Macroindentation of a soft polymer: Identification of hyperelasticity and validation by uni/biaxial tensile tests

In this paper, the Ogden model is employed to characterize the hyperelastic properties of rubber, and on the basis of a pattern search algorithm and the Levenberg-Marquardt algorithm, a professional method that can realize the comprehensive fitting of the uniaxial tension, biaxial tension, planar tension, and simple shear experimental data of hyperelastic materials was developed. The experiment data from Treloar (1944) was fitted very well, and the determined parameters by using this method were proven correct and practical in the numerical verification in ANSYS. Then, the constitutive model of the hyper-viscoelastic materials combining the Ogden model with the generalized Maxwell model was explained in detail, and the parameter identification method was also proposed by using the pattern search method. Then, three groups of relaxation tests of uniaxial tension and four groups of simple shear tests with different loading velocities were conducted to obtain the corresponding virtual experiment data. After discussing the constraints and initial setting values for the undetermined parameters, these virtual data of different loading histories were respectively employed to identify the parameters in the hyper-elastic model, and the accuracy and the reliability of the estimated parameters were also verified in ANSYS.

Parameter Identification Methods for Hyperelastic and Hyper-Viscoelastic Models

Identification of finite viscoelasticity and adhesion effects in nanoindentation of a soft polymer by inverse method

The mechanical behavior of the cortical bone in nanoindentation is a complicated mechanical problem. The finite element analysis has commonly been assumed to be the most appropriate approach to this issue. One significant problem in nanoindentation modeling of the elastic-plastic materials is pile-up deformation, which is not observed in cortical bone nanoindentation testing. This phenomenon depends on the work-hardening of materials; it doesn't occur for work-hardening materials, which suggests that the cortical bone could be considered as a work-hardening material. Furthermore, in a recent study [59], a plastic hardening until failure was observed on the micro-scale of a dry ovine osteonal bone samples subjected to micropillar compression. The purpose of the current study was to apply an isotropic hardening model in the finite element simulations of the nanoindentation of the cortical bone to predict its mechanical behavior. The Johnson-Cook (JC) model was chosen as the constitutive model. The finite element modeling in combination with numerical optimization was used to identify the unknown material constants and then the finite element solutions were compared to the experimental results. A good agreement of the numerical curves with the target loading curves was found and no pile-up was predicted. A Design Of Experiments (DOE) approach was performed to evaluate the linear effects of the material constants on the mechanical response of the material. The strain hardening modulus and the strain hardening exponent were the most influential parameters. While a positive effect was noticed with the Young's modulus, the initial yield stress and the strain hardening modulus, an opposite effect was found with the Poisson's ratio and the strain hardening exponent. Finally, the JC model showed a good capability to describe the elastoplastic behavior of the cortical bone.

https://hal.archives-ouvertes.fr/hal-02282870/document

Application of the Johnson-Cook plasticity model in the finite element simulations of the nanoindentation of the cortical bone.

Micromechanical Characterization of Metal Foams

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®. A linear viscoelastic model for small strain, based on a general Maxwell rheological model is currently applied to describe the rate-dependent 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.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/zamm.201100170

Z. Chen

Papers

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