Visco-hyperelastic constitutive law for modeling of foam’s behavior

Anani, Yavar; Alizadeh, Y.

doi:10.1016/j.matdes.2010.11.010

Cited by 34 publications

(12 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hyperelasticity as an instantaneous elastic behavior is rate independent. When the loading rate is lowest, the loading rate effect on curves is verified to be minimal (Yang & Shim 2004;Anani & Alizadeh 2011). Thus, the experimental data with the low loading rate were chosen to identify the material parameters and validate the model.…”

Section: Resultsmentioning

confidence: 99%

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

Huang

Tang

Yan

et al. 2015

Computer Methods in Biomechanics and Biomedical Engineering

View full text Add to dashboard Cite

The V-W exponential hyperelastic model is adopted to describe the instantaneous elastic response of the periodontal ligament (PDL). The general theoretical framework of constitutive modeling is described based on nonlinear continuum mechanics, and the elasticity tensor used to develop UMAT subroutine is formulated. Nanoindentation experiment is performed to characterize mechanical properties of an adult pig PDL specimen. Then the experiment is simulated by using the finite element (FE) analysis. Meanwhile, the optimized material parameters are identified by the inverse FE method. The good agreement between the simulated results and experimental data demonstrates that the V-W model is capable of describing the mechanical behavior of the PDL. Therefore, the model and its implementation into FE code are validated. By using the model, we simulate the tooth movement under orthodontic loading to predict the mechanical responses of the PDL. The results show that local concentrations of stress and strain in the PDL are found.

show abstract

Section: Resultsmentioning

confidence: 99%

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

Huang

Tang

Yan

et al. 2015

Computer Methods in Biomechanics and Biomedical Engineering

View full text Add to dashboard Cite

show abstract

“…Besides, intermediate spring is considered for hyperelastic materials and constitutive equation can be rewritten:

{boldσ}_{boldo boldv} = - {normalp}_{normalo normalv} boldI + boldF \frac{\partial {normalW}_{normalo normalv}}{\partial boldE} {boldF}^{T}

where

{{normalW}_{normalo normalv} = {normalW}_{normalo normalv} true(normalI}_{1}, {normalI}_{2}, {normalI}_{4} true)

. To predict behavior of rubbers, Kernel function is used :

\frac{\partial {normalW}_{normalo normalv}}{\partial boldE} = {false\int}_{- \infty}^{t} \frac{\partial normalu}{\partial boldE} true({{normalI}_{1}, normalI}_{2}, {normalI}_{4}, normalt ‐ normalτ true) normald normalτ

where

u true({{normalI}_{1}, normalI}_{2}, {normalI}_{4}, normalt - normalτ true)

is the kernel function, which is used to integrate strain energy potential. By considering separate effect for time and deformation, the above equation can be rewritten as follows :

u (|, {{normalI}_{1}, normalI}_{2}, {normalI}_{4}, normalt - normalτ) = U (|, {{normalI}_{1}, normalI}_{2}, {normalI}_{4} true) normalm true(normalt ‐ normalτ)

…”

Section: Theory and Formulationmentioning

confidence: 99%

Modeling of visco‐hyperelastic behavior of transversely isotropic functionally graded rubbers

Anani

Rahimi

2016

Polymer Engineering & Sci

View full text Add to dashboard Cite

In this article, visco-hyperelastic constitutive model is developed to describe the rate-dependent behavior of transversely isotropic functionally graded rubber-like materials at finite deformations. Zener model that consists of Maxwell element parallel to a hyperelastic equilibrium spring is used in this article. Steady state response is described by equilibrium hyperelastic spring and ratedependence behavior is modeled by Maxwell element that consists of a hyperelastic intermediate spring and a nonlinear viscous damper. Modified and reinforced neoHookean strain energy function is proposed for the two hyperelastic springs. The mechanical properties and material constants of strain energy function are graded along the axial direction based on exponential function. A history-integral method has been used to develop a constitutive equation for modeling the behavior of the model. The applied history integral method is based on the Kaye-BKZ theory. The material constant parameters appeared in the formulation have been determined with the aid of available uniaxial tensile experimental tests for a specific material and the results are compared to experimental results. It is then concluded that, the proposed constitutive equation is quite proficient in forecasting the behavior of rubber-like materials in different deformation and wide ranges of strain rate. POLYM. ENG. SCI., 56:342-347, 2016.

show abstract

“…Different strain energy functions are used to model hyperelastic behavior of these materials and there are numerous efforts in the literature on the derivation and/or fitting of various forms of strainenergy functions, such as works of Mooney (1940), Blatz and Ko (1962), Yeoh (1993), Ogden (1972), Beatty (1987). Presenting precise constitutive model to describe hyperelastic behavior of rubber like material is the subject of a lot of researches in the recent years such as works by Anani and Alizadeh (2011), Bao et al (2003), Silva and Bittencourt (2008), Pereira and Bittencourt (2010), Pascon and Coda (2013), Coelho et al (2014), Santos et al (2015), Tomita et al (2008) and Barforooshi and Mohammadi (2016) As functionally graded rubber is the subject of this study it should be noted that graded rubber like materials were created by Ikeda et al (1998) in the laboratory for the first time, a while after these materials have attracted the attention of investigators for modeling these materials behavior under mechanical and geometrical boundary conditions. Some important and novel researches about analysis of inhomogeneous rubber like materials structures are presented in details by Bilgili (2003Bilgili ( ,2004, Batra (2006), Batra and Bahrami (2009), Rahimi (2015,2016).…”

Section: Introductionmentioning

confidence: 99%

On the stability of internally pressurized thick-walled spherical and cylindrical shells made of functionally graded incompressible hyperelastic material

Anani

Rahimi

2018

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

In this paper, stability analysis of thick-walled spherical and cylindrical shells made of functionally graded incompressible hyperelastic material subjected to internal pressure is presented. Instability point happens in the inflation of above mentioned shells and in this paper effect of material inhomogeneity and shell thickness has been investigated. Extended Ogden strain energy function with variable material parameter is used to model the material behavior. To model inhomogeneity, we assume that material parameter varies by a power law function in the radial direction and inhomogeneity factor is a power in the power law function. Analytical method is used to find the internal pressure versus hoop extension ratio relations in explicit form for both of cylindrical and spherical shells and the non-monotonic behavior of the inflation curves is studied. Following this, profile of inflation pressure versus hoop stretch is presented and effect of the inhomogeneity and shell thickness in the onset of instability is studied. The obtained results show that the material inhomogeneity parameter and shell thickness have a significant influence on the stability of above mentioned shells. Thus with selecting a proper material inhomogeneity parameter and shell thickness, engineers can design a specific FGM hollow cylinder that can meet some special requirements.

show abstract

Visco-hyperelastic constitutive law for modeling of foam’s behavior

Cited by 34 publications

References 12 publications

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

Modeling of visco‐hyperelastic behavior of transversely isotropic functionally graded rubbers

On the stability of internally pressurized thick-walled spherical and cylindrical shells made of functionally graded incompressible hyperelastic material

Contact Info

Product

Resources

About