Balé Blaise - Academia.edu (original) (raw)

Papers by Balé Blaise

Research paper thumbnail of Characterization of the Preloaded Hyperelastic Materials Subjected to Linear Vibrations

Journal of Vibration Engineering & Technologies, Dec 25, 2023

This paper proposes the study of the visco-hyperelastic behavior of a rubber sample. This rubber,... more This paper proposes the study of the visco-hyperelastic behavior of a rubber sample. This rubber, coded as the BX rubber sample, is simultaneously loaded and subjected to linear vibrations. A multiplicative non-separable variables law of the Nashif has been used to model the behavior that depends on both stretch and frequency. This method allows splitting the intricately combined test performed jointly on both stretch and frequency. On the one hand, we use Young’s complex modulus E∗(휔) calculated from the experimental data, and on the other hand, the hyperelastic characteristics E(휆) of the same material obtained from the experimental tensile curve. The hyperelastic phenomenological Gent–Thomas model and the hyperelastic molecular Flory–Erman model are used to evaluate the combined complex modulus E∗(휆,휔). We obtain results that go in the physical sense, i.e, Young’s modulus increases when the material is stretched, while the damping decreases.

Research paper thumbnail of Improvement of HIA model and the impact of the inverse Langevin function proposed by Marchi and Arruda

Rheologica Acta, 2020

This research work is devoted to the improvement the Hybrid Integral Aproach (HIA) proposed by Ng... more This research work is devoted to the improvement the Hybrid Integral Aproach (HIA) proposed by Nguessong et al. for the characterization of the nonlinear elastic response of rubber-like materials. The improvement is based on the choice of the approximation of the inverse Langevin function for the molecular part and on the modification of the second term I 2 for the phenomenological part. Thus, in the new proposed model, we retain the approximation of the inverse Langevin function defined by Marchi and Arruda to improve the first term which represents the molecular part. With this approximation, the relative error is very minimal (0.0015%) compared to the others approximation existing. The second term of this proposed model comes from the Gornet et al. model. This model contents six rheological parameters optimized by the Levenberg-Marquardt method. Two sets of experimental data (Treloar data and Nunes and Moreira data), from the literature, are used to compare this proposed model with initial HIA model. With Treloar rubber, data the simple tension suffice to determine the parameter values. Thus, the fit of the experimental data has been shown to provide an accurate response and predictive description in biaxial tension and pure shear with the same sets of material parameters. Unlike with Moreira data, this proposed model gives directly the material parameters in simple shear with good correlation. On the other hand, comparison is made between the proposed model and the HIA model. The proposed model is most efficient, because the proposed model emerges from a very small relative errors with Treloar's experimental data: 0.01 0. 0.04 in simple tension, 0.02 ± 0.006 in biaxial tension and 0.07 ± 0.005 in pure shear.

Research paper thumbnail of Implementation of Particle Swarm Optimization Algorithm in Matlab Code for Hyperelastic Characterization

World journal of mechanics, 2021

The purpose of this paper is to demonstrate the applicability of Particle Swarm Optimization algo... more The purpose of this paper is to demonstrate the applicability of Particle Swarm Optimization algorithm to determine material parameters in incompressible isotropic elastic strain-energy functions using combined tension and torsion loading. Simulation of rubber behavior was conducted from the governing equations of the deformation of a cylinder composed of isotropic hyperelastic incompressible materials. Four different forms of strain-energy function were considered based respectively on polynomial, exponential and logarithmic terms to reproduce load force (N) and torque (M) trends using natural rubber experimental data. After highlighting the minimization of the objective function generated in the fitting process, the study revealed that a particle swarm optimization algorithm could be successfully used to identify the best material parameters and characterize the behavior of rubber-like hyperelastic materials.

Research paper thumbnail of Characterization of pure torsion of a rubber-like cylinder using a hyperelastic model

The European Physical Journal Plus

Research paper thumbnail of A phenomenological expression of strain energy in large elastic deformations of isotropic materials

Iranian Polymer Journal, 2020

A new model is constructed to validate a non-linear elastic response of rubber-like materials. Th... more A new model is constructed to validate a non-linear elastic response of rubber-like materials. The proposed model is phenomenological and is the combination of Rivlin expression truncated in invariant I 1 with a term in I 2 coming from the Hart-Smith model and which has been modified by Gornet et al. This model has five rheological parameters adjusted with a genetic algorithm. The genetic algorithm method is used in binary code and two sets of experimental data (Treloar data and Nunes and Moreira data) from the literature to compare the proposed model. With Treloar rubber data the simple tension suffices for the determination of the parameter values. Thus, the fit of experimental data is shown to provide an accurate response and predictive description in biaxial tension and pure shear with the same sets of material parameters. Unlike, with Moreira data, the proposed model has given direct material parameters in simple shear with good correlation. On the other hand, a comparison is made between the proposed model and the Beda model (2007), Gornet et al. model and hybrid integral approach (HIA) model. The proposed model is the most efficient among three other classical models because the proposed model emerges from very small relative errors with Treloar's experimental data: 0.42 ± 0.08 in simple tension, 0.44 ± 0.07 in biaxial tension and 0.42 ± 0.05 in pure shear. This model also incorporates all the criteria for model validation described in the literature.

Research paper thumbnail of Optimization of the model of Ogden energy by the genetic algorithm method

Applied Rheology, 2019

The model of Ogden, is a density of energy used in the modeling of hyperelastic materials behavio... more The model of Ogden, is a density of energy used in the modeling of hyperelastic materials behavior. This model of energy presents a high number of material parameters to identify. In this paper, we expose a method of identification of these parameters:Genetic Algorithm. This method contrary to the method of Beda-Chevalier, Least Squares, directed programming object method, PSA (Pattern Search Algorithm) and LMA (Levenberg-Marquardt), allows to identify quickly good parameters which give to the Ogden model a very good prediction in uniaxial tension, biaxial tension and pure shear. This prediction is considered to be better becausewe better bring the experimental curve closer to Treloar one with the parameters optimized by the genetic algorithm.

Research paper thumbnail of Characterization of hyperelastic deformation behavior of rubber-like materials

SN Applied Sciences, 2020

This paper proposes a new hyperelastic model for rubber-like matérials applicable over the entire... more This paper proposes a new hyperelastic model for rubber-like matérials applicable over the entire modes of the large deformations. The whole material parameters have been identified using the mathematical approach combined with the genetic algorithm for the best method for the structure of hyperelastic models applicable to incompressible rubber-like materials. The step-by-step method is used on the restricted form by gradually adding a term of the highest degree of the hyperelastic model when the deformation increases. This combination greatly minimizes the difference between experimental data and analytical solutions. It is about a method that is applied to nonlinear behaviors leading to an optimal solution. The power of the model is demonstrated via comparisons with different phenomenological hyperelastic models using the experimental data from the Treloar and Nunes works. According to the littérature, many authors have proposed a model based on both strain invariants but unable to reproduce the équibiaxial deformation mode. This work offers the constitutive hyperelastic model based on both strain invariants I 1 and I 2 with a minimal number of rheological parameters.

Research paper thumbnail of Characterization of the Preloaded Hyperelastic Materials Subjected to Linear Vibrations

Journal of Vibration Engineering & Technologies, Dec 25, 2023

This paper proposes the study of the visco-hyperelastic behavior of a rubber sample. This rubber,... more This paper proposes the study of the visco-hyperelastic behavior of a rubber sample. This rubber, coded as the BX rubber sample, is simultaneously loaded and subjected to linear vibrations. A multiplicative non-separable variables law of the Nashif has been used to model the behavior that depends on both stretch and frequency. This method allows splitting the intricately combined test performed jointly on both stretch and frequency. On the one hand, we use Young’s complex modulus E∗(휔) calculated from the experimental data, and on the other hand, the hyperelastic characteristics E(휆) of the same material obtained from the experimental tensile curve. The hyperelastic phenomenological Gent–Thomas model and the hyperelastic molecular Flory–Erman model are used to evaluate the combined complex modulus E∗(휆,휔). We obtain results that go in the physical sense, i.e, Young’s modulus increases when the material is stretched, while the damping decreases.

Research paper thumbnail of Improvement of HIA model and the impact of the inverse Langevin function proposed by Marchi and Arruda

Rheologica Acta, 2020

This research work is devoted to the improvement the Hybrid Integral Aproach (HIA) proposed by Ng... more This research work is devoted to the improvement the Hybrid Integral Aproach (HIA) proposed by Nguessong et al. for the characterization of the nonlinear elastic response of rubber-like materials. The improvement is based on the choice of the approximation of the inverse Langevin function for the molecular part and on the modification of the second term I 2 for the phenomenological part. Thus, in the new proposed model, we retain the approximation of the inverse Langevin function defined by Marchi and Arruda to improve the first term which represents the molecular part. With this approximation, the relative error is very minimal (0.0015%) compared to the others approximation existing. The second term of this proposed model comes from the Gornet et al. model. This model contents six rheological parameters optimized by the Levenberg-Marquardt method. Two sets of experimental data (Treloar data and Nunes and Moreira data), from the literature, are used to compare this proposed model with initial HIA model. With Treloar rubber, data the simple tension suffice to determine the parameter values. Thus, the fit of the experimental data has been shown to provide an accurate response and predictive description in biaxial tension and pure shear with the same sets of material parameters. Unlike with Moreira data, this proposed model gives directly the material parameters in simple shear with good correlation. On the other hand, comparison is made between the proposed model and the HIA model. The proposed model is most efficient, because the proposed model emerges from a very small relative errors with Treloar's experimental data: 0.01 0. 0.04 in simple tension, 0.02 ± 0.006 in biaxial tension and 0.07 ± 0.005 in pure shear.

Research paper thumbnail of Implementation of Particle Swarm Optimization Algorithm in Matlab Code for Hyperelastic Characterization

World journal of mechanics, 2021

The purpose of this paper is to demonstrate the applicability of Particle Swarm Optimization algo... more The purpose of this paper is to demonstrate the applicability of Particle Swarm Optimization algorithm to determine material parameters in incompressible isotropic elastic strain-energy functions using combined tension and torsion loading. Simulation of rubber behavior was conducted from the governing equations of the deformation of a cylinder composed of isotropic hyperelastic incompressible materials. Four different forms of strain-energy function were considered based respectively on polynomial, exponential and logarithmic terms to reproduce load force (N) and torque (M) trends using natural rubber experimental data. After highlighting the minimization of the objective function generated in the fitting process, the study revealed that a particle swarm optimization algorithm could be successfully used to identify the best material parameters and characterize the behavior of rubber-like hyperelastic materials.

Research paper thumbnail of Characterization of pure torsion of a rubber-like cylinder using a hyperelastic model

The European Physical Journal Plus

Research paper thumbnail of A phenomenological expression of strain energy in large elastic deformations of isotropic materials

Iranian Polymer Journal, 2020

A new model is constructed to validate a non-linear elastic response of rubber-like materials. Th... more A new model is constructed to validate a non-linear elastic response of rubber-like materials. The proposed model is phenomenological and is the combination of Rivlin expression truncated in invariant I 1 with a term in I 2 coming from the Hart-Smith model and which has been modified by Gornet et al. This model has five rheological parameters adjusted with a genetic algorithm. The genetic algorithm method is used in binary code and two sets of experimental data (Treloar data and Nunes and Moreira data) from the literature to compare the proposed model. With Treloar rubber data the simple tension suffices for the determination of the parameter values. Thus, the fit of experimental data is shown to provide an accurate response and predictive description in biaxial tension and pure shear with the same sets of material parameters. Unlike, with Moreira data, the proposed model has given direct material parameters in simple shear with good correlation. On the other hand, a comparison is made between the proposed model and the Beda model (2007), Gornet et al. model and hybrid integral approach (HIA) model. The proposed model is the most efficient among three other classical models because the proposed model emerges from very small relative errors with Treloar's experimental data: 0.42 ± 0.08 in simple tension, 0.44 ± 0.07 in biaxial tension and 0.42 ± 0.05 in pure shear. This model also incorporates all the criteria for model validation described in the literature.

Research paper thumbnail of Optimization of the model of Ogden energy by the genetic algorithm method

Applied Rheology, 2019

The model of Ogden, is a density of energy used in the modeling of hyperelastic materials behavio... more The model of Ogden, is a density of energy used in the modeling of hyperelastic materials behavior. This model of energy presents a high number of material parameters to identify. In this paper, we expose a method of identification of these parameters:Genetic Algorithm. This method contrary to the method of Beda-Chevalier, Least Squares, directed programming object method, PSA (Pattern Search Algorithm) and LMA (Levenberg-Marquardt), allows to identify quickly good parameters which give to the Ogden model a very good prediction in uniaxial tension, biaxial tension and pure shear. This prediction is considered to be better becausewe better bring the experimental curve closer to Treloar one with the parameters optimized by the genetic algorithm.

Research paper thumbnail of Characterization of hyperelastic deformation behavior of rubber-like materials

SN Applied Sciences, 2020

This paper proposes a new hyperelastic model for rubber-like matérials applicable over the entire... more This paper proposes a new hyperelastic model for rubber-like matérials applicable over the entire modes of the large deformations. The whole material parameters have been identified using the mathematical approach combined with the genetic algorithm for the best method for the structure of hyperelastic models applicable to incompressible rubber-like materials. The step-by-step method is used on the restricted form by gradually adding a term of the highest degree of the hyperelastic model when the deformation increases. This combination greatly minimizes the difference between experimental data and analytical solutions. It is about a method that is applied to nonlinear behaviors leading to an optimal solution. The power of the model is demonstrated via comparisons with different phenomenological hyperelastic models using the experimental data from the Treloar and Nunes works. According to the littérature, many authors have proposed a model based on both strain invariants but unable to reproduce the équibiaxial deformation mode. This work offers the constitutive hyperelastic model based on both strain invariants I 1 and I 2 with a minimal number of rheological parameters.