Chapter 8 A Numerical Study of a Biaxial Sollicitation to Set-Up the Displacement Field Measurement of Ex Vivo Mouse Skin J.-S. Affagard, F. Wijanto, R. Rubio Amador, C. Bonod-Bidaud, F. Ruggiero, and J.-M. Allain Abstract The behavior of the skin is an important issue in many applications, but is always not well understood. Nevertheless, skin is well-known to be mainly composed of collagen and has a very hierarchical microstructure that influences its mechanical behavior at different scales. To correlate and to characterize the macroscopic behavior with the microstructure, a bi-axial tensile test coupled with a macroscopic (digital image correlation) and microscopic (second harmonic generation) measurement has been developed. This study aims at presenting the method used to identified the mechanical properties of mice ex vivo skin. A full-field displacement is firstly acquired using digital image correlation (DIC) and, then, a specific finite element model is used to optimize the mechanical properties. The skin is modelled with a Holzapfel hyperelastic behavior which presents the particularity of being strongly based on the microstructure. The purpose of this article is to prepare the identification process. To this aim, a sensitivity approach is developed to choose the configuration with the highest sensitivity. Finally, the displacement and strain field is measured with DIC. Keywords Biomechanics • Biaxial traction • Mice skin • Digital image correlation (DIC) • Anisotropy 8.1 Introduction The behavior of the skin is not always well understood, but is an important issue in many applications where the understanding of soft tissues appears as quite important in order to better understand the organs behaviors in the physiological or pathological context. For instance, the design of devices such as car seats, wheelchairs or razors where stress distribution could be an ergonomic indicator. The understanding of the phenomena involved can be difficult to analyze through in vivo mechanical tests. For this main reason, ex vivo experiments where the mechanical stresses are controlled, are much more frequent. Ex vivo studies can be separated in two categories: uniaxial traction and multiaxial sollicitation. Firstly, with a monotonic tension test, basic biomechanical performances such as elastic modulus and ultimate tensile strength were characterized [1–4]. To go further in the skin mechanical behavior description, the viscoelastic properties were characterized through various strain rates [5–7], relaxation or creep test [8]. Finally, the preconditioning and fatigue were assessed thanks to uniaxial cyclic loading [9]. The multiaxial sollicitation are more relevant to characterize the influence of the microstructure [10, 11]. Indeed, in [12, 13] a biaxial tension was compared with a uniaxial traction. The results highlighted the relaxation differences induced by the transverse loading and a structural theory of the relationships in flat collagenous tissues was then proposed [14]. In [15], a multi-axial experiment was designed to characterise the two dimensional elastic properties of human skin, and, to go further in the mechanical behavior characterisation, from uniaxial and multiaxial sollicitation, to better describe the heterogeneities, the displacement field is measured. In [3, 16] the deformation field is measured on skin tissue. Before analysis, a fine grid is drawn to obtain the displacement field. The results show strong non-linearities from the reorganization of the collagen fibers during the test. In [17, 18], the displacement field was quantified from a uniaxial test to identify the Young’s modulus anisotropy of rat and human skin. Nevertheless, uniaxial testing provides few information on anisotropy and it is therefore necessary to develop multi-axial test. To identify a behavior close to the anisotropic one proposed in [19], a multiaxial tests were performed and coupled with a cross correlation technique [20]. In multiaxial tests, and more particularly in biaxial tests, the difficulties associated with J.-S. Affagard (*) • F. Wijanto • J.-M. Allain Laboratoire de Me´canique des Solides (LMS), Ecole Polytechnique, CNRS, Universite´ Paris-Saclay, 91128 Palaiseau, France e-mail: affagard@lms.polytechnique.fr R. Rubio Amador • C. Bonod-Bidaud • F. Ruggiero Institut de Ge´nomique Fonctionnelle de Lyon, ENS-Lyon, CNRS, Universite´ Lyon 1, Lyon, France #The Society for Experimental Mechanics, Inc. 2017 C.S. Korach et al. (eds.), Mechanics of Biological Systems and Materials, Volume 6, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-41351-8_8 53
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