Parameter re‐identification in nanoindentation problems of viscoelastic polymer layers: small deformation

Abstract

Recently, nanoindentation became a new but all the same a primary testing technique of thin layers. A wide application of nanoindentation in polymeric layers is obstructed by the analysis method, which is used to extract the rate-dependent properties. In the present paper, the inverse method based on the finite element simulation and numerical optimisation is used to characterise the viscoelastic properties of polymers from nanoindentation. First of all, the boundary value problems using nanoindentation of polymer layers considering real geometry, is simulated with the FE code ABAQUS R . A linear viscoelastic model for small strain, based on a general Maxwell rheological model is currently applied to describe the ratedependent material behaviour. The rate-dependent properties of the polymer layer under nanoindentation is investigated with various loading histories: cyclic testing, single step relaxation, monotonic testing, and sinusoidal oscillatory testing. A parameter re-identification strategy offers a deep insight into the relationship between the accuracy of identification and the loading history associated with the rate-dependent material model. A method to choose a suitable loading history to identify the parameters more accurately is recommended.

Parameter Identification Methods for Hyperelastic and Hyper-Viscoelastic Models

“…Hence, the relaxation tests of uniaxial tension and the simple shear tests with different loading velocities are taken as examples in this study. Due to the lack of appropriate data for these experiments, we followed the method applied in Chen et al [24][25][26] and got the corresponding virtual experiment data by using ANSYS, in which we assume the hyperelastic parameters are the same with the last group in Table 1, and the viscoelastic part is characterized by the following Prony series, …”

“…Amin et al proposed an improved hyperelastic constitutive equation for rubbers in compression and shear regimes [1,22,23], the parameters in the equation were identified by experiment data and a nonlinear viscous coefficient was introduced to represent the rate-dependent properties. In recent years, a novel testing technique, named nanoidentation, to identify the material parameters for thin polymer layers was developed, a comprehensive review and the realization of the method for hyperelastic and viscoelastic models are presented by Chen et al [24][25][26] In this paper, the Ogden model is taken to characterize the hyperelastic properties of rubber-like materials. A professional method based on the pattern search algorithm (PSA) [27,28] and the Levenberg-Marquardt algorithm (LMA) [29] was developed to fit the unixial tension, biaxial tension, planar tension, and the simple shear experimental data of hyperelastic materials.…”

“…A professional method based on the pattern search algorithm (PSA) [27,28] and the Levenberg-Marquardt algorithm (LMA) [29] was developed to fit the unixial tension, biaxial tension, planar tension, and the simple shear experimental data of hyperelastic materials. Then, combining the generalized Maxwell model and the Ogden model as the constitutive model, the method that can identify the parameters in the hyper-viscoelastic models by using experimental data with different loading histories was also developed [24,25] and three groups of virtual relaxation tests and four groups of simple shear tests were employed to verify the accuracy and reliability of the proposed method.…”

Axisymmetric indentation of an elastic thin plate by a rigid sphere revisited

“…On the other hand, finite element methods were used by some researchers to investigate the indentation problem of a thin layer (see e.g. Gan et al, [18] Wagih et al [19] and Chen and Diebels [20] ).…”

The influence of chemical degradation and polyethylene glycol on moisture-dependent cell wall properties of archeological wooden objects: a case study of the Vasa shipwreck

“…There it is known to act as a softening plasticizer, breaking secondary hydrogen bonds between the cell wall polymers (Hoffmann 1988;Wallström and Lindberg 1995). Due to short holding times and variations in indentation forces, the measured indentation creep values cannot be regarded as material parameters to the same extent as M and H. Although rheological material parameters can be identified from NI curves in isotropic substrates (Jäger et al 2007;Chen and Diebels 2013), the viscoelastic anisotropic nature of the wood cell wall requires substantially more experimental data in different indentation directions and modeling work to characterize the creep material behavior. Nevertheless, the presented indentation creep data can be used for qualitative comparisons between the tested samples.…”