Publication: Análisis numérico de las propiedades mecánicas del hueso cortical a tamaño micro
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2015
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2015-10-09
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Abstract
En este trabajo se ha logrado crear desde cero un método que genere un volumen representativo de tejido cortical, sobre el cual se imponen numerosos estados de carga, con el objetivo de realizar un análisis de cada uno de ellos. Esto nos permitirá obtener los datos necesarios para poder calcular el valor de todas las constantes elásticas propias de un material anisótropo, y comprender así el comportamiento elástico de este tipo de tejido.
Para la creación del modelo se han utilizado principalmente dos herramientas: el programa de Computer Aided Engineering: Abaqus CAE, que utiliza el metodo de los elementos finitos para resolver problemas de ingeniería mecánica y estructural, y Python, un lenguaje de programación multiusos que mediante scripts nos ha permitido modificar a nuestro antojo le ejecución de ciertas funciones de Abaqus, para así automatizar la generación del modelo todo lo posible.
Se ha utilizado un total de 3 scripts para crear el modelo: el primero está centrado en generar automáticamente la distribución de las osteonas (unidad básica estructural del tejido cortical), de posición aleatoria, y sin contacto entre ellas, creadas una a una hasta que estas ocupen el 65 por ciento del volumen del modelo. El segundo script se encargaba principalmente de asignar las secciones de los materiales a las distintas partes del modelo para facilitar esta tarea y así ahorrar una importante cantidad de tiempo al usuario. Los distintos estados de carga se introducción manualmente para poder modificarlos en cualquier momento, al igual que se seleccionaban manualmente los parámetros que se desea analizar y obtener sus resultados correspondientes. Por último el tercer script se encargaba de realizar el mallado del modelo, crear el análisis y correrlo.
Se ha llevado a cabo un análisis de la sensibilidad de la malla y de la influencia del tamaño del RVE, para crear un modelo que combine precisión y un mínimo coste computacional posible.
Una vez conocidas todas las dimensiones del modelo se han creado 5 modelos finales sobre los que realizar los análisis pertinentes: un total de 45 análisis distintos a contrastar, para obtener los modulos de Young, coeficientes de Poisson y módulos de cortadura de los 5 modelos en todas sus direcciones.
Hemos logrado de esta forma obtener todas las constantes que nos permiten valorar la respuesta mecánica en régimen elástico del tejido cortical.
On this Project we have managed to create from the start a method that generates a representative volume of cortical bone, on which certain loading states are imposed, with the goal of performing an analysis for each one of them. This will allow us to obtain the data necessary to calculate the value of all the elastic constants related to an anisotropic material, so then we get a better understanding of the elastic behavior of this type of tissue. For the creation of the model two tools have been used mainly: the Computer Aided Engineering: Abaqus CAE, which uses the finite element method to solve mechanical and structural engineering related problems, and Python, a multi-functional programming language which by using scripts has allowed us to modify the execution of certain Abaqus functions just as we please, so that we can automate the creation of the model as much as we could. A total of 3 scripts have been used to create the model: the first one is focused on generating automatically the distribution for the osteons (basic level structure of cortical bone tissue), arranged on random positions, without contact between them, and created one by one until the 65& of the volume fraction of the model is occupied by osteons. The second script focuses on relating each of the material sections with is correspondent part of the model in order to make this an easier task and save up quite some time to the user. The different loading states are introduced manually so they can be modified whenever it is required, just as also the parameters meant to be analyzed were selected manually to obtain the correspondent results. Finally the third script concentrates on generating and implementing the mesh for the model, create the analysis and run it. A mesh sensitivity analysis has been performed and also one that determines the influence of the size of the RVE, so that the model created manages to be a combination of precision on the results and the lowest computer expense possible. Once all the dimensions of the model are known, 5 final models have been created, in order to perform all the analysis required: a total of 45 different analysis have been done, so making a contrast with them is possible, to obtain the Young´s modulus, the Poisson´s coefficients and the shear modulus of the 5 different models in all the directions needed. We, this way, have achieved to obtain all the constants that will let us evaluate the mechanical response on the elastic regime of the cortical bone tissue.
On this Project we have managed to create from the start a method that generates a representative volume of cortical bone, on which certain loading states are imposed, with the goal of performing an analysis for each one of them. This will allow us to obtain the data necessary to calculate the value of all the elastic constants related to an anisotropic material, so then we get a better understanding of the elastic behavior of this type of tissue. For the creation of the model two tools have been used mainly: the Computer Aided Engineering: Abaqus CAE, which uses the finite element method to solve mechanical and structural engineering related problems, and Python, a multi-functional programming language which by using scripts has allowed us to modify the execution of certain Abaqus functions just as we please, so that we can automate the creation of the model as much as we could. A total of 3 scripts have been used to create the model: the first one is focused on generating automatically the distribution for the osteons (basic level structure of cortical bone tissue), arranged on random positions, without contact between them, and created one by one until the 65& of the volume fraction of the model is occupied by osteons. The second script focuses on relating each of the material sections with is correspondent part of the model in order to make this an easier task and save up quite some time to the user. The different loading states are introduced manually so they can be modified whenever it is required, just as also the parameters meant to be analyzed were selected manually to obtain the correspondent results. Finally the third script concentrates on generating and implementing the mesh for the model, create the analysis and run it. A mesh sensitivity analysis has been performed and also one that determines the influence of the size of the RVE, so that the model created manages to be a combination of precision on the results and the lowest computer expense possible. Once all the dimensions of the model are known, 5 final models have been created, in order to perform all the analysis required: a total of 45 different analysis have been done, so making a contrast with them is possible, to obtain the Young´s modulus, the Poisson´s coefficients and the shear modulus of the 5 different models in all the directions needed. We, this way, have achieved to obtain all the constants that will let us evaluate the mechanical response on the elastic regime of the cortical bone tissue.
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Keywords
Biomecánica, Propiedades mecánicas, Método de los elementos finitos, Osteona, Canal de Havers, Biomechanic, Finite element method, Osteon, Havers canal