Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental va
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ORIGINAL PAPER
Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability Krishna Kenja1 · Sandeep Madireddy2 · Kumar Vemaganti1 Received: 4 August 2019 / Accepted: 20 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The calibration of hyperelastic constitutive models of soft tissue and tissue surrogates is often treated as an exercise in curve-fitting to the average experimental response, and many of the complicating factors such as experimental boundary conditions and data variability are ignored. In this work, we focus on three questions that arise in this area: the ramifications of ignoring the experimental boundary conditions, the use of local optimizers, and the role of data variability. Using data from a uniaxial extension experiment on a tissue surrogate, we study how these three factors affect the calibration of isotropic hyperelastic constitutive models. Our results show that even with the simplest of constitutive models, it is necessary to look beyond a “good fit” to the average. Keywords Constitutive modeling · Hyperelastic · Bayesian · Uncertainty · Search algorithm · Soft tissue
1 Introduction Hyperelastic constitutive models of soft tissue and tissue surrogates play a critical role in applications like computeraided surgery and functional tissue engineering. These models are often calibrated by fitting the model response to the average experimental data using a least squares minimization procedure, where a local search technique is used to optimize the cost functional. Model calibration here refers to the process of adjusting the parameters of the constitutive model till its prediction is in close agreement with the data in some user-defined sense. Typical experiments such as uniaxial tension and compression (Roan and Vemaganti 2007; Brunon et al. 2010; Chui et al. 2004), indentation (Chai et al. 2013; Samur et al. 2007), and aspiration (Kauer et al. 2002; Nava et al. 2008) inherently lead to non-homogeneous * Kumar Vemaganti [email protected] Krishna Kenja [email protected] Sandeep Madireddy [email protected] 1
Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH 45221‑0072, USA
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, USA
2
deformations in tissue specimens. For example, tension tests involve the use of grips to hold the specimen and some compression tests employ cyanoacrylate glues, which means the deformation gradient is not uniform in the specimen. In compression tests that do not use glue, the friction between the compression platens and the specimen is dismissed as negligible. The non-homogeneous nature of the experimental deformation is generally ignored (Nierenberger et al. 2012; Golbad and Haghpanahi 2012; Karimi et al. 2014; Safshekan et al. 2016; Lagan and Liber-Kneć 2017; Calvo et al. 2009; Martins et al. 2006) so that the model response can be obtained analytically, which
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