The coupled Legendre-Hadamard condition for fiber-reinforced materials: three-dimensional solids and two-dimensional shells

IF 1.9 4区工程技术 Q3 MECHANICS

Continuum Mechanics and Thermodynamics Pub Date : 2025-01-24 DOI:10.1007/s00161-025-01357-0

Mircea Bîrsan, Milad Shirani, David J. Steigmann

引用次数: 0

Abstract

Detailed derivations of the Legendre-Hadamard necessary conditions for energy-minimizing states of fiber-reinforced three-dimensional solids and two-dimensional shells are presented. The underlying conceptual framework is Cosserat elasticity theory in which the Cosserat rotation field controls the orientation of the embedded fibers. This is partially coupled to the continuum deformation gradient by the requirement that the fibers convect as material curves with respect to the matrix material in which they are embedded. The conditions obtained combine the effects of deformation and rotation and subsume previously obtained decoupled inequalities involving these effects separately.

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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.