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Remodelling in statistically oriented fibre-reinforced materials and biological tissues.

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Title: Remodelling in statistically oriented fibre-reinforced materials and biological tissues.
Authors: Grillo, Alfio1 alfio.grillo@polito.it, Wittum, Gabriel2, Tomic, Aleksandar3, Federico, Salvatore4
Source: Mathematics & Mechanics of Solids. Oct2015, Vol. 20 Issue 9, p1107-1129. 23p.
Subjects: Fibrous composites, Tissues -- Models, Distribution (Probability theory), Compressibility, Stress concentration, Energy dissipation
Abstract: We present a mathematical model of structural reorganisation in a fibre-reinforced composite material in which the fibres are oriented statistically, i.e. obey a probability distribution of orientation. Such a composite material exemplifies a biological tissue (e.g. articular cartilage or a blood vessel) whose soft matrix is reinforced by collagen fibres. The structural reorganisation of the composite takes place as fibres reorient, in response to mechanical stimuli, in order to optimise the stress distribution in the tissue. Our mathematical model is based on the Principle of Virtual Powers and the study of dissipation. Besides incompressibility, our main hypothesis is that the composite is characterised by a probability density distribution that measures the probability of finding a family of fibres aligned along a given direction at a fixed material point. Under this assumption, we describe the reorientation of fibres as the evolution of the most probable direction along which the fibres are aligned. To test our theory, we compare our simulations of a benchmark problem with selected results taken from the literature. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics & Mechanics of Solids is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Remodelling in statistically oriented fibre-reinforced materials and biological tissues.
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  Data: <searchLink fieldCode="AR" term="%22Grillo%2C+Alfio%22">Grillo, Alfio</searchLink><relatesTo>1</relatesTo><i> alfio.grillo@polito.it</i><br /><searchLink fieldCode="AR" term="%22Wittum%2C+Gabriel%22">Wittum, Gabriel</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Tomic%2C+Aleksandar%22">Tomic, Aleksandar</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Federico%2C+Salvatore%22">Federico, Salvatore</searchLink><relatesTo>4</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Mechanics+of+Solids%22">Mathematics & Mechanics of Solids</searchLink>. Oct2015, Vol. 20 Issue 9, p1107-1129. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Fibrous+composites%22">Fibrous composites</searchLink><br /><searchLink fieldCode="DE" term="%22Tissues+--+Models%22">Tissues -- Models</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Compressibility%22">Compressibility</searchLink><br /><searchLink fieldCode="DE" term="%22Stress+concentration%22">Stress concentration</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+dissipation%22">Energy dissipation</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: We present a mathematical model of structural reorganisation in a fibre-reinforced composite material in which the fibres are oriented statistically, i.e. obey a probability distribution of orientation. Such a composite material exemplifies a biological tissue (e.g. articular cartilage or a blood vessel) whose soft matrix is reinforced by collagen fibres. The structural reorganisation of the composite takes place as fibres reorient, in response to mechanical stimuli, in order to optimise the stress distribution in the tissue. Our mathematical model is based on the Principle of Virtual Powers and the study of dissipation. Besides incompressibility, our main hypothesis is that the composite is characterised by a probability density distribution that measures the probability of finding a family of fibres aligned along a given direction at a fixed material point. Under this assumption, we describe the reorientation of fibres as the evolution of the most probable direction along which the fibres are aligned. To test our theory, we compare our simulations of a benchmark problem with selected results taken from the literature. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Mathematics & Mechanics of Solids is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1177/1081286513515265
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      – Code: eng
        Text: English
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        PageCount: 23
        StartPage: 1107
    Subjects:
      – SubjectFull: Fibrous composites
        Type: general
      – SubjectFull: Tissues -- Models
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Compressibility
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      – SubjectFull: Stress concentration
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      – SubjectFull: Energy dissipation
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      – TitleFull: Remodelling in statistically oriented fibre-reinforced materials and biological tissues.
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            NameFull: Wittum, Gabriel
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            – D: 01
              M: 10
              Text: Oct2015
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              Y: 2015
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