The student should have knowledge on Infinitesimal Analysis, Linear Algebra and Analytical Geometry and Physics corresponding to the 1st year and 2nd year/1st semester of a 1st cycle of studies in Engineering.
Presentation of the different topics with illustrative practical applications.
The students should solve problems autonomously. Practical examples related to presented topics will be addressed.
Whenever necessary there will be a short overview of the mathematical tools involved in the comprehension of presented topics or problem solving: cartesian tensors, multiple integrals, diferential operators.
- To apply the conservation laws of classical mechanics to problems of biomechanics.
- To determine the forces exerted in different joints of the human body.
- To characterize different materials based on respective uni-axial stress-strain diagram.
- To calculate yielding strains and stresses in materials under different types of forces.
- To solve problems with compressible and incompressible fluids at rest.
- To know a number of models in visco-elasticity.
Introduction: Consequences of Newton's laws: conservation laws. Aplications: determination of the center of mass of an individual, the ballistocardiogram.
Statics: stability of structures in problems of biomedicine.
Deformable media: general concepts; deformation tensor; compatibility conditions; stress tensor; static equilibrium conditions; energy of deformation; Hooke's generalized law; isotropic materials; bidimensional isotropic materials; the Mohr's circle; monotropic and orthotropic materials; yield and rupture criteria; fatigue; aplications to problems in biomedicine involving traction, tortion and flexion.
Constitutive equations of fluids: incompressible and compressible fluids at rest, Euler's equation; viscous fluids, Navier-Stokes equation.
Viscoelasticity: isotropic materials with linear visco-elastic behaviour: Kelvin-Voigt, Maxwell and standard models.
Resolution Problems: 5.0%
Laboratory work or Field work: 15.0%
V. Dias da Silva, Mecânica e Resistência dos Materiais, Edições Zuari, 2004.
C. Providência e C. Sousa, Apontamentos de Biomecânica, 2007.
Y. C. Fung, A first course in continuum mechanics: for physical and biological engineers and scientists, 1994.
J. J. Pedroso de Lima, Biofísica Médica, 2003.
N. Ozkaya e M. Nordin, Fundamentals of biomechanics: equilibrium, motion and deformation, Springer, 1999.
George B. Benedek, Felix M. H. Villars, Physics : with illustrative examples from medicine and biology, vol. 1 : mechanics, Springer, 2000.
B. Bhatia e R. N. Singh, Mechanics of deformable media, IOP, 1986.