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Doctoral Thesis
DOI
10.11606/T.82.2018.tde-20082018-152023
Document
Author
Full name
Gabriel Lopes da Rocha
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2017
Supervisor
Committee
Aguiar, Adair Roberto (President)
Alves, Jose Marcos
Marques, Paulo Mazzoncini de Azevedo
Prado, Edmar Borges Theóphilo
Schutzer, Waldeck
Title in Portuguese
Aplicação da teoria de representação de funções isotrópicas em sólidos hiperelásticos com duas direções de simetria material
Keywords in Portuguese
Base de integridade mínima
Compósito
Elasticidade não linear
Funções isotrópicas
Tecido biológico
Abstract in Portuguese
Aplicamos a teoria de representação de funções isotrópicas para determinar o número mínimo de invariantes independentes necessários para caracterizar completamente a densidade de energia de deformação de sólido hiperelástico com duas direções de simetria material. Expressamos a densidade de energia em termos de dezoito invariantes e extraímos um conjunto de dez invariantes para analisar dois casos de simetria material. No caso de direções ortogonais, recuperamos o resultado clássico de sete invariantes e oferecemos uma justificativa para a escolha dos invariantes encontrados na literatura. Se as direções não são ortogonais, descobrimos que o número mínimo também é sete e corrigimos um erro em fórmula encontrada na literatura. Uma densidade de energia deste tipo é usada para modelar, na escala macroscópica, materiais de engenharia, tais como compósitos reforçados com fibras, e tecidos biológicos, tais como ossos.
Title in English
Application of the theory of isotropic function representation in hyperelastic solids with two materials symmetry directions
Keywords in English
Biological tissue
Composite material
Isotropic functions
Minimum integrity base
Nonlinear elasticity
Abstract in English
We determine the minimum number of independent invariants that are needed to characterize completely the strain energy density of a hyperelastic solid having two distinct material symmetry directions. We use a theory of representation of isotropic functions to express this energy density in terms of eighteen invariants and extract a set of ten invariants to analyze two cases of material symmetry. In the case of orthogonal directions, we recover the classical result of seven invariants and offer a justification for the choice of invariants found in the literature. If the directions are not orthogonal, we find that the minimum number is also seven and correct a mistake in a formula found in the literature. An energy density of this type is used to model, on the macroscopic scale, engineering materials, such as fiber-reinforced composites, and biological tissues, such as bones.
 
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Publishing Date
2018-08-21
 
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