Publication: PROPIEDADES MECÁNICAS EQUIVALENTES PARA ESPUMAS METÁLICAS DE BASE TITANIO
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Date
2019-11
Authors
GONZÁLEZ GÓMEZ, IGNACIO ANDRÉS
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Abstract
Uno de los principales problemas en el desarrollo de osteo-implantes es la diferen-
cia de rigidez entre el material base de reemplazo y el hueso, fenómeno conocido como
“stress-shielding”. Este fenómeno promueve la absorción ósea, lo que incrementa el ries-
go de fractura del material biológico alrededor del implante. Una de las alternativas
planteadas en este trabajo para mitigar este efecto es la de modificar la rigidez de un
implante mediante el diseño optimizado de la estructura interna de espumas metálicas
utilizadas como material de base en el diseño de estos elementos. En este proceso debe
tenerse en cuenta que la manipulación de la estructura celular de la espuma para dis-
minuir su rigidez tiene consecuencias adversas sobre su capacidad para soportar carga.
Debido a la complejidad de la estructura interna del material y posibles costos en la
sı́ntesis y análisis de probetas experimentales con diferentes configuraciones, el presente
trabajo propone generar modelos computacionales de espumas metálicas y estimar sus
propiedades mecánicas equivalentes mediante la simulación numérica. Con este objetivo
se emplearon las estadı́sticas de las distribuciones de los parámetros geométricos del
material poroso obtenidas a partir de imágenes 3D. Estas imágenes fueron obtenidas
mediante la técnica de micro-tomografı́a computarizada (µCT) y sirvieron de base para
crear diferentes modelos CAD de los cuales se extrajeron diferentes volúmenes repre-
sentativos (RVE). Cada RVE es analizado con un protocolo prescrito de desplazamiento
incluyendo condiciones de borde periódicas mediante un código de elementos finitos no
lineal desarrollado para esta aplicación. Las simulaciones numéricas incluyen pruebas
de tracción (xx, yy, zz) y cortante simple (xy, xz, yz). El tensor de esfuerzos efectivo
en cada ensayo fue utilizado para obtener la matriz de constantes elásticas para cada
RVE, y con ella, determinar propiedades mecánicas (módulos de Young, coeficientes de
Poisson y módulos de Rigidez) y las componentes del tensor acústico para un total de
30 RVEs con diferentes porosidades (p = 5 %, 15 %, 30 %, 50 % y 65 %). El rango de
variación de la velocidad de las ondas elásticas transversales se utilizó como criterio
para cuantificar el ı́ndice de anisotropı́a (A∗ ) en cada una de las muestras virtuales.
One of the main problems in the development of osteoimplants is the difference in stiffness between the replacement base material and the bone, a phenomenon known as stress-shielding. This phenomenon promotes bone absorption, which increases the risk of fracture of the biological material around the implant. One of the alternatives proposed in this work to mitigate this effect is the modification of the stiffness of an implant through the design optimization of the internal structure of the metallic foams used as the base material in the design of these elements. In this process it should be taken into account that the modification of the cellular structure of the foam to reduce its stiffness has adverse consequences on its ability to be loaded. Due to the comple- xity of the internal structure of the material and possible costs in the synthesis and analysis of experimental samples with different configurations, the present work propo- ses to generate computational models of metallic foams and estimate their equivalent mechanical properties through numerical simulation. With this purpose the statistics of the distributions of the geometric parameters of the porous material obtained from 3D images were used. These images were obtained using the computed micro-tomography (µCT ) technique and served as the basis for creating different CAD models from which different representative volumes (RVE) were extracted. Each RVE is analyzed with a prescribed displacement protocol including periodic boundary conditions using a non- linear finite element code developed for this application. Numerical simulations include tensile tests (xx, yy, zz) and simple shear (xy, xz, yz). The effective stress tensor in each test was used to obtain the matrix of elastic constants for each RVE, and with it, determine mechanical properties (Young’s modulus, Poisson’s ratio and Rigidity modu- lus) and the acoustic tensor components for a total of 30 RVEs with different porosities (p = 5 %, 15 %, 30 %, 50 % and 65 %). The range of variation of the transverse elastic wave velocity is modified as a criterion to quantify the anisotropy index (A∗ ) in each of the virtual samples.
One of the main problems in the development of osteoimplants is the difference in stiffness between the replacement base material and the bone, a phenomenon known as stress-shielding. This phenomenon promotes bone absorption, which increases the risk of fracture of the biological material around the implant. One of the alternatives proposed in this work to mitigate this effect is the modification of the stiffness of an implant through the design optimization of the internal structure of the metallic foams used as the base material in the design of these elements. In this process it should be taken into account that the modification of the cellular structure of the foam to reduce its stiffness has adverse consequences on its ability to be loaded. Due to the comple- xity of the internal structure of the material and possible costs in the synthesis and analysis of experimental samples with different configurations, the present work propo- ses to generate computational models of metallic foams and estimate their equivalent mechanical properties through numerical simulation. With this purpose the statistics of the distributions of the geometric parameters of the porous material obtained from 3D images were used. These images were obtained using the computed micro-tomography (µCT ) technique and served as the basis for creating different CAD models from which different representative volumes (RVE) were extracted. Each RVE is analyzed with a prescribed displacement protocol including periodic boundary conditions using a non- linear finite element code developed for this application. Numerical simulations include tensile tests (xx, yy, zz) and simple shear (xy, xz, yz). The effective stress tensor in each test was used to obtain the matrix of elastic constants for each RVE, and with it, determine mechanical properties (Young’s modulus, Poisson’s ratio and Rigidity modu- lus) and the acoustic tensor components for a total of 30 RVEs with different porosities (p = 5 %, 15 %, 30 %, 50 % and 65 %). The range of variation of the transverse elastic wave velocity is modified as a criterion to quantify the anisotropy index (A∗ ) in each of the virtual samples.
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Keywords
ESPUMAS DE TITANIO