Elastic linear, bilinear, nonlinear exponential and hyperelastic skin models

Linear, bilinear, exponential and hyperelastic models of human back skin are analyzed. The results showed that the elastic properties of tissues depend on its location and are best described by exponential functions σ = a ·exp( b ·ε) - 1), where a and b are material constants that depend on the localization and orientation of the samples along relation to the Langer lines. The parameters of elastic differential moduli E (ε) of tissues (minimum, average and maximum values) are determined. The differential modulus of elasticity is incremental (increasing with strain from 8.57 to 154.44 MPa), and the regression equation has the form E = a · b ·exp( b ·ε) ( r = 0.998) and very accurately characterizes its elastic behavior. The Young's modulus of samples parallel to the Langer lines is higher than in the oblique (45º) and transverse directions, and in the middle part of the back is higher than in the upper and lower parts ( Eav (ε) = 56.59, 35.76, 21.74 MPa, respectively), the elastic anisotropy coefficient is 3.49. Linear ( r = 0.965) and bilinear ( r = 0.967) elastic models are considered, and the numerical values of the model parameters are determined. To study the hyperelastic properties of the skin, neo-Hooke, Mooney-Rivlin, Ogden, polynomial and Veronda-Westmann ( V - W ) phenomenological models were used. The calculations were carried out using the Mathcad 13.0 computer algebra system and the ANSYS 2022 R 2 multipurpose software package. The parameters of the models and the closeness of the correlation between experimental and calculated data are determined. The correlation coefficient was used as a criterion for the correspondence between models and real properties of tissues. The polynomial model ( r = 0.9997) and the Veronda-Westmann model ( r = 0.999) demonstrated the highest correlation with the experimental values, the Ogden model ( r = 0.891) and the neo-Hookean one ( r = 0.935) demonstrated the lowest correlation with the experimental values. The values of Young's moduli and other elastic and hyperelastic characteristics of tissues were compared to study the factors influencing the mechanical behavior of human back skin.