• Blended Learning & Flipped Classroom

The course introduces to the numerical techniques currently adopted to compute the mechanical response of solids and the fluid dynamics in complex systems. Within the course, the student will practice with two standard commercial codes aimed at structural and fluid-dynamics analysis, respectively. In the last part of the course, students will work in small groups and apply the acquired knowledge and competences by developing new projects in the context of biomedical applications.

Knowledge (DD1): students are expected to acquire notions on continuum mechanics and on numerical techniques to solve partial differential equations. They are also expected to understand the impact of modeling hypotheses and to use their knowledge on real problems.

Competences (DD2): by the end of the course, students are expected to be able to i) formulate and solve complex problems in the field of biomedical engineering, ii) apply engineering methods to the field of biology and biotechnology, iii) use two software packages that well represent the standard commercial solvers in the field of structural mechanics and fluid dynamics, respectively.

Autonomy and communication abilities: after the course, students are expected to operate autonomous decisions about the definition of modelling strategies and design of devices (DD3) and to communicate the results of their activity in clear and concise manner (DD4).

The course is organized in two parts, focused on the analysis of structural mechanics through finite element modeling and on computational fluid dynamics through finite volume modeling, respectively. In both parts, students will be introduced to the computational methods implemented in a commercial code with a mix of lectures and tutorials. At the end of each part, students will develop a project working in small teams.

Part one: finite element modeling and structural mechanics

Solid mechanics and introduction to the finite element method 

The governing equations of solid mechanics will be overviewed. Their weak form and the corresponding discretization and solution will be introduced. In details, standard displacement-based approach will be introduced together with discretization strategies of governing equations, numerical integration issues and algorithms for solution of linear and nonlinear problems.

Principles of solid mechanics simulations: the commercial package Abaqus will be introduced, the main steps for the problem solution including the boundary conditions, meshing algorithms and solution strategies will be reviewed for linear and nonlinear simulations. 

Tutorials: by using Abaqus, students will train in teams on tutorials following a step-by-step guide.

Project: working again in team and using Abaqus, students will have to set and run an analysis to tackle a real-world problem. The problem to be simulated will be exhaustively described in terms of design specifications, but students will have to independently choose how to set their model. At the end of the project, each team will have to produce a report.

Part two: finite volume modeling and fluid dynamics

Introduction to fluid dynamics: the equations governing the conservation of mass, of linear momentum and of energy will be derived and discussed. Their weak form, its discretization and solution will be introduced based on the general scheme of convection-diffusion equations. 

Principles of fluid mechanics simulation: lectures will describe: 

- how to obtain the linear algebraic form of the field equations

- the iterative methods for algebraic system solution, the upwinding schemes, the pressure-velocity coupling algorithms

- how to check convergence and result accuracy.

Tutorials: the commercial package Ansys-Fluent will be introduced. The team of students will work on tutorials, devoted to introducing progressively more complex features of the software package, including the use of user-defined functions.

Project: working again in team and using Ansys-Fluent, students will have to set and run an analysis to tackle a real world problem. The problem to be simulated will be exhaustively described in terms of design specifications, but students will have to independently choose how to set their model. At the end of the project, each team will have to produce a report.

Important Note

This is a limited number access course. The mandatory procedure for access request is here: 

www.ccsbio.polimi.it/laurea-magistrale/?lang=en#Laboratory_Courses_LAB_courses 

• SDG3 - GOOD HEALTH AND WELLBEING

The course aims at creating numerical models able to simulate physiologic and pathologic conditions in particular but not limited to the muscoloskeletal and cardiovascular systems, and eventually with the presence of implantable devices. Reliable models are the base for development of methods for early diagnosis of pathologies. Furthermore, biomaterial and biological tissues mechanics is also a topic of interest in this course. The role of blood fluidynamics in interaction with tissues and devices is also discussed. These methods are keypoints for the development of innovative optimized design of devices as orthopaedic prostheses, for bone augmentation, tissue engineering, cardivascular treatments and procedure. The ultimate goal and clinical impact of these methods are the improvement of life quality and shortening of clinical tratments especially in the post-surgery phase. 

There is no mandatory prerequisite. However, students are expected to have acquired a sound background in continuum mechanics (solids and fluids) and in theory of calculus in previous courses.

Students will be evaluated at the end of the course on the basis of the two reports (one for solid mechanics FEM group-project and one for CFD finite volumes group-project) produced within the end of the course and of an oral examination (presentation&discussion of the projects considering connections with the theoretical aspects of methods) during the exam session.

The final mark will be the average of the marks of each report and of the oral examination. Please note that all three marks must be greater than or equal to 18/30.