关于 $$\Lambda $$ - 分数连续介质力学场

IF 1.9 4区工程技术 Q3 MECHANICS Continuum Mechanics and Thermodynamics Pub Date : 2024-02-14 DOI:10.1007/s00161-024-01282-8

K. A. Lazopoulos, A. K. Lazopoulos

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引用次数: 0

摘要

在定义了分数 $\varLambda $-导数之后，分数 $\varLambda $-应变就已经建立起来了，分数 $\varLambda $-导数具有对应于微分的所有先决条件。此外，在分数分析中只允许全局变分原理。因此，在（\λ\）-分数连续介质力学中产生各种场方程的平衡定律被推导出来，允许在它们的场中存在角。质量、线动量和旋转动量以及能量守恒的基本平衡定律都是在（\λ\）-分式分析的背景下推导出来的。

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On the $\Lambda $-fractional continuum mechanics fields

After defining the fractional $\varLambda $-derivative, having all the prerequisites for corresponding to a differential, the fractional $\varLambda $-strain has already been established. Furthermore, only globally variational principles are allowed in the context of fractional analysis. Hence, balance laws, yielding the various field equations in $\Lambda $-fractional continuum mechanics, are derived, allowing corners in their fields. The basic balance laws of mass, linear and rotational momentum, and energy conservation with jump conditions are derived in the context of $\Lambda $-fractional analysis.

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.