Peridinâmica: estudo da limitação de modelos peridinâmicos baseados em ligações em relação ao coeficiente de Poisson
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Data
2022-02-11
Autores
Santos Junior, Valdir dos
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Universidade Estadual Paulista (Unesp)
Resumo
Durante muitos anos a mecânica do contínuo tem sido aplicada em diversos problemas e obtido resultados satisfatórios, porém, esta propõe um modelo unificado para sólidos, desconsiderando as forças ocorrendo em suas estruturas internas. Quando se trata de análise de estruturas com descontinuidades, como trincas, a mecânica do contínuo tem dificuldade em ser empregada. Baseando-se nisso, uma nova abordagem para este problema foi desenvolvida por Stewart Silling em 2000, a Peridinâmica. Esta é uma teoria moderna que combina a mecânica do contínuo com estudo de trincas, por meio da integração das forças de interação entre partículas próximas separadas por distâncias finitas. Para isso, utiliza-se da Segunda Lei de Newton para fazer a análise dinâmica ocorrendo no interior dos sólidos. O objetivo deste trabalho é estudar e validar o modelo baseado em ligações, LBB (Linearized Bond Based) para materiais com coeficiente de Poisson menor que 0.25, tendo como referência um modelo PMB (Prototype micro brittle). Para isto, será usado um programa feito em MatLab por Túlio Patriota entre 2018 e 2019. O resultado do trabalho foi satisfatório, visto que para o material com coeficiente de Poisson menor que 0,25 os erros do método LBB em relação ao PMB foram de 0,370% para trabalho externo e de 0,446% e 0,402% para os picos do gráfico de densidade de energia de deformação. Para o material com coeficiente de Poisson maior que 0,25 os erros do método LBB em relação ao PMB foram de 11,049% para trabalho externo e de 12,104% e 9,412% para os picos do gráfico de densidade de energia de deformação.
For many years, continuum mechanics has been applied in several problems and obtained satisfactory results, however, it proposes a unified model for solids, disregarding the forces occurring in their internal structures. When it comes to the analysis of structures with discontinuities, such as cracks, continuum mechanics is difficult to be employed. Based on this, a new approach to this problem was developed by Stewart Silling in 2000, Peridynamics. This is a modern theory that combines continuum mechanics with crack study, through the integration of interaction forces between nearby particles separated by finite distances. For this, Newton's Second Law is used to perform the dynamic analysis occurring inside the solids. The objective of this work is to study and validate the bond-based model, LBB (Linearized Bond Based) for materials with a Poisson ratio lower than 0.25, having as reference the PMB (Prototype micro brittle) model. For this, a program made in MatLab by Túlio Patriota between 2018 and 2019 will be used. The result of the work was satisfactory, since for the material with a Poisson ratio lower than 0.25, the errors of the LBB method in relation to the PMB were of 0.370% for external work and 0.446% and 0.402% for peaks in the strain energy density graph. For material with a Poisson ratio greater than 0.25, the errors of the LBB method in relation to the PMB were 11.049% for external work and 12.104% and 9.412% for the peaks of the strain energy density graph.
For many years, continuum mechanics has been applied in several problems and obtained satisfactory results, however, it proposes a unified model for solids, disregarding the forces occurring in their internal structures. When it comes to the analysis of structures with discontinuities, such as cracks, continuum mechanics is difficult to be employed. Based on this, a new approach to this problem was developed by Stewart Silling in 2000, Peridynamics. This is a modern theory that combines continuum mechanics with crack study, through the integration of interaction forces between nearby particles separated by finite distances. For this, Newton's Second Law is used to perform the dynamic analysis occurring inside the solids. The objective of this work is to study and validate the bond-based model, LBB (Linearized Bond Based) for materials with a Poisson ratio lower than 0.25, having as reference the PMB (Prototype micro brittle) model. For this, a program made in MatLab by Túlio Patriota between 2018 and 2019 will be used. The result of the work was satisfactory, since for the material with a Poisson ratio lower than 0.25, the errors of the LBB method in relation to the PMB were of 0.370% for external work and 0.446% and 0.402% for peaks in the strain energy density graph. For material with a Poisson ratio greater than 0.25, the errors of the LBB method in relation to the PMB were 11.049% for external work and 12.104% and 9.412% for the peaks of the strain energy density graph.
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Palavras-chave
Mecânica dos meios contínuos, Dinâmica, Resistência de materiais, MATLAB (Programa de computador), Mechanics of continuous media, Dynamics, Strength of materials, MATLAB (Computer program)