Lumbar interbody fusion is a lumbar surgical procedure that consists of replacing the intervertebral disk with a stiff prosthetic device (the fusion cage), promote bone growth in between the two vertebrae, and finally get them fused into one single rigid unit. In order to that the fusion cage is usually hollow in order to be able to accommodate new bone in its interior. Often this kind of surgery has been considered the only option when disk diseases are severe. The numerical studies described in this paper are oriented to clarify the mechanical behavior of the new vertebral configuration after the fusion cage has been installed. The geometrical model includes vertebrae L5 and S1 and has been directly generated from radiological images, with individual representation of the stiffer cortical bone on the surface and the softer trabecular bone in the interior, as well as the prosthesis device in between the two vertebrae. Two load cases are considered which
correspond to the body in static rest and to the person lifting a weight with his arms. The FE analysis was first performed using a tetrahedral mesh and looking at the results in terms of conventional continuum stresses. A second study took advantage of the fact that cortical bone seems to work as a bending shell. Based on that, a new mesh was developed with the cortical bone made of ‘extruded’ prismatic elements of triangular base, in such way that all integration points through the thickness were aligned and it became possible to calculate the shell forces (moment, shear and axial) associated to the cross-sectional behavior of the cortical shell. In this paper both types of results are presented, in terms of continuum stresses and of shell crosssectional forces. In the biomechanical literature it seems traditional to represent the stresses state by means of the equivalent von Mises stress . However, some studies  show that the behavior of cortical bone is dependent on the hydrostatic pressure (I1 invariant) and also exhibits additional frictional mechanisms. In this article the continuum stress results are discussed using a hyperbolic
model of Mohr-Coulomb type (Hyperbolic Mohr-Coulomb Model) in comparison to traditional von Mises. On the other hand, the results in terms of shell cross-sectional forces make it possible to identify the most critical areas of the two vertebrae in the configurations analyzed.
Lumbar interbody fusion is a lumbar surgical procedure that consists of replacing the intervertebral disk with a stiff prosthetic device (the fusion cage), with the purpose of promoting bone growth in between the two vertebrae and finally fuse them into one single rigid unit. The numerical studies described in this paper are oriented to clarify the mechanical behavior of the new vertebral configuration after the fusion cage has been installed. The geometrical model includes vertebrae L5 and S1 and has been directly generated from radiological images, with individual representation of the stiffer cortical bone on the surface and the softer trabecular bone in the interior, as well as two kinds of prosthesis devices in between the two vertebrae. The resulting stresses are discussed on the basis of a hyperbolic Mohr-Coulomb failure criterion in comparison to traditional von Mises.
Un modelo meso estructural 2D empleado inicialmente en el análisis mecánico del hormigón bajo altas temperaturas, es extendido en este trabajo a un análisis 3D y a un análisis termo-mecánico acoplado más complejo. El material se considera como un compuesto de dos fases, con diferentes leyes de expansión térmica para los áridos y para la matriz y donde cada línea de la malla de EF (o superficie en 3D) representa un potencial camino de fisuración. La distribución de temperatura en toda la muestra a lo largo del tiempo se obtiene mediante un análisis separado de difusión térmica. El incremento de temperaturas para cada punto de la malla combinado con una ley de expansión térmica para cada fase componente conduce a una deformación térmica diferenciada en cada fase, que posteriormente es introducida en el modelo mecánico. Por un lado, se presentan resultados 2D y 3D del análisis termo-mecánico desacoplado, y por otro
lado, se incluyen resultados de un análisis acoplado 2D, donde a medida que el estado de tensiones inducido por la carga térmica da lugar a un desprendimiento del material por “spalling”, se produce un cambio en las condiciones de borde del problema térmico. Algunos de los resultados obtenidos en las simulaciones numéricas 2D y 3D de este trabajo se comparan con resultados experimentales publicados en la bibliografía.
In this paper, an existing meso-structural model for concrete which had been applied to the study of the mechanical effects of high temperatures in 2D, is extended to 3D, and to more complex coupled thermo-mechanical analysis. The material is idealized as a two-phase compositein which all mesh lines (or surfaces in 3D) are potential cracks equipped with fracture-based zero-thickness interface elements. Different thermal expansion laws are assumed for matrix and particles, whereby the deformation mismatch can generate cracking. Temperature distributions are obtained from a separate thermal diffusionanalysis.The thermal analysis is first assumed uncoupled, but then also coupled with the mechanical analysis, as the layers of material spalloff and the boundary conditionsare moved to the new domain boundaries. The new computational results in 3D are compared to basic experimental observations reported in the literature and to the previous computational results obtained in 2D.