Man-Gong Zhang AML, Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China Jinju Chen School of Mechanical and System Engineering, Newcastle University, Newcastle Upon Tyne NE1 7RU, UK; Arthritis Research UK (ARUK) Tissue Engineering Centre, Newcastle University, Newcastle Upon Tyne NE1 7RU, UK Xi-Qiao Feng AML, Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China Yanping Cao 1 AML, Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China e-mail: caoyanping@tsinghua.edu.cn On the Applicability of Sneddon’s Solution for Interpreting the Indentation of Nonlinear Elastic Biopolymers Indentation has been widely used to characterize the mechanical properties of biopoly- mers. Besides Hertzian solution, Sneddon’s solution is frequently adopted to interpret the indentation data to deduce the elastic properties of biopolymers, e.g., elastic modulus. Sneddon’s solution also forms the basis to develop viscoelastic contact models for deter- mining the viscoelastic properties of materials from either conical or flat punch indenta- tion responses. It is worth mentioning that the Sneddon’s solution was originally proposed on the basis of linear elastic contact theory. However, in both conical and flat punch indentation of compliant materials, the indented solid may undergo finite deforma- tion. In this case, the extent to which the Sneddon’s solution is applicable so far has not been systematically investigated. In this paper, we use the combined theoretical, compu- tational, and experimental efforts to investigate the indentation of hyperelastic compliant materials with a flat punch or a conical tip. The applicability of Sneddon’s solutions is examined. Furthermore, we present new models to determine the elastic properties of nonlinear elastic biopolymers. [DOI: 10.1115/1.4027973] Keywords: indentation, biopolymers, dimensional analysis, finite element analysis, inverse method 1 Introduction Mammalian cells respond to the mechanical properties of bio- polymers as an extracellular matrix (ECM) [1–3]. This enables designing biomaterials with tailored mechanical properties for desired tissue regeneration. It has been recently reported that the cells may be more responsive to the local mechanical properties, instead of bulk properties, of ECM [4]. In this sense, measuring the local mechanical properties of biopolymers is of great impor- tance. The micropipette aspiration [5–14] or nanoindentation methods [15–23] can be used for this purpose and the present study is concerned with the latter. Nanoindentation enables characterizing the nano/micro- mechanics of materials, which are effective to assess the local mechanical properties of biopolymers. Many biopolymers are hyperelastic instead of linear elastic when they undergo large de- formation [3,24]. Therefore, it is important to investigate such hyperelastic behavior during indentation. The Sneddon’s solution is widely used in the literature to interpret the indentation responses and infer the elastic properties of compliant materials. However, this classical solution was originally derived by using the linear elastic contact theory and assumes small deformation of the indented solid. To date, it remains unclear to what extent the Sneddon’s solution is applicable to the indentation of biopolymers in the presence of both geometric and material nonlinearities. In the present paper, we will address this issue through dimensional analysis [25] and finite element simulations. To illustrate the deformation mechanisms, we will consider two typical indenter geometries, i.e., flat punch and conical tip, as shown in Fig. 1. The paper is organized as follows. Dimensional analysis is car- ried out in Sec. 2 to characterize the relations between indentation responses and material properties, whose explicit forms are deter- mined by finite element simulations in Sec. 3. Three widely used hyperelastic models are adopted in this study, including neo- Hookean, Mooney–Rivlin, and Arruda–Boyce models. In Sec. 4, the applicability of the Sneddon’s solution to the measurement of the initial shear modulus of biopolymers is examined. Experi- ments were conducted in Sec. 5 to validate the theoretical and computational results. In Sec. 6, the possibility to determine the other hyperelastic properties of biopolymers using the flat punch and conical indentation is discussed. Section 7 gives the conclud- ing remarks. 2 Dimensional Analysis on the Indentation of Hyperelastic Materials First, we use dimensional analysis to correlate the indentation responses and material properties. Dimensional analysis is fre- quently used to derive the relationships between the physical quantities involved in a phenomenon [25] and has been success- fully adopted to analyze the indentation tests [16]. Three typical hyperelastic models, i.e., neo-Hookean, Mooney–Rivlin [26,27] and Arruda–Boyce [28] models are used in this study. These mod- els have been already implemented in commercial finite element software, e.g., ABAQUS [29] and the corresponding strain energy 1 Corresponding author. Contributed by the Applied Mechanics of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 23, 2014; final manuscript received July 4, 2014; accepted manuscript posted July 9, 2014; published online July 16, 2014. Editor: Yonggang Huang. 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