Modern electromagnetic research has penetrated various fields. In recent years, with the rapid development of new technologies such as 5G, electric vehicles, and IoT, the role of electromagnetic analysis has become more and more important. Electromagnetics simulation has been widely and successfully applied to many aspects of electromagnetic performance prediction and design. Under the premise of reasonably setting the model and parameters, electromagnetic simulation can replace experiments in many aspects, and provide great help for the rapid development of electromagnetic devices.

Although electrostatics is a relatively simpler type of electromagnetic analysis, it has a wide range of applications and acts…

With the development of computer graphics, hardware, and 3D printing technology, graphic rendering and its file format based on surface triangle mesh have become more and more popular. In finite element analysis (FEA), engineers sometimes get geometry files based on triangle meshes (such as STL files, etc.) and perform subsequent analysis. Due to the fundamental difference between the surface triangle mesh and the finite element mesh, the surface mesh cannot be directly used in the computation of the finite element method. It is necessary to convert the surface mesh into FEA mesh for the successive analysis. …

Curve fitting is a numerical process often used in data analysis. Its essence is to apply a certain model (or called a function or a set of functions) to fit a series of discrete data into a smooth curve or surface, and numerically solve the corresponding parameters, thereby obtaining the relationship between the coordinates represented by the discrete points and the function. Curve fitting can help us understand the internal connection between data and predict the trend of such problems. …

When a finite element analysis model contains hyperelastic materials, engineers usually have little substantial data to help get the results. Sometimes a lucky engineer will have some tension or compression stress-strain test data, or simple shear test data. Processing and applying these data is a critical step to analyze the hyperelastic models. Particularly, the curve-fitting of these data to obtain the material constants is of importance. In this article, we will learn about the test data related to the hyperelastic model and its curve fitting. An example of curve-fitting in MatEditor will be given at the end of this article.

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The core loss of magnetic components plays an important role in engineering practices. Particularly at high-frequency conditions, the loss of magnetic components accounts for a large proportion of the energy loss of the whole unit. Most manufacturers provide the core loss curve in the product manuals. The core loss also has corresponding theoretical models and coefficients. Some core material manufacturers give these coefficients, but some manufacturers do not provide it. In this scenario, the user needs to perform curve-fitting on the core loss curves to obtain the parameters by themselves. …

In previous articles, we have introduced Arruda-Boyce, neo-Hookean, Mooney-Rivlin, Yeoh, Gent, Blatz-Ko and other hyperelastic models that often used in nonlinear finite element analysis. Now we will be discussing a special and widely applied hyperelastic model: Ogden. A versatile model that can be used for rubber, polymer, and biological tissues. The Ogden model has been successfully applied to the analysis of o-rings, seals and other industrial products. Its most special feature in the theoretical algorithm is that the principal stretches are used as the independent variable, rather than the strain tensor invariant. Like other hyperelastic models such as Mooney-Rivlin, Ogden…

We have introduced the hyperelastic models commonly used in finite element analysis such as Arruda-Boyce, neo-Hookean, Mooney-Rivlin, Yeoh, and Gent. In this article, we will be discussing a very special hyper-elastic model: Blatz-Ko. The most hyperelastic models are mainly designed for incompressible materials, while Blatz-Ko is very suitable for modeling the compressible hyperelastic materials, such as the foamed rubber. Because of the simplicity of math form, Blatz-Ko has been one of the most widely used constitutive models for compressible isotropic nonlinearly elastic solids. Blatz-Ko model is named after Dr. Blatz and Dr. Ko, for their contribution to this hyperelastic model.

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In previous articles, we introduced Arruda-Boyce, neo-Hookean, Mooney-Rivlin, and Yeoh hyperelastic models. Today, let’s discuss another well-known hyperelastic model: Gent. A phenomenological model of rubber elasticity that is based on the concept of limiting chain extensibility. In this model, a simple mathematical form is used to describe the nonlinear constitutive model of rubber. Like most hyperelastic models, Gent is a model named after a person’s surname. Thanks to Dr. Gent for his contribution to this hyperelastic model.

In 1996, Gent published a short paper called “A new constitutive relation for rubber” in the journal “Rubber Chemistry and Technology” that proposed…

Previously, we discussed the Arruda-Boyce, neo-Hookean, and Mooney-Rivlin models. In this article, we will be talking about the Yeoh hyperelastic model, also called the Reduced Polynomial model. Yeoh model is anther hyperelastic model named after a person’s surface name, to thank Oon Hock Yeoh for his contribution to the rubber mechanics.

In 1990, Yeoh noted in investigations on a black-filled rubber that the material showed a significant decrease of shear modulus at low strains. Later he observed the same phenomena in unfilled rubber. Yeoh proposed to consider the observation in the hyperelastic model by adding an exponentially decaying term to…

In previous articles, we have introduced the hyperelastic model in nonlinear finite element analysis, and also introduced the well-known Arruda-Boyce and neo-Hookean models in detail. Today we will be discussing another famous hyperelastic model: Mooney-Rivlin.

Mooney-Rivlin is named after the surname combination of two physicists, M. Mooney and R. S. Rivlin. In 1940, Mooney published a paper entitled “A theory of large elastic deformation” in the Journal of Applied Physics. Eight years later, in 1948, Rivlin published a paper “Large elastic deformations of isotropic materials” in Philosophical Transactions of the Royal Society of London. Those two papers build the essence…

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