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  • Springer Science and Business Media LLC  (3)
  • Ricker, Alexander  (3)
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  • Springer Science and Business Media LLC  (3)
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  • 1
    Online Resource
    Online Resource
    Systematic Fitting and Comparison of Hyperelastic Continuum Models for Elastomers
    Springer Science and Business Media LLC ; 2023
    In:  Archives of Computational Methods in Engineering Vol. 30, No. 3 ( 2023-04), p. 2257-2288
    Details
    In: Archives of Computational Methods in Engineering, Springer Science and Business Media LLC, Vol. 30, No. 3 ( 2023-04), p. 2257-2288
    Abstract: Hyperelasticity is a common modeling approach to reproduce the nonlinear mechanical behavior of rubber materials at finite deformations. It is not only employed for stand-alone, purely elastic models but also within more sophisticated frameworks like viscoelasticity or Mullins-type softening. The choice of an appropriate strain energy function and identification of its parameters is of particular importance for reliable simulations of rubber products. The present manuscript provides an overview of suitable hyperelastic models to reproduce the isochoric as well as volumetric behavior of nine widely used rubber compounds. This necessitates firstly a discussion on the careful preparation of the experimental data. More specific, procedures are proposed to properly treat the preload in tensile and compression tests as well as to proof the consistency of experimental data from multiple experiments. Moreover, feasible formulations of the cost function for the parameter identification in terms of the stress measure, error type as well as order of the residual norm are studied and their effect on the fitting results is illustrated. After these preliminaries, invariant-based strain energy functions with decoupled dependencies on all three principal invariants are employed to identify promising models for each compound. Especially, appropriate parameter constraints are discussed and the role of the second invariant is analyzed. Thus, this contribution may serve as a guideline for the process of experimental characterization, data processing, model selection and parameter identification for existing as well as new materials.
    Type of Medium: Online Resource
    ISSN: 1134-3060 , 1886-1784
    URL: Article
    DOI: 10.1007/s11831-022-09865-x
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2276736-8
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    Online Resource
  • 2
    Online Resource
    Online Resource
    Multiplicative, Non-Newtonian Viscoelasticity Models for Rubber Materials and Brain Tissues: Numerical Treatment and Comparative Studies
    Springer Science and Business Media LLC ; 2023
    In:  Archives of Computational Methods in Engineering Vol. 30, No. 5 ( 2023-06), p. 2889-2927
    Details
    In: Archives of Computational Methods in Engineering, Springer Science and Business Media LLC, Vol. 30, No. 5 ( 2023-06), p. 2889-2927
    Abstract: In many aspects, elastomers and soft biological tissues exhibit similar mechanical properties such as a pronounced nonlinear stress–strain relation and a viscoelastic response to external loads. Consequently, many models use the same rheological framework and material functions to capture their behavior. The viscosity function is thereby often assumed to be constant and the corresponding free energy function follows that one of the long-term equilibrium response. This work questions this assumption and presents a detailed study on non-Newtonian viscosity functions for elastomers and brain tissues. The viscosity functions are paired with several commonly used free energy functions and fitted to two different types of elastomers and brain tissues in cyclic and relaxation experiments, respectively. Having identified suitable viscosity and free energy functions for the different materials, numerical aspects of viscoelasticity are addressed. From the multiplicative decomposition of the deformation gradient and ensuring a non-negative dissipation rate, four equivalent viscoelasticity formulations are derived that employ different internal variables. Using an implicit exponential map as time integration scheme, the numerical behavior of these four formulations are compared among each other and numerically robust candidates are identified. The fitting results demonstrate that non-Newtonian viscosity functions significantly enhance the fitting quality. It is shown that the choice of a viscosity function is even more important than the choice of a free energy function and the classical neo-Hooke approach is often a sufficient choice. Furthermore, the numerical investigations suggest the superiority of two of the four viscoelasticity formulations, especially when complex finite element simulations are to be conducted.
    Type of Medium: Online Resource
    ISSN: 1134-3060 , 1886-1784
    URL: Article
    DOI: 10.1007/s11831-023-09889-x
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2276736-8
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    Online Resource
  • 3
    Online Resource
    Online Resource
    Comparison of discontinuous damage models of Mullins-type
    Springer Science and Business Media LLC ; 2021
    In:  Archive of Applied Mechanics Vol. 91, No. 10 ( 2021-10), p. 4097-4119
    Details
    In: Archive of Applied Mechanics, Springer Science and Business Media LLC, Vol. 91, No. 10 ( 2021-10), p. 4097-4119
    Abstract: The Mullins effect is a characteristic property of filled rubber materials whose accurate and efficient modelling is still a challenging task. Innumerable constitutive models for elastomers are described in the literature. Therefore, this contribution gives a review on some widely used approaches, presents a classification, proves their thermodynamic consistency, and discusses reasonable modifications. To reduce the wide range of models, the choice is restricted to those which reproduce the idealised, discontinuous Mullins effect. Apart from the theoretical considerations, two compounds were produced and tested under cyclic uniaxial and equibiaxial tension as well as pure shear. Based on this experimental data, a benchmark that compares the fitting quality of the discussed models is compiled and favourable approaches are identified. The results are a sound basis for establishing novel or improving existing rubber models.
    Type of Medium: Online Resource
    ISSN: 0939-1533 , 1432-0681
    URL: Article
    DOI: 10.1007/s00419-021-02026-9
    RVK:
    ZG 1100
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2021
    detail.hit.zdb_id: 500644-2
    detail.hit.zdb_id: 1476349-7
    detail.hit.zdb_id: 1056088-9
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