Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review

Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

Uncertainty Quantification in Composite Materials

The random nature of the micro-structural attributes in materials in general and composite material systems in particular requires expansion of material modeling in a way that will incorporate their inherent uncertainty and predict its impact on material properties and mechanical response in multiple scales. Despite the importance of capturing and modeling material randomness, there are numerous challenges in structural characterization that are yet to be addressed. The work presented in this essay takes a few steps towards an improved material modeling approach which encompasses structural randomness in order to produce a more realistic representation of material systems. For this end a computational framework was developed to generate a realistic representative volume element which reflects the inherent structural randomness. First stochastic structural elements were identified and registered from imaging data and parameters were assigned to represent those elements. Statistical characterization of the random attributes was followed by the construction of a representative volume element which shared the same structural statistical characteristics with the original material system. The resultant statistical equivalent representative volume element (SERVE) was then used in finite element simulations which provided homogenized properties and mechanical response predictions. The suggested framework was developed and then implemented on 3 different material systems. Image processing and analysis in one of the material systems extended the original scope of this work to solving a machine vision and learning problem. Object segmentation for the purpose object and pattern recognition has been a long standing subject of interest in the field of machine vision. Despite the significant attention given to the development of segmentation and recognition methods, the critical challenge of separating merged objects did not share the spotlight. A simple yet original approach to overcome this hurdle was developed using unsupervised classification and separation of objects in 3D. Lower dimensionality classifiers were joined to provide a powerful higher dimensionality classification tool. The robustness of this approach is illustrated through its implementation on two case studies of merged objects. Applications of this methodology can further extend from structural classification to general problems of clustering and classification in various fields

An interactive geometry modeling and parametric design platform for isogeometric analysis

In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples—an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA

Rational tensor product Bézier volumes

AbstractFree form volumes in rational Bézier representation are derived via homogeneous coordinates. Some properties and constructions are presented and two applications of free form volumes are discussed: definition of solid primitives and curve and surface modelling by the way of volume deformation

Boundary integration of polynomials over an arbitrary linear hexahedron in Euclidean three-dimensional space

This paper is concerned with explicit integration formulas and algorithms for computing volume integrals of trivariate polynomials over an arbitrary linear hexahedron in Euclidean three-dimensional space. Three different approaches are discussed. The first algorithm is obtained by transforming a volume integral into a sum of surface integrals and then into convenient and computationally efficient line integrals. The second algorithm is obtained by transforming a volume integral into a sum of surface integrals over the boundary quadrilaterals. The third algorithm is obtained by transforming a volume integral into a sum of surface integrals over the triangulation of boundary. These algorithms and finite integration formulas are then followed by an application example, for which we have explained the detailed computational scheme. The symbolic finite integration formulas presented in this paper may lead to efficient and easy incorporation of integral properties of arbitrary linear polyhedra required in the engineering design process. © 1998 Elsevier Science S.A. All rights reserved

Simulation Based on Trivariate NURBS and Isogeometric Analysis of a Spur Gear

The approach provides simulation of the gear design with high-precision profile configuration parameters to accurately predict its load capacity and stress state, which requires incessant efforts, as gear failure modes depend largely on its profile representation. The finite element analysis (FEA) is a well-known effective computational method, which many authors used to estimate the gear tooth strength against the primary failure modes of gears. This method is not only known to be time-consuming but often expensive, it employs approximate geometry that resulted in a coarse mesh.Данный подход позволяет моделировать конструкцию зубчатой передачи с высокоточными параметрами геометрии профиля для достоверного прогнозирования допускаемой нагрузки и напряженного состояния, что требует постоянных исследований, поскольку вид разрушения зубчатой передачи в значительной мере зависит от способа задания ее профиля. Конечноэлементный анализ хорошо известный эффективный вычислительный метод, который многие авторы использовали для оценки прочности зубьев зубчатого колеса в условиях независимых отказов зубчатых передач. Известно также, что этот метод не только трудоемкий, но и зачастую дорогостоящий, использует приближенную геометрию, что дает в результате неточную сеть