Nanomechanics of polymer gels and biological tissues: A critical review of analytical approaches in the Hertzian regime and beyond

We survey recent progress in the application of nanoindentation to characterize the local mechanical properties of polymer gels and biological tissues. We review the theories, analytical models based thereon, and data processing techniques commonly used to determine elastic properties of these classes of materials by instrumented nanoindentation. Examples from the testing of synthetic and biological gels are used to illustrate the limitations of existing theories and approaches. Emphasis is placed on the need for contact mechanics models that more accurately represent the large-strain behaviour of soft matter.