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Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: Application to planar soft tissues
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Sanjay Pant ,
Chung-Hao Lee
Computer Methods in Applied Mechanics and Engineering, Volume: 404, Start page: 115812
Swansea University Author:
Sanjay Pant
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DOI (Published version): 10.1016/j.cma.2022.115812
Abstract
Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy d...
| Published in: | Computer Methods in Applied Mechanics and Engineering |
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| ISSN: | 0045-7825 |
| Published: |
Elsevier BV
2023
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa62031 |
| Abstract: |
Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress-strain data obtained from biaxial experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantageof a GP-based model is that, in addition to the mean value, it provides a probability density (i.e. associated uncertainty) for the strain energy density. To simulate the effect of this uncertainty, a non-intrusive stochastic finite element analysis (SFEA) framework is proposed. The proposed frameworkis verified against an artificial dataset based on the Gasser–Ogden–Holzapfel model and applied to a real experimental dataset of a porcine aortic valve leaflet tissue. Results show that the proposed framework can be trained with limited experimental data and fits the data better than several existing models. The SFEA framework provides a straightforward way of using the experimental data and quantifying the resulting uncertainty in simulationbased predictions. |
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| Keywords: |
Constitutive modeling, nonlinear elasticity, tissue biomechanics, Gaussian processes, stochastic finite element analysis, machine learning |
| College: |
Faculty of Science and Engineering |
| Funders: |
Support from the National Institutes of Health (NIH) Grant R01 HL159475 and the Presbyterian Health
Foundation Team Science Grants is greatly acknowledged |
| Start Page: |
115812 |