Data-driven hyperelasticity, Part I: A canonical isotropic formulation for rubberlike materials

Dal, Hüsnü; Denli, Funda Aksu; Açan, Alp Kağan; Kaliske, Michael

doi:10.1016/j.jmps.2023.105381

Cited by 8 publications

(2 citation statements)

References 72 publications

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“…The fitting results (R-squared more than 0.998) proved that the mechanical behavior of all the compositions tested corresponded to the polynomial model, applicable when the energy of the deformation was continuously differentiable several times with respect to three strain invariants for compressible materials and two invariants for incompressible ones [43]. The polynomial model fits well to describe the material characteristics in the finite element method (FEM) and corresponds to the recommendation provided in [68], where various functional forms and math expressions were proposed to describe invariants for deformation tensors and principal stretches, and the polynomial model was presented as the most suitable for hyper-elastic materials.…”

Section: Discussionsupporting

confidence: 58%

Biodegradable Carrageenan-Based Force Sensor: An Experimental Approach

Žaimis,

Petronienė,

Dzedzickis

et al. 2023

Sensors

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The development of low-cost biodegradable pressure or force sensors based on a carrageenan and iron (III) oxide mix is a promising way to foster the spread of green technologies in sensing applications. The proposed materials are inexpensive and abundant and are available in large quantities in nature. This paper presents the development and experimental study of carrageenan and iron (III)-oxide-based piezoresistive sensor prototypes and provides their main characteristics. The results show that glycerol is required to ensure the elasticity of the material and preserve the material from environmental impact. The composition of the carrageenan-based material containing 1.8% Fe2O3 and 18% glycerol is suitable for measuring the load in the range from 0 N to 500 N with a sensitivity of 0.355 kΩ/N when the active surface area of the sensor is 100 mm2. Developed sensors in the form of flexible film have square resistance dependence to the force/pressure, and due to the soft original material, they face the hysteresis effect and some plastic deformation effect in the initial use stages. This paper contains extensive reference analysis and found a firm background for a new sensor request. The research covers the electric and mechanical properties of the developed sensor and possible future applications.

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Section: Discussionsupporting

confidence: 58%

Biodegradable Carrageenan-Based Force Sensor: An Experimental Approach

Žaimis,

Petronienė,

Dzedzickis

et al. 2023

Sensors

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“…4 Model-free data-driven (DD) modeling is another concept of how material behavior can be represented in numerical models, showing great potential for modeling rubber-like materials. Dal et al 5 used data-driven models and showed that even lower order polynomial bases could produce a sufficient prognosis. The modified invariant concept could further increase the prognosis with low polynomial order.…”

Section: Introductionmentioning

confidence: 99%

Stability study of the compressible Mooney-Rivlin hyperelastic model

Fodor,

Kossa

2024

The Journal of Strain Analysis for Engineering Design

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The unstable behavior of the isotropic, compressible Mooney-Rivlin hyperelastic model is investigated and described. The constitutive equation is parameterized with the help of the ground-state Poisson’s ratio and the dimensionless ratio of the material parameters [Formula: see text] and [Formula: see text]. Transverse stretch solutions are obtained for standard homogeneous loading modes, and the stress solutions are computed numerically for the physically permitted range of the ground-state Poisson’s ratio. We introduce a numerical technique to isolate subdomains with non-unique transverse stretch responses. Our analysis revealed some limitations of the model and allowed us to make critical observations about the strengths and weaknesses of the model. The analyses we present are essential to understand the characteristics of this widely used hyperelastic model. The novel results have important implications for the application of the isotropic, compressible Mooney-Rivlin hyperelastic material model.

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A data‐driven constitutive model for soft biological tissues

Açan,

Tikenoğullari,

Dal

2023

Proc Appl Math and Mech

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Constitutive modeling of soft biological tissues is crucial for biomedical simulations and a deep understanding of tissue mechanics. Classical constitutive models have a fixed mathematical expression, however, the microstructure and the corresponding macro‐mechanical response of different tissue types can vary significantly. A model that works for one tissue may not work for another kind of tissue, and choosing the right model may become challenging. To solve this issue, this study introduces a new data‐driven approach to creating a unified model for predicting the mechanical response of various tissue classes. The proposed model is based on B‐Spline approximations and assumes the strain energy function can be divided into volumetric, isotropic, and anisotropic components. The B‐Spline ansatz replaces partial derivatives of free energy energy function with respect to invariants with control points and polynomial degree, and allows the use of existing dispersion models. The model adapts its control point values to reduce the error between data and prediction until a threshold is reached, and is thermodynamically consistent through the use of optimization constraints. The model is demonstrated on various biological tissues, showing excellent fitting capabilities with a minimal number of control points. The outcome is a generic framework that can model any tissue given the data from experiments and imaging techniques.

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Data-driven hyperelasticity, Part I: A canonical isotropic formulation for rubberlike materials

Cited by 8 publications

References 72 publications

Biodegradable Carrageenan-Based Force Sensor: An Experimental Approach

Biodegradable Carrageenan-Based Force Sensor: An Experimental Approach

Stability study of the compressible Mooney-Rivlin hyperelastic model

A data‐driven constitutive model for soft biological tissues

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