Applications of fractional constitutive models for finite deformation to viscoelastic materials

2014 ◽  
Author(s):  
Masataka Fukunaga ◽  
Nobuyuki Shimizu ◽  
Hideyuki Tsukui
Keyword(s):  
Finite Deformation ◽  
Constitutive Models ◽  
Viscoelastic Materials

Fractional Derivative Constitutive Models for Finite Deformation of Viscoelastic Materials

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Masataka Fukunaga ◽  
Nobuyuki Shimizu
Keyword(s):  
Fractional Derivative ◽  
Stress Tensor ◽  
Finite Deformation ◽  
Dynamical Behavior ◽  
Strain Tensor ◽  
Constitutive Models ◽  
Cauchy Stress ◽  
Viscoelastic Materials ◽  
Kirchhoff Stress Tensor ◽  
Biot Stress

A methodology to derive fractional derivative constitutive models for finite deformation of viscoelastic materials is proposed in a continuum mechanics treatment. Fractional derivative models are generalizations of the models given by the objective rates. The method of generalization is applied to the case in which the objective rate of the Cauchy stress is given by the Truesdell rate. Then, a fractional derivative model is obtained in terms of the second Piola–Kirchhoff stress tensor and the right Cauchy-Green strain tensor. Under the assumption that the dynamical behavior of the viscoelastic materials comes from a complex combination of elastic and viscous elements, it is shown that the strain energy of the elastic elements plays a fundamental role in determining the fractional derivative constitutive equation. As another example of the methodology, a fractional constitutive model is derived in terms of the Biot stress tensor. The constitutive models derived in this paper are compared and discussed with already existing models. From the above studies, it has been proved that the methodology proposed in this paper is fully applicable and effective.

An experimental assessment of internal variables constitutive models for viscoelastic materials

2015 ◽  
Vol 50-51 ◽  
pp. 27-40 ◽  
Author(s):  
F.C.L. Borges ◽  
D.A. Castello ◽  
C. Magluta ◽  
F.A. Rochinha ◽  
N. Roitman
Keyword(s):  
Constitutive Models ◽  
Internal Variables ◽  
Viscoelastic Materials ◽  
Experimental Assessment

A Novel Planar Tension Test of Rubber for Evaluating the Prediction Ability of the Modified Eight-Chain Model under Moderate Finite Deformation

2005 ◽  
Vol 78 (5) ◽  
pp. 879-892 ◽  
Author(s):  
Yong Xia ◽  
Yi Dong ◽  
Yuanming Xia ◽  
Wei Li
Keyword(s):  
Finite Deformation ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Grid Method ◽  
Tension Test ◽  
Chain Model ◽  
Prediction Ability ◽  
Rubber Material ◽  
Deformation State ◽  
Heterogeneous Deformation

Abstract In this paper, a novel planar tension test is applied to evaluate the prediction ability of the rubber constitutive models under moderate finite deformation. Based on the automated grid method, it is found that in planar test, deformation in the center region of the specimen is homogeneous but that of the whole specimen is heterogeneous. With three dimensional (3D) finite element (FE) modeling, both the load-stretch relationship and the deformation fields predicted by various constitutive models are obtained under heterogeneous deformation state of the planar tension. By comparing FEA results to the test results, the prediction abilities of these constitutive models are evaluated. According to the results of this heterogeneous planar tension test, the modified eight-chain model is found to be more successful than the eight-chain model and the Van del Waals model in predicting the observed hyperelastic behaviors of rubber material under different deformation states.

Application of Irreversible Thermodynamics in Finite Viscoelastic Deformations

1965 ◽  
Vol 32 (3) ◽  
pp. 623-629 ◽  
Author(s):  
George Lianis
Keyword(s):  
Constitutive Equation ◽  
Finite Deformation ◽  
Small Deviation ◽  
Irreversible Thermodynamics ◽  
The State ◽  
Reference State ◽  
Static Deformation ◽  
Viscoelastic Materials ◽  
Long Time ◽  
Dynamic Strains

In this paper, Onsager’s principle of irreversible thermodynamics is applied to viscoelastic materials subjected to finite deformation. The constitutive equation of Ref. [10] for small dynamic strains superposed on a finite static deformation is used. The state of the resulting deformation can be considered as a small deviation from an equilibrium reference state. The latter is the state of equilibrium of a material subjected to a finite deformation in which the material is maintained for a long time.

Constitutive Law of Finite Deformation Elastoplasticity With Proportional Loadings

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
H. Darijani ◽  
R. Naghdabadi
Keyword(s):  
Constitutive Equation ◽  
Finite Deformation ◽  
Constitutive Models ◽  
Pressure Vessels ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Proportional Loading ◽  
Von Mises ◽  
Plastic Parts

In this paper, decomposition of the total strain into elastic and plastic parts is investigated for extension of elastic-type constitutive models to finite deformation elastoplasticity. In order to model the elastic behavior, a Hookean-type constitutive equation based on the logarithmic strain is considered. Based on this constitutive equation and assuming the deformation theory of Hencky as well as the yield criteria of von Mises, the elastic-plastic behavior of materials at finite deformation is modeled in the case of the proportional loading. Moreover, this elastoplastic model is applied in order to determine the stress distribution in thick-walled cylindrical pressure vessels at finite deformation elastoplasticity.

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