Parameter Estimation and Strain Energy Model Class Selection for a Hyperelastic Composite Under Compression

Lucas da Silva Asth; Kauê Calenzani de Lima; Carolina Seixas Moreira; Diego Campos Knupp; Leonardo Tavares Stutz

doi:10.63595/vetor.v36i1.20864

Authors

Lucas da Silva Asth Polytechnic Institute, State University of Rio de Janeiro, Nova Friburgo, Brazil https://orcid.org/0000-0002-6189-1068
Kauê Calenzani de Lima Polytechnic Institute, State University of Rio de Janeiro, Nova Friburgo, Brazil https://orcid.org/0009-0002-7217-4299
Carolina Seixas Moreira Department of Mechanical Engineering, State University of Rio de Janeiro, Rio de Janeiro, Brazil https://orcid.org/0000-0002-0175-9102
Diego Campos Knupp Polytechnic Institute, State University of Rio de Janeiro, Nova Friburgo, Brazil https://orcid.org/0000-0001-9534-5623
Leonardo Tavares Stutz Polytechnic Institute, State University of Rio de Janeiro, Nova Friburgo, Brazil https://orcid.org/0000-0003-3005-765X

DOI:

https://doi.org/10.63595/vetor.v36i1.20864

Keywords:

Hyperelastic materials, Strain energy model, Inverse problem, Transitional Markov Chain Monte Carlo (TMCMC)

Abstract

The study of the mechanical behavior of human muscle tissues has received increasing attention due to its relevance in biomechanical and biomedical applications, and is often described by hyperelastic models because of its nonlinear response under mechanical loading. In this context, constitutive modeling requires the definition of an appropriate strain energy density function; however, there is still no universal model capable of satisfactorily representing all classes of soft hyperelastic materials, which makes the use of systematic methodologies for parameter identification and model selection essential. Thus, the present work aims to apply a Bayesian inverse problem approach, through the Transitional Markov Chain Monte Carlo (TMCMC) method, to determine, based on experimental data from uniaxial compression tests carried out on a pure hyperelastic material and on a hyperelastic composite reinforced with unidirectional fibers, which strain energy density models best represent the observed response. The TMCMC method stands out for providing a robust and efficient exploration of posterior distributions, allowing not only the estimation of constitutive parameters, but also the quantification of the uncertainties associated with these parameters and the probabilistic comparison among competing models through Bayesian evidence. The results highlight the importance of using methods that explicitly incorporate experimental and inferential uncertainties, since different models may present similar fits under an exclusively deterministic analysis.

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