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1049-AA06-06

Indentation of Nonlinearly Viscoelastic Solids Michelle L Oyen Engineering Department, Cambridge University, Trumpington Street, Cambridge, United Kingdom

ABSTRACT Much recent attention has been focused on the indentation of linearly viscoelastic solids, and analysis techniques have been developed for polymeric material characterization. However, there has been relatively little progress made in the development of analytical approaches for indentation of nonlinearly viscoelastic materials. Soft biological tissues tend to exhibit responses which are nonlinearly viscoelastic and are frequently modeled using a decomposition of the relaxation or creep function into a product of two functions, one time-dependent and the other stress- or strain-level dependent. Consideration here is for soft biological tissue-like responses, exhibiting approximately quadratic stress-strain behavior, which can be alternatively cast as linear dependence of elastic modulus on strain level. An analytical approach is considered in the context of indentation problems with flat punch, spherical and conical indenter shapes. Hereditary integral expressions are developed and solved for typical indentation experimental conditions including indentation creep, load-relaxation and monotonic constant load- or displacement-rate tests. Primary emphasis is on the deconvolution of material and geometrical nonlinearities during an indentation experiment. The simple analytical expressions that result from this analysis can be implemented for indentation characterization of soft biological tissues without the need for computationally- intensive inverse finite element approaches. INTRODUCTION Depth-sensing (instrumented) indentation testing, in which load and displacement are monitored during contact of a probe with a material surface, is a popular technique for measurement of local mechanical properties of a wide variety of engineering materials. This has been due in part to the wide-spread availability of commercial instruments for small-scale contact testing (“Nanoindentation”) along with the development of routine analytic technique for elastic-plastic [1,2], viscoelastic [3,4], poroelastic [5] and viscous-elastic-plastic [6,7] mechanical property deconvolution. Because of the capability for localized testing, nanoindentation testing is particularly well-suited to the mechanical analysis of biological materials, in which the mechanical properties can vary substantially from point to point [8]. These property variations result from local variations in tissue composition and microstructure, and the variations are frequently associated with the length-scales of extracellular matrix components (i.e. length scales of tens of nanometers to micrometers) and of cell activity (i.e. length scales of micrometers to tens of micrometers).

In common practice, the extensive load-displacement (P−h) responses are nonlinear under conditions of spherical or conical-pyramidal indentation even when the material is linearly elastic ( σ = Eε ). This nonlinearity