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Theoretical Biomechanics Structures and Solids

Prof. Bigoni, University of Trento

 

Course Schedule

From 15 September to 19 December

Mondays from 14.30 to 16.30 - Room C2 (Mesiano)

Tuesdays from 17.30 to 19.30 - Room C2 (Mesiano)

 

COURSE OUTLINE

1. Introduction
- Motivation: Masonry and the microstructure of nacre. Truss structures, the vulture’s wing and the vertebrates. The Brunelleschi dome and the way natural shells are broken. Impact: the egg and the skull. The cytoskeleton and tensegrity. Nonlinear solid mechanics and soft tissues. Brain mechanics.

2. Elementary structures
- Motivation: how living organisms transmit loading
- Statically determined structures: bending moment distrubution in tetrapods; bending moment in a limb of a bird
- Statically indetermined structures: insects and arachnids

3. Linear Solid Mechanics
- Motivation: stress in the arteries; the 4 ways of breaking a chalk
- A brief overview of tensor algebra and analysis
- Kinematics of a solid (and fluid) body
- Dynamics during motion of a solid (and fluid) body. Particularization to quasi-static motion
- Linear elastic constitutive equations
- Boundary value problem (uniqueness, Navier equations)
- Failure criteria
- Solutions: (1) arteries; (2) beams subject to internal forces; (3) failure of chalk or bone; (4) wave propagation in solids
- Curiosities: Isotropy and pebbles; transversal shrinking under compression

4. Complex structures
- The shark tooth
- The human femur and hip complex
- The human forearm complex
- Truss structures (vulture’s wing, sand dollars and the vertebrate skeleton)
- Tensegrity (a model for the cell cytoskeleton)

5. Buckling
- The size of bones (allometry)
- Curiosities: Hedgehog needles, Alan Turing, the gastrulation, and the growth of sunflower; Brain convolutions; Flutter & snake locomotion; The coating of seawolf nuclear submarines; Did someone really chop the last tree down on Easter Island? Should towers necessarily lean? Coke cans and dislocations in solids.

6. Fracture Mechanics
- Motivation: bones & chalk, rodent teeth and the shape of the hop stem cross section
- Stiffness & strength are not the only concepts
- Stress intensity factor & criticality
- Curiosities: Pizarro, the emeralds and the Dominican monk who knew the difference between strength and toughness; liberty ships; the mother-of-peral toughness.

7. Nonlinear Solid Mechanics
- Motivation: soft tissues (aneurysms in arteries)
- Kinematics of a solid (and fluid) body
- Dynamics during motion of a solid (and fluid) body.
- Nonlinear elastic constitutive equations: neo Hookean material & incompressibility
- A simple solution: an artery subject to internal pressure
- Curiosities: The disastrous effect of finite element techniques (dedicated to C.A. Truesdell).
Elastic energy and insect jumping. Are bones polar materials?

8. Two-phases tissues
- Motivation: the hydrated nauture of brain parenchyma, cartilage and all soft tissues
- An exercise in consolidation theory and a comparison with experimental results on human brain tissue
- Curiosities: Silly putty, continental drift and cranial artificial deformations

 

References:
- C.R. Ethier & C.A. Simmons ‘Introductory biomechanics’ Cambridge University Press, 2007
- J.Z. Young ‘The life of Mammals’ Oxford University Press, 1957
- D. Bigoni ‘Nonlinear Solid Mechanics’ Cambridge University Press, 2012
- The Feynman Lectures in Physics, Vol II, Sections 38 and 39.
- J.R. Rice Solid Mechanics article on Encyclopædia Britannica.
- H.J. Cooke, K.F.P. Burkitt & W.B. Barker ‘Biology’ Longmans, 1949
- D'Arcy W. Thompson ‘On growth and form’ (1919) Dover reprint 1992