Comparative Analysis of Nonlinear Viscoelastic Models Across Common Biomechanical Experiments

• Published in: Journal of elasticity Vol. 145; no. 1-2; pp. 117 - 152
• Main Authors: Zhang, Will, Capilnasiu, Adela, Nordsletten, David
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2021; Springer Nature B.V
• Subjects: Automotive Engineering; Biomechanical engineering; Biomechanics; Classical Mechanics; Constitutive equations; Constitutive relationships; Mathematical models; Model forms; Parameter identification; Physics; Physics and Astronomy; Prediction models; Strain; Tissue engineering; Viscoelasticity; Viscoelasticity; Biomechanics; Tissue mechanics; 74D05; Rheology; 26A33; Fractional viscoelasticity; 35R11; 74D10; 34K37; 74S40; 34A08
• ISSN: 0374-3535; 1573-2681
• DOI: 10.1007/s10659-021-09827-7

Biomechanical modeling has a wide range of applications in the medical field, including in diagnosis, treatment planning and tissue engineering. The key to these predictive models are appropriate constitutive equations that can capture the stress-strain response of materials. While most applications rely on hyperelastic formulations, experimental evidence of viscoelastic responses in tissues and new numerical techniques has spurred the development of new viscoelastic models. Classical as well as fractional viscoelastic formulations have been proposed, but it is often difficult from the practitioner perspective to identify appropriate model forms. In this study, a systematic examination of classical and fractional nonlinear isotropic viscoelastic models is presented (consider six primary forms). Consideration is given for common testing paradigms, including varying strain or stress loading and dynamic conditions. Models are evaluated across model parameter spaces to assess the range of behaviors exhibited in these different forms across all tests. Similarity metrics are introduced to compare thousands of models, with exemplars for each type of model presented to illustrate the response and behavior of different model variants. The parameter analysis does not only identify how the models can be tailored, but also informs on the model complexity and fidelity. These results illustrate where these common models yield physical and non-physical behavior across a wide range of tests, and provide key insights for deciding on the appropriate viscoelastic modeling formulations.