Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model

The collagen network in skin is largely responsible for the nonlinear mechanical stress-strain response of skin. We hypothesize that the force-stretch response of collagen is governed by the entropics of long-chain molecules. We show that a constitutive model derived from the statistical mechanics of long-chain molecules, corresponding to the fibrous collagen network in skin, captures the mechanical response of skin. A connection between the physiologically meaningful parameters of network molecular chain density and free length of collagen fibers and the constitutively significant parameters of initial modulus and limiting stretch is thus established. The relevant constitutive law is shown to have predictive capabilities related to skin histology by replicating in vivo and in vitro experimental results. From finite element simulations, this modeling approach predicts that the collagen network in hypertrophic scars is more dense and the constituent collagen fibers have shorter free lengths than in healthy skin. Additionally, the model is shown to predict that as rat skin ages, collagen network density increases and fiber free length decreases. The importance of knowledge of the in situ stress state for analyzing skin response and validating constitutive laws is also demonstrated.