Abstract
The strain energy function of hyperelastic material models must fulfill some mathematical conditions to satisfy requirements such as numerical stability and physically plausible mechanical behavior. In the framework of computer simulations with Newton-type methods, numerical stability is assured by the positive definiteness of the tangent operator. The Baker-Ericksen inequalities, on the other hand, are sufficient and necessary conditions in order to guarantee that the material behaves in a physically plausible way, although they are rarely taken into account during parameter identification. The present work proposes a modification in the strain energy function of a previously developed model for isotropic rubber-like materials. The new expression for W allows the satisfaction of both of the aforementioned requirements. The complete constitutive framework for its implementation in a Finite Element code is provided. Representative examples are analyzed and to show the superior performance when compared to well-known models found in the specialized literature both for homogeneous and non-homogeneous cases of deformation.
Highlights
The increasing application of rubber-like materials in engineering components and structures throughout the last decades has led engineers to better understand the inherently non-linear mechanical behavior of this class of materials
When dealing with hyperelastic materials, due to the large variety of different materials, together with the fact that both their chemical composition and manufacturing process strongly affect their mechanical behavior in service, it is virtually impossible to define one single strain energy function that would work to any hyperelastic material
A hyperelastic model providing simultaneously numerical stability and consistent physical behavior is proposed for rubber-like materials in the context of finite element method (FEM). This was accomplished by a mathematical modification in the strain energy function of the model proposed by Hoss et al (2011), as it was detected that their original model was not able to fulfill both requirements at the same time
Summary
The increasing application of rubber-like materials in engineering components and structures throughout the last decades has led engineers to better understand the inherently non-linear mechanical behavior of this class of materials. When dealing with hyperelastic materials, due to the large variety of different materials, together with the fact that both their chemical composition and manufacturing process strongly affect their mechanical behavior in service, it is virtually impossible to define one single strain energy function that would work to any hyperelastic material. In this sense, the ultimate goal of researchers in the field is to propose a strain energy function that models accurately the largest possible majority of different rubber-like materials, while calibrating them from a set of experimental data and predicting with acceptable accuracy their mechanical behavior when subjected to different deformation modes.
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