Fractional and fractal order effects in soft elastomers: Strain rate and temperature dependent nonlinear mechanics

Stanisauskis, Eugenia; Mashayekhi, Somayeh; Pahari, Basanta R.; Mehnert, Markus; Steinmann, Paul; Oates, William S.

doi:10.1016/j.mechmat.2022.104390

Cited by 9 publications

(4 citation statements)

References 22 publications

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“…Recent studies in the field of fractional calculus 11,42 and fractal diffusion in materials 8,10 have spurred efforts to understand how both fractal and fractional order operators offer new insights into complex material behavior . 1,3,21,26,32,36,38,43 Since we are analysing heat transfer properties on 2D fractals, a properly scaled version of the non-integer derivative, known as the fractal derivative, is considered to build a surrogate model.…”

Section: Fractal Diffusion Modelingmentioning

confidence: 99%

“…37 Recent research shows the fractal order model assumptions provide insight into simulating viscoelasticity on elastomers and deriving temperature-dependent constitutive behavior. 24,28,36 Examples of perfect monofractals are given in Fig. 1, which shows the original Mandelbrot set on the left and the Koch snowflake, another iterative fractal, on the right.…”

Section: Introductionmentioning

confidence: 99%

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Multifractal analysis of heat transport in DLA structures

Carvajal,

Oates,

Pahari

2024

Behavior and Mechanics of Multifunctional Materials XVIII

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Multifractal analysis originated from the desire to obtain a deeper understanding of materials that follow random fractal structures. Complex systems display diverse degrees of irregularity and self-similarity on multiple scales that cannot be adequately described by a single fractal dimension due to uncertainties as well as deterministic changes in structure at different length and time scales. The multifractal spectrum measures the distribution of a specific property across different scales or levels within a system using a range of exponents. These properties can encompass anything from turbulence intensity in fluid flow to the distribution of heat flow through a solid. Each exponent in the spectrum corresponds to a particular level of irregularity, and a broad range of exponents indicates more complexity. Multifractal measures have a range of applications, from biology to mechanical engineering, among many others. In multifunctional materials used in adaptive systems, a more accurate description of material properties, such as viscoelasticity, heat transport, phase transformations, often involves considering information about their underlying fractal material structure. This study goes beyond fractals to include randomness in terms of multifractal measures. This involves analysis of the Renyi entropy. We evaluate this approach by examining heat transport in DLA structures which display multifractal properties. Renyi entropy is relevant here due to its entropy order parameter's close connection to the multifractal spectrum. In fact, the multifractal spectrum can be directly calculated through the generalized Renyi entropy dimension and a box-counting process. We investigate the multifractality of different DLA structures and leverage this insight to better understand heat diffusion processes using fractal-order diffusion equations; however, the methodology is more broadly applicable to a wide range of multiphysics problems involving energy transport over complex media.

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Section: Fractal Diffusion Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of heat transport in DLA structures

Carvajal,

Oates,

Pahari

2024

Behavior and Mechanics of Multifunctional Materials XVIII

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“…The molecular dynamics model we derive here relies on the entropy of a given system and our approach is similar to the relative Shannon entropy 6,7 and Renyi entropy formulation of the polymer deformation process. 4 We will only present a 1D dimensional case but the idea can be extended to higher dimensions.…”

Section: Entropy Dynamics Approach To Molecular Dynamicsmentioning

confidence: 99%

Game theoretic simulations and entropy dynamics framework for modeling complex material interactions

Pahari

Ogunlana

Oates

2023

Behavior and Mechanics of Multifunctional Materials XVII

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Molecular dynamics is a technique used to understand how the interactions between atoms control complex material behavior under internal and external forces. We use a game theoretical approach to simulate molecular interactions, build material surrogates, and study material nature as a function of the Coulomb potential. The electric Coulomb potential is applicable in studying electromagnetic properties, for instance, electrical conductivity and dielectric permittivity. We investigate how probability densities of material positions and charges influence the diffusion process induced by this potential. By exploiting the information hidden in the seemingly random molecular exchanges, we show that an information-theoretical measure of entropy can describe the dynamics of material interactions. In particular, we use the Renyi entropy to derive posterior density representing the most likely particle distribution after these exchanges and thus connect molecular dynamics to entropy dynamics.

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“…On an industrial scale, it turned out to be effective to use polymer matrices with conductive dispersed additives. Variations between the properties of elastomer matrices [ 6 ] and conductive disperse additives make it possible to form a wide range of materials with various properties [ 7 ]. The dynamic development of electric vehicles is accompanied by new types of tasks that affect the improvement of microclimate technologies [ 8 ].…”

Section: Introductionmentioning

confidence: 99%

Changes in the Electrophysical Parameters of Nanomodified Elastomers Caused by Electric Current’s Passage

Shchegolkov

Zemtsova

et al. 2023

Polymers

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The development of reliable and effective functional materials that can be used in various technological fields and environmental conditions is one of the goals of modern nanotechnology. Heating elements’ manufacturing requires understanding the laws of heat transfer under conditions of different supply voltages, as this expands the possibilities of such materials’ application. Elastomers based on silicon-organic compounds and polyurethane modified with multi-walled carbon nanotubes (MWCNTs) were studied at various concentrations of Ni/MgO or Co-Mo/MgO and voltages (220, 250, and 300 V). It was found that an increase in voltage from 220 to 300 V leads to an initial increase in specific power on one-third followed by a subsequent decrease in a specific power when switched on again to 220 V (for −40 °C) of up to ~44%. In turn, for a polyurethane matrix, an increase in voltage to 300 V leads to an initial peak power value of ~15% and a decrease in power when switched on again by 220 V (for −40 °C) to ~36% (Ni/MgO -MWCNT). The conducted studies have shown that the use of a polyurethane matrix reduces power degradation (associated with voltage surges above 220 V) by 2.59% for Ni/MgO–based MWCNT and by 10.42% for Co-Mo/MgO. This is due to the better heat resistance of polyurethane and the structural features of the polymer and the MWCNT. The current studies allow us to take the next step in the development of functional materials for electric heating and demonstrate the safety of using heaters at a higher voltage of up to 300 V, which does not lead to their ignition, but only causes changes in electrophysical parameters.

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Fractional and fractal order effects in soft elastomers: Strain rate and temperature dependent nonlinear mechanics

Cited by 9 publications

References 22 publications

Multifractal analysis of heat transport in DLA structures

Multifractal analysis of heat transport in DLA structures

Game theoretic simulations and entropy dynamics framework for modeling complex material interactions

Changes in the Electrophysical Parameters of Nanomodified Elastomers Caused by Electric Current’s Passage

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