A Chaos and Fractal Dynamic Approach to the Fracture Mechanics

Alves, Lucas Máximo; Lobo, Rui F. M.

doi:10.1007/3-540-32023-7_17

Cited by 3 publications

(3 citation statements)

References 27 publications

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“…One proposal attempts to explain the instability process on fast crack growth were made before 8,9 but without any clear experimental comparison. Now in this paper, a fundamental principle was introduced, which allow us to obtain the iterated equations and enabling to foresee the dissipation pattern in a complete mathematical scenario, from non-linear dynamical equations up to the fractal bifurcation map.…”

Section: Discussionmentioning

confidence: 99%

“…( 17) follows naturally from Eq. ( 1) and was deduced as a special case, by taking the fracture of a semi-infinite Griffith plate 8 . Therefore, it depends on the phenomenology, i.e., in which case the dynamic fracture was applied.…”

Section: Discussionmentioning

confidence: 99%

“…These structures and patterns typically exhibit a branched geometry that can be characterized as a fractal, between a finite range of scales min ≤ ≤ max ) 3,4 . However, there is not yet a complete treatment in Mechanics and Non-Equilibrium Thermodynamics able to describe all this phenomenology, from the unstable dynamic until to the growth of a dissipation structure or the fractal pattern formation [5][6][7][8][9] . From the basic assumption that there is a delay of rates and speeds between the system input and output, a principle of maximum energy dissipation was postulated and corresponding dynamic evolution equations were obtained.…”

Section: Introductionmentioning

confidence: 99%

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The possibility to predict crack patterns on dynamic fracture

Alves

Lobo

2017

Int J Fract

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The Maximum Energy Dissipation Principle (MEDP) for dynamics fracture, far from equilibrium, proposed by Slepyan was modified. This modification includes a decoupling between the injected and dissipated energy by adding of a time delay and a description of the ruggedness produced by dissipation patterns. A time delayed energy conservation equation is deduced and dynamical equations that describe the dynamical system evolution were obtained in analogous way to the Slepyan's calculations. The conditions for the rising of the instability process were presented by a bifurcation map. These results shown that the theoretical framework proposed can describe the instability process along with dissipation patterns formation. This proposal was applied to dynamics fracture where it was possible to explain the results obtained by Fineberg-Gross for the fast crack propagation in PMMA. For unstable or dynamical crack propagation it is shown the possibility to predict crack patterns using this MEDP for other experimental configurations.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The possibility to predict crack patterns on dynamic fracture

Alves

Lobo

2017

Int J Fract

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References

2017

Handbook of Structural Life Assessment

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Nonclinical research areas of future importance for clinical therapies: Exploring the concepts of nonlinearity in dentistry

Jalali¹,

Hasselgren

2021

J Conserv Dent

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Linear system analysis has been dominating medical and dental research, and most of the research achievements in these fields have come from applying a reductionist view of nature. However, biologic systems are fundamentally nonlinear with highly composite dynamics made up of numerous interacting elements and feedback loops, therefore studying them as linear models may not result in an accurate representation of their true features. The authors reviewed and utilized some of the principles of chaos and nonlinearity and extended them to clinical dentistry, from cracked tooth and flare-up after root canal procedures to the outcome of clinical treatments. Utilization of the concepts of chaos and sensitive dependence on initial conditions, and the concepts of self-organization, stigmergy, and fractals may help us to understand some of the puzzles that have not been solved by conventional linear models. The goal of this paper is to present some areas within nonclinical research that we believe will have important roles in the development of future clinical examination methods and therapies.

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A Chaos and Fractal Dynamic Approach to the Fracture Mechanics

Cited by 3 publications

References 27 publications

The possibility to predict crack patterns on dynamic fracture

The possibility to predict crack patterns on dynamic fracture

References

Nonclinical research areas of future importance for clinical therapies: Exploring the concepts of nonlinearity in dentistry

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