Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters

Mahnken, Rolf

doi:10.1007/s00419-021-02069-y

Cited by 8 publications

(3 citation statements)

References 50 publications

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“…This raised well-posed concerns for their formulation. These were covered recently via the direct inclusion of the physical and mechanical constraints into the neural network [124][125][126].…”

Section: Hyper-elastic Materialsmentioning

confidence: 99%

Probabilistic Analysis of Composite Materials with Hyper-Elastic Components

Kamiński

Sokołowski

2022

Materials

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This work is a comprehensive literature overview in the area of probabilistic methods related to composite materials with components exhibiting hyper-elastic constitutive behavior. A practical area of potential applications is seen to be rubber, rubber-like, or even rubber-based heterogeneous media, which have a huge importance in civil, mechanical, environmental, and aerospace engineering. The overview proposed and related discussion starts with some general introductory remarks and a general overview of the theories and methods of hyper-elastic material with a special emphasis on the recent progress. Further, a detailed review of the current trends in probabilistic methods is provided, which is followed by a literature perspective on the theoretical, experimental, and numerical treatments of interphase composites. The most important part of this work is a discussion of the up-to-date methods and works that used the homogenization method and effective medium analysis. There is a specific focus on random composites with and without any interface defects, but the approaches recalled here may also serve as well in sensitivity analysis and optimization studies. This discussion may be especially helpful in all engineering analyses and models related to the reliability of elastomers, whose applicability range, which includes energy absorbers, automotive details, sportswear, and the elements of water supply networks, is still increasing, as well as areas where a stochastic response is the basis of some limit functions that are fundamental for such composites in structural health monitoring.

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Section: Hyper-elastic Materialsmentioning

confidence: 99%

Probabilistic Analysis of Composite Materials with Hyper-Elastic Components

Kamiński

Sokołowski

2022

Materials

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“…Typically, accuracy comparisons rely on stress-strain curves derived from strain energy functions [9,10], wherein stress-strain curves from three mechanical tests are compared with model predictions. Recent studies [10][11][12][13][14] have compared the accuracy of a large number of hyperelastic models, deriving their own strain energy functions. Studies have also explored how fitting algorithm formulations affect the generation of material parameters and prediction accuracy [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…Recent studies [10][11][12][13][14] have compared the accuracy of a large number of hyperelastic models, deriving their own strain energy functions. Studies have also explored how fitting algorithm formulations affect the generation of material parameters and prediction accuracy [12][13][14]. Studies have examined accuracy under biaxial deformation [15], comparing model-predicted stress with mechanical test results.…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Various Hyperelastic Models and Element Types for Finite Element Analysis

Lin,

Le Roux de Bretagne,

Grasso

et al. 2023

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This study aims to evaluate the precision of nine distinct hyperelastic models using experimental data sourced from the existing literature. These models rely on parameters obtained through curve-fitting functions. The complexity in finite element models of elastomers arises due to their nonlinear, incompressible behaviour. To achieve accurate representations, it is imperative to employ sophisticated hyperelastic models and appropriate element types and formulations. Prior published work has primarily focused on the comparison between the fitting models and the experimental data. Instead, in this study, the results obtained from finite element analysis are compared against the original data to assess the impact of element formulation, strain range, and mesh type on the ability to accurately predict the response of elastomers over a wide range of strain values. This comparison confirms that the element formulation and strain range can significantly influence result accuracy, yielding different responses in various strain ranges also because of the limitation with the curve fitting tools.

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A statistically based strain energy function for polymer chains in rubber elasticity

Mahnken

Mirzapour

2022

Arch Appl Mech

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Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters

Cited by 8 publications

References 50 publications

Probabilistic Analysis of Composite Materials with Hyper-Elastic Components

Probabilistic Analysis of Composite Materials with Hyper-Elastic Components

Comparative Analysis of Various Hyperelastic Models and Element Types for Finite Element Analysis

A statistically based strain energy function for polymer chains in rubber elasticity

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