Entropy dynamics approach to fractional order mechanics with applications to elastomers

Oates, William S.; Stanisaukis, Eugenia; Pahari, Basanta R.; Mashayekhi, Somayeh

doi:10.1117/12.2582423

Cited by 11 publications

(3 citation statements)

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“…Future work is focused on how the fractional order depends on the underlying structure of the material which may irreversibly evolve during large deformation and cyclic loading. Given recent observations in elastomers (Mashayekhi et al, 2019; Oates et al, 2021) and broader work connecting fractals and fractional calculus operators (Tarasov, 2010; West and Grigolini, 2010; West et al, 2012) new predictive models may be created that accommodate fractal and multifractal coupling in thermodynamic models. The microscopic evolution of auxetic foams has been studied (McDonald et al, 2011) with analytical models used to explain strain dependent mechanical properties of cellular models (Gibson and Ashby, 1997; Masters and Evans, 1996) as well as auxetic foams (Duncan et al, 2017).…”

Section: Discussionmentioning

confidence: 99%

Finite deformation and fractional order viscoelasticity of an auxetic foam

Stanisauskis

Miles

Oates

2022

Journal of Intelligent Material Systems and Structures

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Auxetic foams exhibit novel mechanical properties due to their unique microstructure for improved energy-absorption and cavity expansion applications that have fascinated the scientific community since their inception. Given the advancements in material processing and performance of polymer open cell auxetic foams, there is a strong desire to fully understand the nonlinear rate-dependent deformation of these materials. The influence of nonlinear compressibility is introduced here along with relaxation effects to improve model predictions for different stretch rates and finite deformation regimes. The viscoelastic behavior of the material is analyzed by comparing fractional order and integer order calculus models. All results are statistically validated using maximum entropy methods to obtain Bayesian posterior densities for the hyperelastic, auxetic, and viscoelastic parameters. It is shown that fractional order viscoelasticity provides [Formula: see text]–[Formula: see text] improvement in prediction over integer order viscoelastic models when the model is calibrated at higher stretch rates where viscoelasticity is more significant.

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Section: Discussionmentioning

confidence: 99%

Finite deformation and fractional order viscoelasticity of an auxetic foam

Stanisauskis

Miles

Oates

2022

Journal of Intelligent Material Systems and Structures

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“…Shannon's pioneering work in the field of information theory resulted in many advancements, including a widely-used measure of entropy known as Shannon entropy. 34 This entropy offers a valuable tool for improving our understanding of nonlinear, rate-dependent mechanics 6,25 and can be further extended to advanced forms of thermodynamic entropy. 16 For a random variable represented by X having n potential outcomes with corresponding probabilities p 1 , p 2 , .…”

Section: Entropy and Multifractalsmentioning

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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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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“…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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Entropy dynamics approach to fractional order mechanics with applications to elastomers

Cited by 11 publications

References 0 publications

Finite deformation and fractional order viscoelasticity of an auxetic foam

Finite deformation and fractional order viscoelasticity of an auxetic foam

Multifractal analysis of heat transport in DLA structures

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

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