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Statistical mechanics of bone damage: a constitutive model.

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Title: Statistical mechanics of bone damage: a constitutive model.
Authors: García-Vilana, S.1 (AUTHOR), Sánchez-Molina, D.1 (AUTHOR) david.sanchez-molina@upc.edu
Source: European Biophysics Journal. May2025, Vol. 54 Issue 3, p185-200. 16p.
Subjects: Statistical mechanics, Compact bone, Tensile tests, Damage models, Bone mechanics, Digital image correlation
Abstract: After the elastic regime is surpassed, cortical bone exhibits significant microcracking in its post-elastic mechanical behavior. This work develops a thermodynamically consistent, nonlinear constitutive model based on statistical mechanics, designed to predict the stress–strain relationship and the progression of inter-osteon microcracking. To assess the model's sufficiency, precise tensile and bending tests were performed in comparison to empirical curves that illustrated theoretical predictions of constitutive relationships. Moreover, entropy increases were quantitatively assessed using model parameters refined through experimental data. A large-size sample was utilized, comprising 51 dog-bone-shaped cortical bone specimens from the 4th ribs of various subjects for uniaxial tensile tests, and 15 complete fourth ribs for bending tests. Displacement and strain fields were meticulously recorded using digital image correlation and video analysis. The model demonstrated robustness, accurately fitting the data from all experimental specimens and revealing correlations between constitutive parameters and anthropometric variables. Entropy calculations provide insights into the behavior of the bone under varying strains: microcracking is minimal at low strains with stress nearly proportional to strain, escalating significantly beyond a critical threshold, thus challenging the linear relationship between stress and strain. [ABSTRACT FROM AUTHOR]
Copyright of European Biophysics Journal is the property of Springer Nature 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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  Data: <searchLink fieldCode="AR" term="%22García-Vilana%2C+S%2E%22">García-Vilana, S.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sánchez-Molina%2C+D%2E%22">Sánchez-Molina, D.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> david.sanchez-molina@upc.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22European+Biophysics+Journal%22">European Biophysics Journal</searchLink>. May2025, Vol. 54 Issue 3, p185-200. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Statistical+mechanics%22">Statistical mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Compact+bone%22">Compact bone</searchLink><br /><searchLink fieldCode="DE" term="%22Tensile+tests%22">Tensile tests</searchLink><br /><searchLink fieldCode="DE" term="%22Damage+models%22">Damage models</searchLink><br /><searchLink fieldCode="DE" term="%22Bone+mechanics%22">Bone mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Digital+image+correlation%22">Digital image correlation</searchLink>
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  Label: Abstract
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  Data: After the elastic regime is surpassed, cortical bone exhibits significant microcracking in its post-elastic mechanical behavior. This work develops a thermodynamically consistent, nonlinear constitutive model based on statistical mechanics, designed to predict the stress–strain relationship and the progression of inter-osteon microcracking. To assess the model's sufficiency, precise tensile and bending tests were performed in comparison to empirical curves that illustrated theoretical predictions of constitutive relationships. Moreover, entropy increases were quantitatively assessed using model parameters refined through experimental data. A large-size sample was utilized, comprising 51 dog-bone-shaped cortical bone specimens from the 4th ribs of various subjects for uniaxial tensile tests, and 15 complete fourth ribs for bending tests. Displacement and strain fields were meticulously recorded using digital image correlation and video analysis. The model demonstrated robustness, accurately fitting the data from all experimental specimens and revealing correlations between constitutive parameters and anthropometric variables. Entropy calculations provide insights into the behavior of the bone under varying strains: microcracking is minimal at low strains with stress nearly proportional to strain, escalating significantly beyond a critical threshold, thus challenging the linear relationship between stress and strain. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of European Biophysics Journal is the property of Springer Nature 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: 10.1007/s00249-025-01749-9
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 185
    Subjects:
      – SubjectFull: Statistical mechanics
        Type: general
      – SubjectFull: Compact bone
        Type: general
      – SubjectFull: Tensile tests
        Type: general
      – SubjectFull: Damage models
        Type: general
      – SubjectFull: Bone mechanics
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      – SubjectFull: Digital image correlation
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      – TitleFull: Statistical mechanics of bone damage: a constitutive model.
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              M: 05
              Text: May2025
              Type: published
              Y: 2025
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