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

Shutov, A. V.

doi:10.1002/nme.5724

Cited by 20 publications

(9 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Robust and efficient numerical procedures for the case where

ψ_{kin 1}

and

ψ_{kin 2}

are of neo‐Hookean type are presented in []. The case where

ψ_{kin 1}

and

ψ_{kin 2}

are of Mooney‐Rivlin type can be dealt with using an explicit update formula from []. The model is implemented into the nonlinear FEM‐code MSC.MARC.…”

Section: Illustration Problem: Model With Combined Isotropic‐kinematimentioning

confidence: 99%

Parameter identification in elasto‐plasticity: distance between parameters and impact of measurement errors

Shutov

Kaygorodtseva

2019

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

A special aspect of parameter identification in finite‐strain elasto‐plasticity is considered. Namely, we analyze the impact of the measurement errors on the resulting set of material parameters. In order to define the sensitivity of parameters with respect to the measurement errors, a mechanics‐based distance between two sets of parameters is introduced. Using this distance function, we assess the reliability of certain parameter identification procedures. The assessment involves introduction of artificial noise to the experimental data; the noise can be both correlated and uncorrelated. An analytical procedure to speed up Monte Carlo simulations is presented. As a result, a simple tool for estimating the robustness of parameter identification is obtained. The efficiency of the approach is illustrated using a model of finite‐strain viscoplasticity, which accounts for combined isotropic and kinematic hardening. It is shown that dealing with correlated measurement errors, most stable identification results are obtained for non‐diagonal weighting matrix. At the same time, there is a conflict between the stability and accuracy.

show abstract

“…Robust and efficient numerical procedures for the case where

ψ_{kin 1}

and

ψ_{kin 2}

are of neo‐Hookean type are presented in []. The case where

ψ_{kin 1}

and

ψ_{kin 2}

are of Mooney‐Rivlin type can be dealt with using an explicit update formula from []. The model is implemented into the nonlinear FEM‐code MSC.MARC.…”

Section: Illustration Problem: Model With Combined Isotropic‐kinematimentioning

confidence: 99%

Parameter identification in elasto‐plasticity: distance between parameters and impact of measurement errors

Shutov

Kaygorodtseva

2019

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular,

. A non-iterational generalization of this formula to cover the energy storage of the Mooney-Rivlin type is presented in Reference [ 53 ].…”

Section: Methodsmentioning

confidence: 99%

Parameter Identification and Validation of Shape-Memory Polymers within the Framework of Finite Strain Viscoelasticity

2021

Self Cite

View full text Add to dashboard Cite

Shape-Memory Polymers (SMPs) can be stretched to large deformations and recover induced strains when exposed to an appropriate stimulus, such as heat. This emerging class of functional polymers has attracted much interest and found applications in medicine and engineering. Nevertheless, prior to any application, their physical and mechanical properties must be thoroughly studied and understood in order to make predictions or to design structures thereof. In this contribution, the viscoelastic behavior of a polyether-based polyurethane (Estane) and its rate- and temperature-dependent behavior have been studied experimentally and by the mean of simulations. The model-inherent material parameters are identified with the assumption of the thermo-rheological complexity. Here, the numerical results of uni-axial stress relaxations were compared with the associated experiments in conjucation with the Levenberg-Marquard optimization method to determine the parameters of the Prony equation. The ability of the model to simulate the thermo-mechanical properties of Estane was evaluated by data-rich experimental observations on tension and torsion in various temperature ranges. Heterogeneous tests are included into the experimental program to cover a broader spectrum of loading scenarios.

show abstract

“…The use of the spline-based strain energy functions is discussed in [17]. Efficient numerics for the Mooney-Rivlin elastic potential is described in [34].…”

Section: Constitutive Equationsmentioning

confidence: 99%

“…A significant aspect of the w-invariance is the transformations of initial conditions for plastic strains (see [38] for a general discussion of w-invariance). Another important implication of the w-invariance is that it allows us to build efficient computational algorithms [33,34].…”

Section: Introductionmentioning

confidence: 99%

Combined experimental/theoretical approach to residual stresses within multiplicative elasto-plasticity

Tagiltsev¹,

Shutov²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The finite strain kinematics of the viscoplastic material is modelled by the multiplicative decomposition of the deformation gradient tensor. Numerical algorithms originally developed for unstressed materials are extended to materials with pre-stresses. Owing to the weak invariance of constitutive equations, the incorporation of pre-stresses happens without additional costs. Thus, the advocated approach is especially efficient. A novel experimental/theoretical method for assessment of residual stresses in welded structures is presented; the method combines advantages of purely experimental and theoretical approaches. To demonstrate the applicability of the proposed procedure, we simulate plate welding. As an example we show that the procedure allows to extrapolate the filed of residual stresses away from the measurement points.As another example, we address the reduction of weldment-related residual stresses by mechanical treatment.

show abstract

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

Cited by 20 publications

References 53 publications

Parameter identification in elasto‐plasticity: distance between parameters and impact of measurement errors

Parameter identification in elasto‐plasticity: distance between parameters and impact of measurement errors

Parameter Identification and Validation of Shape-Memory Polymers within the Framework of Finite Strain Viscoelasticity

Combined experimental/theoretical approach to residual stresses within multiplicative elasto-plasticity

Contact Info

Product

Resources

About