Convexity and Quasiconvexity in a Cosserat Model for Fiber-Reinforced Elastic Solids

An inequality of the quasiconvexity type is derived in the context of a Cosserat model for fiber-reinforced elastic solids in which the Cosserat rotation field accounts for the kinematics of the embedded fibers, modeled as extensible, unshearable spatial rods. This is shown to be equivalent to the r...

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Bibliographic Details
Published inJournal of elasticity Vol. 154; no. 1-4; pp. 555 - 567
Main Authors Shirani, M., Steigmann, D. J.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.11.2023
Springer Nature B.V
Subjects
Biomechanics
Classical and Continuum Physics
Classical Mechanics
Convexity
Engineering
Fiber reinforced materials
Kinematics
Materials Science
Mathematical Applications in the Physical Sciences
Strain energy
Theoretical and Applied Mechanics
Quasiconvexity
Cosserat elasticity
74A60
Fiber-reinforced materials
74A05
Convexity
74B20
74A30
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ISSN0374-3535
1573-2681
DOI10.1007/s10659-022-09963-8

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Summary:An inequality of the quasiconvexity type is derived in the context of a Cosserat model for fiber-reinforced elastic solids in which the Cosserat rotation field accounts for the kinematics of the embedded fibers, modeled as extensible, unshearable spatial rods. This is shown to be equivalent to the requirement that the fiber bend-twist strain vector associated with an energy minimizer be a point of convexity of the operative strain-energy function. The analysis requires careful consideration of constraints associated with the fact that fibers are convected by the continuum deformation field as material curves.
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ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-022-09963-8