Simulated Soft Tissue Nanoindentation: A Finite Element Study

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Abstract
To address the growing interest in nanoindentation for biomaterials, the following finite element study investigated the influence of indentation testing protocol and substrate geometry on quasi-static and dynamic load-displacement behavior of linear viscoelastic materials. For a standard linear solid, the conventional quasi-static indentation modulus, EQS, fell between the instantaneous and equilibrium modulus of the model. EQS approached the equilibrium modulus only for indentation unloading times 1000 times greater than the characteristic relaxation time of the model. It was nearly insensitive to other changes in the indentation testing protocol, such as tip radius and penetration depth, exhibiting variations of only 5–10%. Dynamic nanoindentation provided a quantitatively accurate assessment of the complex dynamic modulus (within ±12%) for a range material of parameters at physiologically relevant testing parameters. Both quasi-static and dynamic moduli calculated from the irregular surfaces varied with the size and shape of the irregularities but were still within 10% of the smooth surface values for penetration depths larger than the dimensions of the surface irregularities.