A large deformation framework for compressible viscoelastic materials: Constitutive equations and finite element implementation

Hasanpour, K.; Ziaei-Rad, Saeed; Mahzoon, Mojtaba

doi:10.1016/j.ijplas.2008.06.012

Cited by 47 publications

(28 citation statements)

References 58 publications

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“…Following the standard approach adopted in plasticity [32,34] and also used for viscoelastic response of materials (see, e.g., [10,12,19] among others), we assume a multiplicative decomposition of the deformation gradient into an elastic part F e , defined with respect to an intermediate stress free configuration, and a viscoelastic one F v , defined with respect to the initial configuration, i.e. :…”

Section: Constitutive Model Developmentmentioning

confidence: 99%

“…Thus, the compressible or nearly incompressible constitutive models are preferable and no constraint is required to be satisfied in displacement-based FEA (finite element analysis) [17,18]. Moreover, the material is assumed to be nearly incompressible using a convenient penalization value of the bulk modulus [19].…”

Section: Introductionmentioning

confidence: 99%

“…However, they did not present the finite element implementation of their model. Hasanpour et al [19] modified the model proposed by Huber and Tsakmakis [10] and presented a compressible viscoelastic constitutive model. Moreover, they implemented the proposed model in a finite element code and investigated the response of an elastomeric bushing to various loadings.…”

Section: Introductionmentioning

confidence: 99%

“…Naghdabadi et al / Finite Elements in Analysis and Design 62 (2012)[18][19][20][21][22][23][24][25][26][27] …”

mentioning

confidence: 99%

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A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation

Naghdabadi

Baghani

Arghavani

2012

Finite Elements in Analysis and Design

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Section: Constitutive Model Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Naghdabadi et al / Finite Elements in Analysis and Design 62 (2012)[18][19][20][21][22][23][24][25][26][27] …”

mentioning

confidence: 99%

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A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation

Naghdabadi

Baghani

Arghavani

2012

Finite Elements in Analysis and Design

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“…The foundations of linear viscoelasticity on the basis of the Boltzmann formulation were published, for example, by Coleman (1961). Rheological constitutive models to represent the nonlinear viscoelastic behaviour of rubber can be found in many publications, for example, Baris and Edwards (1993), Hasanpour et al (2009), Haupt and Lion (2002), Holzapfel (1996), Middendorf (2001) or Miehe and Keck (2000), Sedlan (2001), Amin et al (2006) to name a few. Numerical aspects of the finite element implementation of finite viscoelasticity are discussed, for example, by Simo and Huges (2000) and Reese and Govindjee (1998) or Miehe and Keck (2000) and Govindjee and Simo (1992).…”

Section: Introductionmentioning

confidence: 99%

Amplitude dependence of filler-reinforced rubber: Experiments, constitutive modelling and FEM – Implementation

Rendek

Lion

2010

International Journal of Solids and Structures

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a b s t r a c tThe focus of the present paper is the experimental investigation, the constitutive representation and the numerical simulation of the amplitude dependence of filler-reinforced elastomers. A standard way to investigate the dynamic properties of viscoelastic materials is via the dynamic modulus which is obtained from stress signals due to harmonic strain excitations. Based on comprehensive experimental data, an amplitude-dependent constitutive model of finite viscoelasticity is developed. The model is based on a modified Maxwell chain with process-dependent viscosities which depend on additional internal state variables. The evaluation of this thermodynamically consistent model is possible in both the time domain, via stress-time signals, and in the frequency domain, via the dynamic modulus. This property is very profitable for the parameter identification process. The implementation of the constitutive model into the commercial finite element code ANSYS with the user-programmable feature (UPF) USERMAT for large deformations in updated Lagrange formulation is presented. This implementation allows simulating the time-dependent behaviour of rubber components under arbitrary transient loading histories. Due to physical and geometrical nonlinearities, these simulations are not possible in the frequency domain. But, transient FEM computations of large loading histories are sometimes not possible in an acceptable time. In the context of the parameter identification the fundamental ideas are presented, how this problem has been solved. Transient FEM simulations of real rubber components are also shown to visualize the properties of the model in the context of the transient material behaviour.

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Efficient time stepping for the multiplicative Maxwell fluid including the Mooney‐Rivlin hyperelasticity

Shutov

2017

Numerical Meth Engineering

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A popular version of the finite-strain Maxwell fluid is considered, which is based on the multiplicative decomposition of the deformation gradient tensor. The model combines Newtonian viscosity with hyperelasticity of the Mooney-Rivlin type; it is a special case of the viscoplasticity model proposed by Simo and Miehe in 1992. A simple, efficient, and robust implicit time-stepping procedure is suggested. Lagrangian and Eulerian versions of the algorithm are available, with equivalent properties. The numerical scheme is iteration free, unconditionally stable, and first order accurate. It exactly preserves the inelastic incompressibility, symmetry, and positive definiteness of the internal variables and w-invariance. The accuracy of the stress computations is tested using a series of numerical simulations involving a nonproportional loading and large strain increments. In terms of accuracy, the proposed algorithm is equivalent to the modified Euler backward method with exact inelastic incompressibility; the proposed method is also equivalent to the classical integration method based on exponential mapping. Since the new method is iteration free, it is more robust and computationally efficient. The algorithm is implemented into MSC.MARC, and a series of initial boundary value problems is solved to demonstrate the usability of the numerical procedures.

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A large deformation framework for compressible viscoelastic materials: Constitutive equations and finite element implementation

Cited by 47 publications

References 58 publications

A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation

A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation

Amplitude dependence of filler-reinforced rubber: Experiments, constitutive modelling and FEM – Implementation

Efficient time stepping for the multiplicative Maxwell fluid including the Mooney‐Rivlin hyperelasticity

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