Viscohyperelastic Calibration in Mechanical Characterization of Soft Matter
The usual assumption made in mechanical characterization of soft tissues with Atomic Force Microscopy (AFM) is that the specimen behaves as a purely elastic material. Recent investigations have shown that in the case of immature porcine zona pellucida (ZP
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Viscohyperelastic Calibration in Mechanical Characterization of Soft Matter E. Ficarella, L. Lamberti, M. Papi, M. De Spirito, and C. Pappalettere Abstract The usual assumption made in mechanical characterization of soft tissues with Atomic Force Microscopy (AFM) is that the specimen behaves as a purely elastic material. Recent investigations have shown that in the case of immature porcine zona pellucida (ZP) samples viscous effects become more significant for sharp tips. Interestingly, a linear relationship between the limit indentation rate and the geometry of the AFM probe was derived, which is similar to the relationship existing between hardness and radius of curvature of the indenter typically observed for elasto-plastic materials. This study will analyze soft biotissues with different elasticity and viscous properties showing different response to nanoindentation. The relationship between limit indentation rate and tip geometry will be derived for each material to confirm previous experimental observations. Keywords Soft matter • Mechanical characterization • Atomic force microscopy • Probe geometry • Indentation rate • Viscous effects
5.1
Introduction
Atomic Force Microscopy (AFM) is very suitable for mechanical characterization of soft matter because the nanometric dimensions of the probe allow to analyze the local behavior of the sample while other techniques causing microscopic deformations of the sample can only monitor equivalent properties of a large amount of material. In the last 10 years, AFM was used for characterizing mechanical behavior of cells and biopolymer networks [1–8]. Aspects related to calibration of nanoindentation measurements [9], sensitivity of finite indentation response to probe geometry [10] and residual stresses [11] also were studied. The typical assumption made in atomic force spectroscopy is that materials are purely elastic: different constitutive laws ranging from linear elasticity to hyperelasticity were hypothesized. Viscoelastic effects can be neglected if quasi-static tests are performed [12]. However, recent investigations [13] proved that viscous forces may govern the nanoindentation response of biopolymer networks even at rather low indentation rate. Experimental determination and modeling of viscoelastic behavior of soft materials is well documented in literature [13–22]. The present authors developed a visco-hyperelastic model to describe the nanoindentation response of immature porcine zona pellucida (ZP) membranes [23]. The hyperelastic behavior was described by the Arruda-Boyce constitutive law while the viscous response was defined by a N-terms Prony series expansion of the dimensionless relaxation modulus. By comparing finite element computations and AFM data at different indentation rates, it was possible to separate hyperelastic behavior and viscous effects. In [24], a systematic study attempted to determine for each geometric configuration of the AFM tip, the limit indentation rate above which viscous effects must be taken into account to correctly deter
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