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

Autores

Lucas da Silva Asth Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil https://orcid.org/0000-0002-6189-1068
Kauê Calenzani de Lima Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil https://orcid.org/0009-0002-7217-4299
Carolina Seixas Moreira Departamento de Engenharia Mecânica, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brasil https://orcid.org/0000-0002-0175-9102
Diego Campos Knupp Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil https://orcid.org/0000-0001-9534-5623
Leonardo Tavares Stutz Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Nova Friburgo, Brasil https://orcid.org/0000-0003-3005-765X

DOI:

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

Palavras-chave:

Materiais hiperelásticos, Modelo de energia de deformação, Problema inverso, Transitional Markov Chain Monte Carlo (TMCMC)

Resumo

O estudo do comportamento mecânico de tecidos musculares humanos tem recebido crescente atenção devido à sua relevância em aplicações biomecânicas e biomédicas, sendo frequentemente descrito por modelos hiperelásticos em razão de sua resposta não linear sob carregamentos mecânicos. Nesse contexto, a modelagem constitutiva requer a definição de uma função de energia de deformação apropriada; entretanto, ainda não existe um modelo universal capaz de representar satisfatoriamente todas as classes de materiais hiperelásticos macios, o que torna fundamental o uso de metodologias sistemáticas para identificação paramétrica e seleção de modelos. Assim, este trabalho tem como objetivo aplicar uma abordagem Bayesiana de solução de problemas inversos, por meio do método Transitional Markov Chain Monte Carlo (TMCMC), para determinar, com base em dados experimentais de ensaios de compressão uniaxial realizados em um material hiperelástico puro e em um compósito hiperelástico reforçado por fibras unidirecionais, quais modelos de energia de deformação melhor representam a resposta observada. O método TMCMC destaca-se por promover uma exploração robusta e eficiente das distribuições posteriores, permitindo não apenas a estimação dos parâmetros constitutivos, mas também a quantificação das incertezas associadas a esses parâmetros e a comparação probabilística entre modelos concorrentes por meio da evidência Bayesiana. Os resultados evidenciam a importância do uso de métodos que incorporam explicitamente as incertezas experimentais e inferenciais, uma vez que diferentes modelos podem apresentar ajustes semelhantes sob uma análise exclusivamente determinística.

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