Biomechanics

It is advisable to have basic knowledge of:

• Physics in the areas of:
• Kinematics of a Particle and of Particle Systems;
• Dynamics of a Particle and of Particle Systems.

• Mathematics, in the areas of:
• Integral and Differential Calculus;
• Linear Algebra, namely at the level of matrix calculation.

Theoretical classes are aimed at the theoretical exposition of the subject, making, in many cases, a consolidation of the subjects taught using illustrative examples.

Theoretical-practical classes are designed to solve exercises related to the subjects taught in the theoretical classes.

The objective of this curricular unit is to provide students with knowledge of fundamental laws in the field of mechanics of rigid bodies and deformable bodies with relevance in the area of ​​Biomedical Engineering, fundamental for a better understanding of biomechanical parameters, both in static and dynamic situations, in order to understand the loads to which the different components of the human body are subjected, immobilization devices for therapy, as well as the analysis of projects of orthopedic prostheses and devices involving biomechanical parameters. Students should therefore acquire skills in terms of fundamental principles and laws in the different areas of Biomechanics taught, know how to apply knowledge in concrete practical situations, interpret and discuss the physical meaning of numerical expressions and critically analyze the results obtained in solving problems , as well as autonomously deepen knowledge in the area.

1.Vector Calculus:
  1.1 Scalars and vectors;
  1.2 Graphical representation of vectors;
  1.3 Bound, sliding and free vectors;
  1.4 Graphical operations with free vectors: multiplication by a scalar, addition and subtraction;
  1.5 Unit vectors;
  1.6 Projection of a vector along an arbitrary direction;
  1.7 Cartesian representation of vectors: components of a vector, position vector, module of a vector, directing cosines;
  1.8 Analytical operations with vectors: multiplication of a vector by a scalar, addition and subtraction of vectors, dot product, cross product, scalar triple product, and derivative of a vector.

2. Systems of Forces and Couples:
  2.1 Newton’s laws;
  2.2 Types of forces;
  2.3 Torque of a force with respect to a point and an axis;
  2.4 Resultant force and resultant torque;
  2.5 Force couple and torque of a force couple;
  2.6 Equivalent systems of forces;
  2.7 Reduction of a system of forces to a minimum system: concurrent forces (Varignon’s Theorem), coplanar forces and parallel forces;
  2.8  Central axis of a system of forces.

3. Statics:
  3.1 Free body Diagram;
  3.2 Systems of forces in equilibrium;
  3.3 Applications to biomechanics.

4. Stress and Stain:
  4.1 Internal axial forces, stresses and strains;
  4.2 Internal shear forces, stresses and strains;
  4.3 Stress-strain diagrams and main properties of materials;
  4.4 Poisson’s ratio;
  4.5 Stress tensor, strain tensor and stiffness tensor;
  4.6 Stress and strain transformations;
  4.7 Principal stresses and maximum shear stress;
  4.8 Stresses and strains in pure torsion;
  4.9 Stresses and strains in pure bending;
  4.10 Stresses and strains of combined loadings.

5. Mechanical Properties of Biological Materials:
  5.1 Viscoelasticity: modeling with springs and dashpots;
  5.2 Models of Maxwell, Kelvin-Voigt, and standard linear solid.
  5.3 Time-dependent material response to stresses: creep, recovery and relaxation curves.

6. Rigid body dynamics:
  6.1 Angular momentum of a particle: motion in a plane surface, circular motion; angular momentum conservation theorem;
  6.2 Angular momentum of a rigid body;
  6.3 Moment of inertia: principal axis of inertia and Steiner’s theorem;
  6.4 Derivation of the equation of the rotational dynamics of the rigid body;
  6.5 Kinetic energy of a rigid body: translational and rotational kinetic energy.

NAO

• Özkaya, N., Nordin, M. (1999). Fundamentals of Biomechanics: Equilibrium, Motion, and Deformation (2nd Edition). New York : Springer, Cop.
  ISBN: 978-0-387-98283-0. Cota da Biblioteca: 11-1-12 (ISEC) – 15469; 11-1-13 (ISEC) – 15470; 11-1-14 (ISEC) – 15471.
  

• Huston, R. L. (2009). Principles of Biomechanics. CRC Press, 2009. Boca Raton [etc.]: CRC Press, Cop.
  ISBN: 978-0-8493-3494-8. Cota da Biblioteca: 11-1-9 (ISEC) – 15280; 11-1-10 (ISEC) – 15355.
  

• Bedford, A., Fowler, W. (2008). Engineering Mechanics: Statics (5th Edition). Singapore [etc.] : Prentice Hall, Cop.
  ISBN: 978-981-06-7939-2. Cota da Biblioteca: 5-5-59 (ISEC) V.1º v. – 15236; 5-5-60 (ISEC) V.2º v. – 15237; 5-5-60CD (ISEC) V.CD-ROM – 15236CD.
  

• Bedford, A., Fowler, W. (2008). Engineering Mechanics: Dynamics (5th Edition). Singapore [etc.] : Prentice Hall, Cop.
  ISBN: 978-981-06-7939-2. Cota da Biblioteca: 5-5-57 (ISEC) V.1º v. – 15234; 5-5-58 (ISEC) V.2º v. – 15235; 5-5-58CD (ISEC) V.CD-ROM – 15234CD.

• Pedroso de Lima, J.J. (2005). Biofísica Médica. Coimbra: Imprensa da Universidade.
  ISBN: 972-8704-56-9. Cota da Biblioteca: 12-1-20 (ISEC) -15962.
  

• Peterson, D. R., Bronzino, J. D. (2008). Biomechanics: principles and applications. Boca Raton [etc.] : CRC Press, Cop.
  ISBN: 978-0-8493-8534-6. Cota da Biblioteca: 11-1-11 (ISEC) – 15354.
  

• Oomens, C., Brekelmans, M., Baaijens, F. (2009). Biomechanics: concepts and computation. Cambridge: Cambridge University Press.
  ISBN: 978-0-521-87558-5. Cota da Biblioteca: 11-1-7 (ISEC) – 15193.
  

• Richards, J. (2008). Biomechanics in clinic and research: an interactive teaching and learning course. Edinburgh [etc.] : Churchill Livingstone/Elsevier, Cop.
  ISBN: 978-0-443-10170-0. Cota da Biblioteca: 11-1-6 (ISEC – 14856.
  

• Benedek, G., Villars, F. M. H. (2000) Physics With Illustrative Examples from Medicine and Biology: Mechanics (2nd Edition). New York: Springer-Verlag.
  ISBN: 978-0-387-98769-9.