The sobol sensitivity analysis of the pressure, stresses, and displacement arising from poroelastic modelling of hard mechanical systems
Asghari H. Miller L. Penta R. Melnikov A. Spitas C. Merodio J.
December 2025Nature Research
Scientific Reports
2025#15Issue 1
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 has the highest influence on the pressure, the stress components and displacements. We find that the Poisson ratio plays a greater role than shear in the pressure response, and the shear counts more than the other parameters in the radial and circumferential stresses. There are key joint interactions between the Biot’s coefficient and the Poisson ratio, the non-dimensionalised radius 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.
Biot’s poroelasticity , Hard mechanical systems , Sobol statistical method
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Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Kabanbay Batyr 53, Astana, 010000, Kazakhstan
Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow, G1 1XH, United Kingdom
School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, United Kingdom
Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Ningbo, China
Departamento de Matematica Aplicada a las TIC, Universidad Politecnica de Madrid, Madrid, Spain
Institute of Mathematics, Faculty of Technical Physics, Information Technology and Applied Mathematics, Lodz University of Technology, Lodz, Poland
Department of Mathematics
Department of Mathematics and Statistics
School of Mathematics and Statistics
Department of Mechanical
Departamento de Matematica Aplicada a las TIC
Institute of Mathematics
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