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In this research, the hyperelastic strain energy density function based on the exponential–logarithmic invariant is extended to the visco-hyperelastic constitutive model to describe the mechanical characteristics of the rate dependence and large deformations of rubber-like materials. On the basis of the general regression neural network (GRNN) technique, a parameter identification approach for the visco-hyperelastic model is designed. In addition, the proposed research scheme is verified using various uniaxial experimental data of rubber-like materials. The comparison results reveal that the predicted stress responses agree well with the experimental data under different loading conditions. This paper concludes that the present model can describe the mechanical behavior of rubber-like materials and that the GRNN-based approach is practicable for parameter identification of complex visco-hyperelastic constitutive models. [ABSTRACT FROM AUTHOR]

A statistically based strain energy is proposed for rubber-like materials at large stretches. It is based on the micro-mechanically vectorial modeling of a single polymer chain, and its entropy is used in order to account for the entropic elasticity of rubbery macromolecules. We propose a framework for derivation of a microscopic free energy function based on a multidimensional form of a generic normal (Gauss) probability distribution function (pdf). Homogenization of the microscopic free energy by means of statistical tools renders a macroscopic free energy. The random variables of the general formulation are specified as bond angle differences, representing bending and torsion, respectively, for each bead of the single chain. A further step is a formulation of both quantities in terms of the applied stretch, which eventually renders the macroscopic strain energy as a hyperelastic energy function. Additionally, we propose a methodology to satisfy a normalization condition for the related integral of the pdf over the constraint statistic domain. A numerical example illustrates the capability of the proposed energy function to simulate the S-shape behavior of the well-known experimental data for vulcanized rubbers by Treloar (Trans Faraday Soc 40:59–70, 1944). [ABSTRACT FROM AUTHOR]

A three parameter novel hyperelastic strain energy function is introduced in this paper for soft and rubber-like materials. The function integrates a non-separable exponential component with a single term Ogden-type polynomial-like function, resulting in an exponential-polynomial based strain energy function. This helps in capturing both small and large deformation (stretch) behaviours of hyperelastic materials. The structure of the model is simple and validated against several experimental datasets including rubbers, hydrogel, and soft tissues. The model is reported to capture key material behaviors, including strain stiffening and various deformation paths. Through comparative studies with well-known models like the Ogden (six parameters) and Yeoh (three parameters), the model's effectiveness is established. Furthermore, the model successfully addresses pressure-inflation instability in thin spherical balloons. It's applicability extends to biological materials, as evidenced by its effectiveness in characterizing porcine brain tissue and a monkey's bladder. [Display omitted] • A three parameter strain energy function for soft and rubber-like materials has been developed. • Combined an exponential component with an Ogden-type polynomial term. • Experimental data of rubbers, hydrogel, and soft tissue are used to validate the model. • The model effectively addresses pressure-inflation instability in thin spherical balloons. • Advantages of the model are illustrated through comparisons with Ogden and Yeoh models. [ABSTRACT FROM AUTHOR]

The application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure (P ) – inflation (λ or v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials. [ABSTRACT FROM AUTHOR]

In constitutive modelling of rubber-like materials, the strain-hardening effect at large deformations has traditionally been captured successfully by non-Gaussian statistical molecular-based models involving the inverse Langevin function, as well as the phenomenological limiting chain extensibility models. A new model proposed by Anssari-Benam and Bucchi (Int. J. Non Linear Mech. 2021; 128; 103626. DOI: 10.1016/j.ijnonlinmec.2020.103626), however, has both a direct molecular structural basis and the functional simplicity of the limiting chain extensibility models. Therefore, this model enjoys the benefits of both approaches: mathematical versatility, structural objectivity of the model parameters, and preserving the physical features of the network deformation such as the singularity point. In this paper we present a systematic approach to constructing the general class of this type of model. It will be shown that the response function of this class of models is defined as the [1/1] rational function of I 1 , the first principal invariant of the Cauchy–Green deformation tensor. It will be further demonstrated that the model by Anssari-Benam and Bucchi is a special case within this class as a rounded [3/2] Padé approximant in λ c (the chain stretch) of the inverse Langevin function. A similar approach for devising a general I 2 term as an adjunct to the I 1 part of the model will also be presented, for applications where the addition of an I 2 term to the strain energy function improves the fits or is otherwise required. It is concluded that compared with the Gent model, which is a [0/1] rational approximation in I 1 and has no direct connection to Padé approximations of any order in λ c , the presented new class of the molecular-based limiting chain extensibility models in general, and the proposed model by Anssari-Benam and Bucchi in specific, are more accurate representations for modelling the strain-hardening behaviour of rubber-like materials in large deformations. [ABSTRACT FROM AUTHOR]

The Mullins effect represents a softening phenomenon observed in rubber-like materials and soft biological tissues. It is usually accompanied by many other inelastic effects like for example residual strain and induced anisotropy. In spite of the long term research and many material models proposed in literature, accurate modeling and prediction of this complex phenomenon still remain a challenging task. In this work, we present a novel approach using deep symbolic regression (DSR) to generate material models describing the Mullins effect in the context of nearly incompressible hyperelastic materials. The two step framework first identifies a strain energy function describing the primary loading. Subsequently, a damage function characterizing the softening behavior under cyclic loading is identified. The efficiency of the proposed approach is demonstrated through benchmark tests using the generalized the Mooney–Rivlin and the Ogden–Roxburgh model. The generalizability and robustness of the presented framework are thoroughly studied. In addition, the proposed methodology is extensively validated on a temperature-dependent data set, which demonstrates its versatile and reliable performance. • Deep symbolic regression is applied to automatically generate accurate analytical models capturing the Mullins effect in elastomers. • Highly specific damage models accurately representing complex characteristics of the Mullins effect, including temperature-dependent effects are generated. • Validation of the framework with multiple data sets, including temperature-dependent experimental results. • Robustness and generalizability of the proposed framework under sparse data conditions are demonstrated. [ABSTRACT FROM AUTHOR]

In this contribution, a new form of the strain energy function is proposed to describe the hyperelastic behavior of rubber-like materials under various deformation. The proposed function represents an invariant-based model and contains two material parameters. The model was tested with the experimental data of vulcanized rubbers, collagen and fibrin. The material parameters are kept constant for a material subjected to different types of loading. Good agreement between model and experimental data was obtained for all materials. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we extend the Sussman–Bathe spline-based hyperelastic isotropic model to predict the behavior of transversely isotropic isochoric materials. The model is based on an uncoupled decomposition of the stored energy function and a generalization of the inversion formula used by Sussman and Bathe. The present extension introduces some approximations that, in all studied cases, do not yield relevant deviations from the experimental data. The isotropic model results in a particular case of the present formulation. Several possibilities of user-prescribed experimental data are addressed. The model is used to predict experiments of calendered rubber and of biological tissues. [Copyright &y& Elsevier]

The paper proposes benchmark problems on exact solutions of hyper-elastic analysis, which can be used to evaluate analysis capabilities of rubber-like materials provided by a finite element program or other approximate solution methods. Special attention was concentrated on analysis and derivation of the exact solutions for the thick-walled rubber cylinders under internal pressure and axial extension, the thick-walled rubber balloons under internal pressure and the rubber cylinders under torsion or tension-torsion. Deformation and stress analysis on the above three cases were conducted to provide equations and methods for data processing. Exact standard solutions of the problems combined with the strain energy function of generalized high-order polynomials are given. Numerical examples and evaluation results of two commercial packages that are in common use (ABAQUS and ANSYS) are presented. Good agreements are found in the comparisons between the present exact standard solutions and the simulation results. [ABSTRACT FROM AUTHOR]