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<p>We perform a sensitivity analysis to investigate the influence of material input parameters on the pressure, stresses, and displacement of an isotropic porous solid cylinder representing hard mechanical systems such as the bone. We model the system using the governing equations of Biot’s poroelasticity in cylindrical polar coordinates, where the solutions are found by enforcing radial boundary conditions. The sensitivity analysis is carried out on the solutions for the pressure, stress components and displacement using ranges of the investigated parameters representative of the bone. Our study finds that the time <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(t^*\)</EquationSource> </InlineEquation> has the highest influence on the pressure, the stress components and displacements. We find that the Poisson ratio <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\nu\)</EquationSource> </InlineEquation> plays a greater role than shear <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mu\)</EquationSource> </InlineEquation> in the pressure response, and the shear <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mu\)</EquationSource> </InlineEquation> counts more than the other parameters in the radial and circumferential stresses. There are key joint interactions between the Biot’s coefficient <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> and the Poisson ratio <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\nu\)</EquationSource> </InlineEquation>, the non-dimensionalised radius <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(R^*\)</EquationSource> </InlineEquation> of the bone, and the Biot’s modulus <i>M</i> when investigating interstitial pressure, which is a key value in bone remodelling and fracture healing. This study paves the way to a deeper understanding of the interplay of all the parameters that are necessary to capture the true behaviour of hard mechanical systems such as the bone and its potential remodelling.</p>

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The sobol sensitivity analysis of the pressure, stresses, and displacement arising from poroelastic modelling of hard mechanical systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月23日

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  • Hadi Asghari,
  • Laura Miller,
  • Raimondo Penta,
  • Andrey Melnikov,
  • Christos Spitas,
  • Jose Merodio

摘要

We perform a sensitivity analysis to investigate the influence of material input parameters on the pressure, stresses, and displacement of an isotropic porous solid cylinder representing hard mechanical systems such as the bone. We model the system using the governing equations of Biot’s poroelasticity in cylindrical polar coordinates, where the solutions are found by enforcing radial boundary conditions. The sensitivity analysis is carried out on the solutions for the pressure, stress components and displacement using ranges of the investigated parameters representative of the bone. Our study finds that the time \(t^*\) has the highest influence on the pressure, the stress components and displacements. We find that the Poisson ratio \(\nu\) plays a greater role than shear \(\mu\) in the pressure response, and the shear \(\mu\) counts more than the other parameters in the radial and circumferential stresses. There are key joint interactions between the Biot’s coefficient \(\alpha\) and the Poisson ratio \(\nu\) , the non-dimensionalised radius \(R^*\) of the bone, and the Biot’s modulus M when investigating interstitial pressure, which is a key value in bone remodelling and fracture healing. This study paves the way to a deeper understanding of the interplay of all the parameters that are necessary to capture the true behaviour of hard mechanical systems such as the bone and its potential remodelling.