title: Finite element simulation for the mechanical characterization of soft biological materials by atomic force microscopy.
abstract: The characterization of the mechanical properties of soft materials has been traditionally performed through uniaxial tensile tests. Nevertheless, this method cannot be applied to certain extremely soft materials, such as biological tissues or cells that cannot be properly subjected to these tests. Alternative non-destructive tests have been designed in recent years to determine the mechanical properties of soft biological tissues. One of these techniques is based on the use of atomic force microscopy (AFM) to perform nanoindentation tests. In this work, we investigated the mechanical response of soft biological materials to nanoindentation with spherical indenters using finite element simulations. We studied the responses of three different material constitutive laws (elastic, isotropic hyperelastic and anisotropic hyperelastic) under the same process and analyzed the differences thereof. Whereas linear elastic and isotropic hyperelastic materials can be studied using an axisymmetric simplification, anisotropic hyperelastic materials require three-dimensional analyses. Moreover, we established the limiting sample size required to determine the mechanical properties of soft materials while avoiding boundary effects. Finally, we compared the results obtained by simulation with an estimate obtained from Hertz theory. Hertz theory does not distinguish between the different material constitutive laws, and thus, we proposed corrections to improve the quantitative measurement of specific material properties by nanoindentation experiments.
authors.affiliation: Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research, Department of Mechanical Engineering, University of Zaragoza, Zaragoza, Spain. Electronic address: claraval@unizar.es.
authors.forename: C
authors.initials: C
authors.lastname: Valero
authors.affiliation: Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research, Department of Mechanical Engineering, University of Zaragoza, Zaragoza, Spain.
authors.forename: B
authors.initials: B
authors.lastname: Navarro
authors.affiliation: Institute for Bioengineering of Catalonia, 08028 Barcelona, Spain; Centro de Investigación Biomédica en Red de Enfermedades Respiratorias, 28029 Madrid, Spain; Facultat de Medicina, Universitat de Barcelona, 08036 Barcelona, Spain.
authors.forename: D
authors.initials: D
authors.lastname: Navajas
authors.affiliation: Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research, Department of Mechanical Engineering, University of Zaragoza, Zaragoza, Spain.
authors.forename: J M
authors.initials: JM
authors.lastname: García-Aznar
mesh_terms: D003198:Computer Simulation; D004548:Elasticity; D020342:Finite Element Analysis; D008422:Materials Testing; D018625:Microscopy, Atomic Force; D008954:Models, Biological; D013314:Stress, Mechanical
keywords: AFM; Cell mechanics; FEM; Nanoindentation; Soft-tissue