Papers by Author: Manuel Doblaré

Abstract: Bone Tissue Engineering is a fast growing interdisciplinary branch of research that aims to find adequate replacements or scaffolds for bone, in order to improve its ability to regenerate itself. The present work summarizes the most relevant functional properties of bone and its ability of adaptation, remarking the most crucial characteristics that these replacements must fulfill for appropriate bone regeneration, including the correct selection of the material and structure. The second part presents current trends in computational modeling of bone remodeling and bone ingrowth within scaffolds, with special emphasis on the description of two different mathematical approaches to model these biological regenerative events. We demonstrate that computational modeling is a useful tool for bone scaffold design that allows considering multiple factors some of them very difficult to evaluate experimentally.

Abstract: The Extended Finite Element Method (XFEM), has become a well-known tool to simulate crack propagation problems using non-structured meshes avoiding the remeshing process usually needed in this type of problems and allowing the inclusion of appropriate shape functions that reflect the asymptotic displacement field, near the crack tip, via a partition of unity fracture approach. However, in this kind of numerical applications, all the variables involved have been considered as deterministic (defined by a single given value), despite the well-known uncertainty associated to many of them (external loads, geometry and material properties, among others). The combination of the XFEM and probabilistic techniques is here proposed and formulated allowing treating fracture mechanics problems from a probabilistic point of view. We present the implementation of this probabilistic extended finite element method and apply it to the prediction of the appearance and propagation of a femur’s neck fracture under probabilistic loads.