Programma dettagliato e risultati di apprendimento attesi
The course introduces to the multiscale modeling techniques using in different fields of biomechanics. Along the course the student will visit aspects of molecular dynamics to describe the mechanical behavior of the most common constituents of biological tissue from first principles. Different methodologies will then be explored to incorporate this information into models on the micro-, meso- and macro-scale for applications in bone and cardiovascular mechanics. Along the course, different numerical techniques will be discussed the student will practice with them on specific project applications.
The course is organized in three parts. In the first part, students will be introduced to the theoretical and numerical basis of molecular dynamics. The second part will be dedicated to the modelling of compact and trabecular bone at the nano- and micro-scale. The third part will discuss continuum based damage models of soft tissue at the macroscale.
Each part comprises a series of lectures, according to the following scheme:
Molecular dynamics of collagen tissue:Collagen plays a critical role in many biological tissues including tendon, bone, teeth, cartilage among others. Collagen shows, as many other biological materials do, a complex hierarchical structure ranging from the nanoscopic scale of polypeptides to microscopic collagen fibers. Due to its relatively simple structure collagen molecules have been also studied using molecular dynamics (MD) approach. This theoretical framework is a powerful tool to establish from the first principles the material behavior and also to discover the molecular origins of pathological states. In this part of the course after a brief introduction on the theory behind this method, different molecular models will be described and discussed. In particular collagen will be used to explain how nanoscale features of a given material can be used to inform upper level structures and to drive useful information on the meso and macro scale behavior.
Bone modeling:During the lectures models for predicting the elastic properties of compact and trabecular bone on the basis of the nano and micro scale organization of its constituents (water, collagen and mineral phase) will be presented. Multi-scale analytical approaches based on Eshelby solutions as well as computational methods based on asymptotic approaches will be discussed. Micro-Computer Tomography - based Finite element models for the estimation of the macroscopic elastic modulus of three dimensional architecture of trabecular bone will also be presented.
Continuum based damge models of soft tissue:Deterministic and stochastically based three-dimensional finite-strain damage models for fibrous biological soft tissues, accounting for separate contributions on damage for the matrix and the fibers will be presented. Both models are compared in terms of their numerical performance and qualitative predictions under different loading conditions. Continuum damage mechanics is used to describe the softening behavior of soft tissues under large deformation, making use of the concept of internal variables which provides a very general description of materials involving irreversible effects. In the stochastic model, statistical aspects related to the distribution of fiber length lead to the strain-driven damage model for the fibrous part. Numerical implementation within the finite element framework will be discussed.
Laboratory activities start after the lecture sessions. Projects related to the three different parts of the course will assigned to the students randomly. The students will work for a total of six weeks working in groups of two. For each project, students will have to issue a short report and give a short presentation (see Innovative teaching section).
Expected learning results
Knowledge of basic strategies for the numerical solution of biomechanical problems. Students will have the ability to clearly and comprehensively communicate a problem statement, solution methods, results, and limitations of the solution.
Note Sulla Modalità di valutazione
Evaluation:evaluation of the final report and presentation at the end of the course. The final vote will be constituted by the sum of the reports’ evaluation (1/2 each) and the final presentation (1/2). Oral exam is not mandatory.
Innovative teaching:To complement the project activities and to stimulate active learning, the structuring skills of thinking and knowledge and the assessment among colleagues, the projects will be discussed and presented in flipped/blended classroom modality by each group.
Intervallo di svolgimento dell'attività didattica
Calendario testuale dell'attività didattica
Molecular dynamics of collagen tissue: 6 hours
Bone modeling: 10 hours
Continuum based damge models of soft tissue: 10 hours
Laboratory and Project: 4 hours
Andrew R leach, Molecular modelling: principles and applications, Editore: Pearson, Prentice Hall, Anno edizione: 2001, ISBN: 978-0582382107
Jianmin Qu and Mohammed Cherkaoui,, Fundamentals of micromechanics of solids, Editore: John Wiley & Sons, Anno edizione: 2006, ISBN: 978-0-471-46451-8
Gerhard Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering, Editore: Wiley, Anno edizione: 2000, ISBN: 978-0471823193
Gautieri A, Vesentini S, Redaelli A, Buehler MJ., Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up. Nano letters, Anno edizione: 2011, Fascicolo: 11(2): 757-66
Markus J Buehler, Nature designs tough collagen: Explaining the nanostructure of collagen fibrils. PNAS, Anno edizione: 2006, Fascicolo: 103 (33) 12285-12290
Oftadeh, R., Entezari, V., Spörri, G., et al., Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone. Journal of the Royal Society Interface, Anno edizione: 2015, Fascicolo: 12 (106), art. no. 20150070
Hamed, E., Jasiuk, I., Yoo, A., Lee, Y., Liszka, T, Multi-scale modelling of elastic moduli of trabecular bone. Journal of the Royal Society Interface, Anno edizione: 2012, Fascicolo: 9 (72), pp. 1654-1673.
Jose F. Rodriguez , Fernando Cacho, Jose A. Bea, Manuel Doblare, A stochastic-structurally based three dimensional finite-strain damage model for fibrous soft tissue. Journal of the Physics and Mechanics of Solids, Anno edizione: 2006, Fascicolo: 54: 864¿886
V. Alastrue, J.F. Rodriguez, B. Calvo, M. Doblare, Structural damage models for fibrous biological soft tissues. International Journal of Solids and Structures, Anno edizione: 2007, Fascicolo: 44: 5894¿5911
Mix Forme Didattiche
Tipo Forma Didattica
laboratorio di progetto
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese