Solid Biomechanics After attending the course, students will know: - the forces and the stress field in materials and structures resulting from dynamic loads - one degree of freedom linear systems, free and forced vibration, main damping mechanisms, shocks and impacts, random excitation - many degrees of freedom linear systems, free and forced oscillations, decoupling of motion equations and system simplification, proportional and non-proportional dissipative mechanisms. - human vibration, biological sensors, frequency dependencies for human response to vibration, European legislation and health risks - analytical and numerical approaches to the solution of simple nonlinear systems After attending the course, students will be able to: - Simplify and model real biomechanical systems for the evaluation of static and dynamic stresses (shock and vibration analysis) - Use analytical and numerical commercial software for the structures dynamics - numerically solve systems of nonlinear differential equation - asses the risk associated with exposure to vibration and calculate trauma severity index Fluid Biomechanics The student will acquire a complete familiarity with conservation equations of mass and momentum in the three-dimensional form and in their application to open and closed systems. Conservation equation of energy will be studied in mono-dimensional form. The solution of equations in the contest of examples or exercises will be obtained without the use of specific computational methods (finite elements/volumes) which will be used in further courses, but putting an accurate phase of physical interpretation of understudying phenomena before the calculation phase. Specific attention will be paid on the application of provided methods to the analysis of biological fluids flow, with the needing attention to unsteady flows, ducts with complex geometries, in cylindrical ducts for Newtonian viscous fluids and not, for particles fluids. One part of the course will provide the methods for more traditional applications like pressure drop of steady flow in ducts, the thrust on walls, etc. The student will be tutored during exercises and meeting sessions aimed at the completion of single knowledge will be available. Communication skills will be developed during the exercises and the self-assessment testing. During the written exam the student will have to answer to general questions in order to highlight his own ability to frame complex problems in a rational and physically correct way. Learning will be promoted by exercise formulation and by the type of teaching materials. Much attention is placed in providing exercises as a translation of an in-depth physical understanding in quantitative analysis of involved features, not as quiz or pure moments of mathematical calculation.

Solid Biomechanics Basic knowledge of mathematics, linear differential equations Mechanical behaviour of materials, linear elasticity, stress and strain analysis, static and fatigue structural design. Fluid Biomechanics Basic knowledge of mathematics, physics, informatics, mechanical engineering and fundamentals of thermodynamics as learned in the 3-year program of Biomedical Engineering.

Solid Biomechanics Frontal lessons - dynamic stresses in structures: geometric, material and contact non-linearities - one degree of freedom linear systems, - undamped and damped free vibration - viscous, structural and coulomb damping - experimental determination of damping, internal damping of materials, nonlinear approaches - harmonic forced vibration, motion of constraint - shock and impact stresses, impulsive and step forces, transient analysis - general forcing, Duhamel integral - stresses caused by non-deterministic phenomena, random vibrations, stationary and ergodic processes - human vibrations, European legislation and health risks - calculation of daily exposure to vibrations Laboratory activities - analytical and numerical solution of a linear one degree of freedom system, sine forcing - impact response: analytical and numerical solution - numerical solution of simple nonlinear systems: coulomb damping and rebound of a falling mass - two degree of freedom system: numerical solution, constraint excitation Fluid Biomechanics 1. Hydrostatics 2. Bernoulli's equation and its applications 3. Pressure drop of steady flows in ducts, the thrust on walls 4. Conservation equations of mass and momentum 5. Shell balance 6. Applications of conservation equations for problems solving 7. Turbulence, Kolmogorov theory Laboratory activities Exercises. Exercise activities are focused on problem solving starting from the formulation of a simple model able to describe and study a real problem, not from a provided equation. Exercises have to be faced with an analytical approach (the use of calculation algorithms for the solution of complex fluid-dynamic problems is subject of study of other courses of the same address) in order to stimulate the attention of students to the physics of phenomena and to them describing mathematics.

Solid Biomechanics Teaching is divided into about 30 hours of frontal lessons, 10 hours exercises and 10 hours of computer lab. Fluid Biomechanics Theoretical lessons (30 h) + exercise (20 h). The frequency to the course is not mandatory to take the final examination.

Solid Biomechanics a) G. Genta: “Principi e Metodologie delle Progettazione Meccanica”, Levrotto & Bella (To). b) Handouts on the some lessons and exercises c) Directive 2002/44/EC - risks from vibration: health and safety requirements. Fluid Biomechanics Bird, Stewart, Lightfoot "Transport Phenomena". (optional) Slides, scientific articles and laboratory assignments provided by the teacher.

Exam: Written test;

Solid Biomechanics For admission to examination an elaborate containing the laboratory exercises must be uploaded by the student. The final mark will be obtained with a written examination consisting of 2 open theory questions and 1 exercise. This exercise report a real problem, its solution requires an appropriate preliminary operation of modeling and simplification made by the student. This creative process is one of the most important parts of the exam, since it allows to evaluate the acquired abilities in the analysis of a new real situation. The final mark is obtained by averaging marks relative to theory and exercise (taking into account decimals). Fluid Biomechanics Comprehension of the course topic and ability in the use of the introduces mathematical tools (i.e., conservation laws for energy/mass/momentum). Ability to discern and use the appropriate tool in biomedical and broadly engineering fields. Ability to build an appropriate logical path using the mathematical tools explained in class (i.e. conservation laws for energy/mass/momentum), with appropriate selection of the simplifications specifically to the presented problem. The final mark will be obtained with a written examination consisting of at least 2 open theory questions and at least 2 exercises. Exercises report a real problem, its solution requires an appropriate preliminary operation of modeling and simplification made by the student. This creative process is one of the most important parts of the exam, since it allows to evaluate the acquired abilities in the analysis of a new real situation.The two sections Theory and Exercise generally weight equally in light of the final evaluation. The score of each part will be specified in the exam text. The final score will be calculated as the sum of the single parts. Clarity and rigour will be necessary to obtain the "lode". It is not possible to consult any material during the examination. The examination results will be published in the Portale della Didattica, together with a date to view the exam and ask for clarifications.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.