse problem; Skin.

Figure 1

The stress-stretch curve of the skin samples harvested from the pig body along different directions, the in vitro tests were made at 2500 s⁻¹ strain rate, two curves exhibit damage effect at a higher stretch, the model fails to fit the curves, the plot after Ref. .

Figure 2

The collagen fibre (bright/bright red colour) network in the cross-section of the rhino and pig back skin dermis, (a) rhino in Ref.  (b) pig in Ref. .

Figure 3

(a) The Langer’s lines, (b) the fibre mesh, (c) the 2D mobile fibre network proposed in Ref.  with slip joints, and (d) a 2D mobile fibre network with fixed joints, and (e) a woven 2D network in Ref. .

Figure 4

Locations of the skin of interest, with the two specimens harvested along the spine and the perpendicular directions, and the mean fibre orientation β is shown on the right.

Figure 5

The Cauchy stress-stretch curves from the GOH and the damage models of the human skin samples, compared to the experimental data from, Ref. for case A (the GOH model with κ and β fixed), case B (damage model with, κ fixed), case C (damage model with β fixed), case D (damage model with both β and κ fixed), and case E (damage model with both β and κ free).

Figure 6

The computed and measured Cauchy stress-stretch curves of animal and human skins, for case F: swine back skin at the strain rate of 2500 s⁻¹ in Ref. , case G: swine back skin at the strain rate of 0.01 s⁻¹ in Ref. , case H, swine belly skin, case I: foetal calf back skin, case J, human back skin at the strain rate of 0.012 s⁻¹, and case K, rhino back skin.

Figure 7

The partial derivatives of the strain energy function plotted against the stretches in Case B for specimen 1 and specimen 2. These are plotted as two groups, with the group-II (∂W/∂μ, ∂W/∂ζ, ∂W/∂k ₁, ∂W/∂k ₂, ∂W/∂m) being the orders of magnitude smaller than the group-I (∂W/∂β, ∂W/∂κ, ∂W/∂ξ).

Figure 8

The Cauchy stress components σ ₁, σ ₂, plotted in terms of fibre stretch λ _f. Tissue damage occurs at the stretches when the stresses peak. In cases G, I and J, damage occurs in fibres only since both specimen are damaged at the same fibre stretch. However, in case H, some damage must exist in the matrix as the two samples are damaged at different fibre stretches.