The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Mario J Juha - One of the best experts on this subject based on the ideXlab platform.
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total lagrangian finite element formulation of the flory rehner free energy function
Revista Facultad De Ingenieria-universidad De Antioquia, 2013Co-Authors: Mario J JuhaAbstract:The total Lagrangian finite element implementation of the Flory-Rehner free-energy function in the framework of a Hyperelastic Material model is addressed. It is explicitly given all the equations required to implement this Material model in an implicit nonlinear finite element analysis, particularly, it is shown how to derive the so-called algorithmic or consistent linearized tangent moduli in the Lagrangian description. Some analytical and numerical results for different boundary-value problems are presented to validate the implementation.
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total lagrangian finite element formulation of the flory rehner free energy function formulacion de elemento finito total lagrangiano de la funcion de energia libre de flory rehner
2013Co-Authors: Mario J JuhaAbstract:The total Lagrangian finite element implementation of the Flory-Rehner free-energy function in the framework of a Hyperelastic Material model is addressed. It is explicitly given all the equations required to implement this Material model in an implicit nonlinear finite element analysis, particularly, it is shown how to derive the so-called algorithmic or consistent linearized tangent moduli in the Lagrangian description. Some analytical and numerical results for different boundary-value problems are presented to validate the implementation.
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total lagrangian finite element formulation of the flory rehner free energy function
arXiv: Numerical Analysis, 2012Co-Authors: Mario J JuhaAbstract:We address the total Lagrangian finite element implementation of the Flory-Rehner free-energy function in the framework of a Hyperelastic Material model. We explicitly give all the equations required to implement this Material model in an implicit nonlinear finite element analysis, particularly, we show how to derive the so-called algorithmic or consistent linearized tangent modulus in the Lagrangian description. Some analytical and numerical results for different boundary-value problems are presented to validate the implementation.
A H Eskandari - One of the best experts on this subject based on the ideXlab platform.
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developing a visco Hyperelastic Material model for 3d finite deformation of elastomers
Finite Elements in Analysis and Design, 2018Co-Authors: Shayan Fahimi, Mostafa Baghani, Mohammad Reza Zakerzadeh, A H EskandariAbstract:Abstract In this research, using a phenomenological strain energy function, a 3D visco-Hyperelastic constitutive equation for the finite deformation of elastomers is developed. For the quasi-static response, a strain energy function, composed of two exponential terms, is employed. The same energy function is considered as the kernel in the hereditary integral approach to derive the visco-Hyperelastic model for the time-dependent response. To reduce the number of Material parameters, an inverse power-law function between relaxation time and strain rate is proposed. Discretization of the analytical formulation of the visco-Hyperelastic model in time is performed to be used in numerical simulations. This approach provides a recursive formulation to update the stress in each time step based on the deformation history. Then, the model is used to study the behavior of elastomeric bushing in radial, torsional and axial deformations. In all these cases, the Material parameters are determined by applying a multi-objective optimization algorithm, in which the objective function is the difference between experimental and numerical results. The proposed visco-Hyperelastic model shows accurate results for elastomers under 3D quasi-static and time-dependent loadings. Moreover, the accuracy of the results is not dependent on the amount of strain, the strain rate, and modes of deformation.
Fazil O Sonmez - One of the best experts on this subject based on the ideXlab platform.
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visco Hyperelastic Material modeling using nested linkage mechanisms
International Journal of Solids and Structures, 2020Co-Authors: Umut M Ozcan, Cetin Yilmaz, Fazil O SonmezAbstract:Abstract In this study, basic linear lumped elements such as springs and dashpots are used in nested linkage mechanisms in order to simulate the mechanical behavior of visco-Hyperelastic Materials. The proposed mechanism model containing two nested linkages can show initial softening followed by hardening response under quasi-static loading, which is commonly displayed by Hyperelastic Materials. Hence, Material nonlinearity is simulated by geometric nonlinearity of the linkage mechanism. The mechanism also displays relaxation, hysteresis, and dynamic stiffness responses of viscoelastic Materials with the help of dashpot elements. Visco-Hyperelastic Material behavior is closely approximated by the proposed mechanism model for the four different test scenarios, i.e., quasi-static loading, ramp-and-hold loading, hysteresis, and dynamic stiffness tests. It is shown that nonlinearity and frequency dependency of visco-Hyperelastic Materials is successfully captured.
Shayan Fahimi - One of the best experts on this subject based on the ideXlab platform.
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developing a visco Hyperelastic Material model for 3d finite deformation of elastomers
Finite Elements in Analysis and Design, 2018Co-Authors: Shayan Fahimi, Mostafa Baghani, Mohammad Reza Zakerzadeh, A H EskandariAbstract:Abstract In this research, using a phenomenological strain energy function, a 3D visco-Hyperelastic constitutive equation for the finite deformation of elastomers is developed. For the quasi-static response, a strain energy function, composed of two exponential terms, is employed. The same energy function is considered as the kernel in the hereditary integral approach to derive the visco-Hyperelastic model for the time-dependent response. To reduce the number of Material parameters, an inverse power-law function between relaxation time and strain rate is proposed. Discretization of the analytical formulation of the visco-Hyperelastic model in time is performed to be used in numerical simulations. This approach provides a recursive formulation to update the stress in each time step based on the deformation history. Then, the model is used to study the behavior of elastomeric bushing in radial, torsional and axial deformations. In all these cases, the Material parameters are determined by applying a multi-objective optimization algorithm, in which the objective function is the difference between experimental and numerical results. The proposed visco-Hyperelastic model shows accurate results for elastomers under 3D quasi-static and time-dependent loadings. Moreover, the accuracy of the results is not dependent on the amount of strain, the strain rate, and modes of deformation.
Thomas Schuster - One of the best experts on this subject based on the ideXlab platform.
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on the linearization of identifying the stored energy function of a Hyperelastic Material from full knowledge of the displacement field
Mathematical Methods in The Applied Sciences, 2017Co-Authors: Julia Seydel, Thomas SchusterAbstract:We compute a local linearization for the nonlinear, inverse problem of identifying the stored energy function of a Hyperelastic Material from the full knowledge of the displacement field. The displacement field is described as a solution of the nonlinear, dynamic, elastic wave equation, where the first Piola–Kirchhoff stress tensor is given as the gradient of the stored energy function. We assume that we have a dictionary at hand such that the energy function is given as a conic combination of the dictionary's elements. In that sense, the mathematical model of the direct problem is the nonlinear operator that maps the vector of expansion coefficients to the solution of the Hyperelastic wave equation. In this article, we summarize some continuity results for this operator and deduce its Frechet derivative as well as the adjoint of this derivative. Because the stored energy function encodes mechanical properties of the underlying, Hyperelastic Material, the considered inverse problem is of highest interest for structural health monitoring systems where defects are detected from boundary measurements of the displacement field. For solving the inverse problem iteratively by the Landweber method or Newton-type methods, the knowledge of the Frechet derivative and its adjoint is of utmost importance. Copyright © 2016 John Wiley & Sons, Ltd.
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on the linearization of identifying the stored energy function of a Hyperelastic Material from full knowledge of the displacement field
arXiv: Analysis of PDEs, 2015Co-Authors: Julia Seydel, Thomas SchusterAbstract:We consider the nonlinear,inverse problem of computing the stored energy function of a Hyperelastic Material from the full knowledge of the displacement field. The displacement field is described as solution of the nonlinear, dynamic, elastic wave equation, where the first Piola-Kirchhoff stress tensor is given as the gradient of the stored energy function. We assume that we have a dictionary at hand such that the energy function is given as a conic combination of the dictionary's elements. In that sense the mathematical model of the direct problem is the nonlinear operator that maps the vector of expansion coefficients to the solution of the Hyperelastic wave equation. In this article we summarize some continuity results for this operator and deduce its Fr\'{e}chet derivative as well as the adjoint of this derivative. Since the stored energy function encodes mechanical properties of the underlying, Hyperelastic Material, the considered inverse problem is of highest interest for structural health monitoring systems where defects are detected from boundary measurements of the displacement field. For solving the inverse problem iteratively by the Landweber method or Newton type methods, the knowledge of the Fr\'{e}chet derivative and its adjoint is of utmost importance.