Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues

Aggarwal, A. , Jensen, B. S. , Pant, S. and Lee, C.-H. (2023) Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues. Computer Methods in Applied Mechanics and Engineering, 404, 115812. (doi: 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, focusing on planar, hyperelastic and incompressible soft tissues. Specifically, the strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress–strain data obtained from biaxial stretching experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantage of 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 framework is 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. The 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 simulation-based predictions.

• Item Type: Articles
• Additional Information: Support from the National Institutes of Health (NIH) Grant R01 HL159475 and the Presbyterian Health Foundation Team Science Grants is greatly acknowledged.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Jensen, Dr Bjorn and Aggarwal, Dr Ankush
• Authors: Aggarwal, A., Jensen, B. S., Pant, S., and Lee, C.-H.
• College/School: College of Science and Engineering > School of Computing Science; College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computer Methods in Applied Mechanics and Engineering
• Publisher: Elsevier
• ISSN: 0045-7825
• ISSN (Online): 1879-2138
• Published Online: 10 December 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Computer Methods in Applied Mechanics and Engineering 404: 115812
• Publisher Policy: Reproduced under a Creative Commons License