高对比度刚性纤维增强复合材料均质化产生的具有扭转的第二和第三梯度材料

IF 1.9 4区工程技术 Q3 MECHANICS Continuum Mechanics and Thermodynamics Pub Date : 2024-01-29 DOI:10.1007/s00161-024-01278-4

Mustapha El Jarroudi

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引用次数: 0

摘要

摘要我们研究了由弹性基体与截面为圆形的高对比度三维弹性刚性纤维接触而成的弹性材料的均质化问题。基体与纤维之间的相互作用由局部界面粘附定律描述。假设纤维中的拉梅常数和粘合剂的刚度系数具有适当的数量级，我们推导出一类变形能，其中包括第二梯度函数、第三梯度函数和与内扭转相关的函数能。

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A second and third gradient material with torsion resulting from the homogenization of a highly contrasted rigid fibre-reinforced composite

We study the homogenization of an elastic material made of an elastic matrix in contact with highly contrasted three-dimensional elastic rigid fibres with circular cross section. The interaction between the matrix and the fibres is described by a local interface adhesion law. Assuming that the Lamé constants in the fibres and the stiffness coefficient of the adhesive have appropriate orders of magnitude, we derive a class of deformation energies involving second gradient functionals, third gradient functionals, and a functional energy associated with inner torsion.

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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.