On hyperelastic modeling of metals

In this study, the possibilities of hyperelastic modeling of metallic materials are discussed. The so-called four-parameter model which was postulated by Goel et al. (Int. J. Solids Struct. 48:2977-2986, 2011) in order to simulate the mechanical behavior of metals is analyzed. Experimental data obtained for various materials are utilized to investigate the ability of the aforementioned model to mimic the stress-strain response of metals. For many of the analyzed materials, very good curve-fitting results are achieved. The finite element (FE) implementation of this particular model is not straightforward as the derivatives of the stored energy function are undefined in the natural undeformed state. In this work, a method allowing to overcome this problem is proposed. What is more, it is found that another elastic energy function which was proposed by Knowles (Int. J. Fract. 13:611-639, 1977) is very effective at simulating the highly nonlinear stress-strain characteristics of some metals such as aluminum or brass, for instance. A general-purpose user subroutine UMAT (User's MATerial) has been developed allowing to implement any first invariant-based hyperelastic models into the FE program CalculiX. The UMAT code is attached in the Appendix. The subroutine is utilized in several FE simulations in order to verify its performance. The available experimental data are used to determine the material parameters of the popular Ramberg-Osgood model. It is found that the discussed hyperelastic models allow to describe the mechanical response of metals more accurately than the Ramberg-Osgood model. Furthermore, it is demonstrated that the hyperelastic models are characterized by better convergence during the FE analysis.

Automated summary

This study discusses the potential of hyperelastic modeling for metallic materials, analyzing the performance of a four-parameter model and another elastic energy function. A general-purpose user subroutine is developed to implement hyperelastic models, and their accuracy in describing the mechanical response of metals is verified using experimental data. The study also highlights the superior convergence of hyperelastic models in finite element analysis.