On finite linear viscoelasticity of incompressible isotropic materials

Haupt, Peter; Lion, Alexander

doi:10.1007/bf01171450

Cited by 111 publications

(65 citation statements)

References 29 publications

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“…It can be seen from Table 4 that the parameters in different groups are almost the same with each other, and the weights u 1 and u 2 are almost accurately identified with the relaxation time a bit deviated from its true value. However, an abnormal negative value −0.001, extremely close to 0, of the weight u3 is observed even though we have set constraints for all the weights as shown in Equation (20), this unusual phenomenon may be an indication of the weight u3 redundant for the problem.…”

Section: Verification Of the Identified Resultsmentioning

confidence: 99%

“…Besides, taking the third group as an example, the linear constraint equations for the parameters during iterations are shown in Equation (20).…”

Section: Constraints and Initial Values Of Parametersmentioning

confidence: 99%

“…In such a framework, Huber and Tsakmak is generalized the application range of the so-called three-parameter solids to the finite deformation [19]. Haupt et al proposed a fairly simple identification method for the constants in a finite viscoelasticity model [20]. Yoshida et al presented a constitutive model comprised by an elastoplastic body with a strain-dependent isotropic hardening law and a hyperelastic body with a damage model [21].…”

Section: Introductionmentioning

confidence: 99%

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Parameter Identification Methods for Hyperelastic and Hyper-Viscoelastic Models

Wang

2016

Applied Sciences

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Abstract:In this paper, the Ogden model is employed to characterize the hyperelastic properties of rubber, and on the basis of a pattern search algorithm and the Levenberg-Marquardt algorithm, a professional method that can realize the comprehensive fitting of the uniaxial tension, biaxial tension, planar tension, and simple shear experimental data of hyperelastic materials was developed. The experiment data from Treloar (1944) was fitted very well, and the determined parameters by using this method were proven correct and practical in the numerical verification in ANSYS. Then, the constitutive model of the hyper-viscoelastic materials combining the Ogden model with the generalized Maxwell model was explained in detail, and the parameter identification method was also proposed by using the pattern search method. Then, three groups of relaxation tests of uniaxial tension and four groups of simple shear tests with different loading velocities were conducted to obtain the corresponding virtual experiment data. After discussing the constraints and initial setting values for the undetermined parameters, these virtual data of different loading histories were respectively employed to identify the parameters in the hyper-elastic model, and the accuracy and the reliability of the estimated parameters were also verified in ANSYS.

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Section: Verification Of the Identified Resultsmentioning

confidence: 99%

“…Besides, taking the third group as an example, the linear constraint equations for the parameters during iterations are shown in Equation (20).…”

Section: Constraints and Initial Values Of Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parameter Identification Methods for Hyperelastic and Hyper-Viscoelastic Models

Wang

2016

Applied Sciences

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“…This approach can be found e.g. in [3] and [4]. The equilibrium part of the model is formulated using a compressible hyperelastic Neo-Hookean relation and the overstress as the sum of partial overstresses belonging to the Maxwell series.…”

Section: Constitutive Materials Model Finite Viscoelsticity Consideredmentioning

confidence: 99%

Material behaviour of filler‐reinforced rubber materials under cyclic loading processes, experiments and FEM‐simulations based on finite viscoelasticity.

Lion

2009

Proc Appl Math and Mech

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A threedimensional constitutive model of finite viscoelasticity will be presented. It considers the amplitude dependence and is based on a Maxwell chain with intrinsic time scales. This type of viscoelasticity is thermodynamically consistent and provides a basis for modelling other effects (e.g. temperature dependence). The parameter identification for this model is possible in both the frequency and the time domain. Some finite element implementation and simulation results in the time domain are presented. The numerical simulation of multifrequent and other more complicated loading processes is possible only in the time domain. A very interesting loading process is a cyclic deformation with changing amplitudes in order to simulate the transient dynamic behavior of the Payne-effect.

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“…The formulation is based on process dependent viscosities as in the previous works of HAUPT and LION [10,11] within a thermodynamic framework. It accounts for thermally and chemically induced volume changes using a ternary multiplicative split of the deformation gradient into mechanical, thermal and chemical parts.…”

Section: Introductionmentioning

confidence: 99%

Effective Meso and Macro Properties for Fibre-Reinforced-Polymer Curing Coupled to Visco-Elasticity

Mahnken¹,

Dammann²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Our work presents a three-scale model for temperature-dependent visco-elastic effects accompanied by curing, which are important phenomena in a resin transfer molding (RTM) process. The effective bulk quantities in dependence on the degree of cure are obtained by homogenization for a representative unit cell (micro-RVE) on the heterogeneous microscale. To this end, an analytic solution is derived by extension of the well known composite spheres model. Voigt and Reuss bounds resulting from the assumption of a homogeneous matrix are compared to the effective quantities. During curing and subsequent mechanical loading, the periodic mesostructure defined by a visco-elastic polymeric matrix and linear-thermo-elastic carbon fibres is taken into account as a representative unit cell (meso-RVE) subjected to thermo-mechanical loading on the mesoscale. Homogenization of the mesoscale by volume averaging is applied to obtain the effective properties for the fully cured composite on the macroscale, e.g. the macroscopic anisotropic thermal expansion coefficient. In the examples we simulate the curing process as well as mechanical loading of the cured part with the finite-element-method.2398

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On finite linear viscoelasticity of incompressible isotropic materials

Cited by 111 publications

References 29 publications

Parameter Identification Methods for Hyperelastic and Hyper-Viscoelastic Models

Parameter Identification Methods for Hyperelastic and Hyper-Viscoelastic Models

Material behaviour of filler‐reinforced rubber materials under cyclic loading processes, experiments and FEM‐simulations based on finite viscoelasticity.

Effective Meso and Macro Properties for Fibre-Reinforced-Polymer Curing Coupled to Visco-Elasticity

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