## Modelling and instrumented nanoindentation of compliant and hydrated materials

Biological tissues are highly dynamic structures that undergo constant remodelling over an individual's life to sustain the multiple mechanical stimuli to which they are subjected. Tissue function and behaviour are intimately related to the native tissue's hierarchical structure. It has been observed that ageing and age-related disease often lead to an altered mechanical response of a tissue, and as a consequence, results in a reduction of life quality in the ageing population. Therefore over the last couple of decades the has been a growing interest in relating tissue physiological functions with observed mechanical response. \\ Contact based techniques such as nanoindentation have been often used to extract the material properties of soft polymers, gels, and tissues over the last decade, showing a promising potential for tissue characterisation over a range of length scales. However, multiple issues arise when characterising highly compliant and hydrated materials (e.g. soft tissues, and hydrogels) since indentation devices were initially engineered for hard material characterisation. In this work experimental indentation is combined with iterative Finite Element Analysis to extract meaningful mechanical properties from indentation time-displacement curves. The time-dependent behaviour of thin films deposited onto stiff substrates was studied because this represents the format of histological sections, commonly used for the study of tissue. For this purpose two model materials exhibiting time-dependent mechanical response similar to human tissue were chosen: PDMS and pHEMA with EGDMA as cross-linker.The present work addresses a well-known issue for thin material characterisation via indentation: the so-called thickness effect. A strong influence of specimen thickness was observed on the nanoindentation response of the films and the material properties extracted using the Oliver and Pharr analysis. Hence a fully automated iterative FE algorithm was used to extract the viscoelastic and poroelastic material properties from the indentation data. It is demonstrated that the onset of the substrate effect occurs normalized film thickness $\delta_{norm} \leqslant 10$ where $\delta_{norm}=\frac{\delta}{\sqrt{Rh}}$ ($\delta:$ film thickness, $R:$ indenter radius,$h:$indentation depth). If a half space condition is assumed, the error in the estimation of the shear (and elastic) modulus via the Hertz contact theory is over a factor of 3.5 to 4.5 for films with a thickness of \$\delta