Topics in continuum and structural mechanics

Lecturers: Davide Bigoni (DICAM/UNITN)

Timetable:  22 November - 2 December 2021

Schedule: 

The course lasts 16 hours, 9 of which are shared with the "Theoretical Biomechanics" course.

Monday  22/11 16:30-18:30  (2 hours) together with Theoretical Biomechanics
Tuesday 23/11 10:00-13:00  (3 hours) only for PhD students
Tuesday 23/11 17:30-19:30  (2 hours) together with Theoretical Biomechanics
Monday 29/11 16:30-19:30  (3 hours) together with Theoretical Biomechanics
Tuesday 30/11 17:30-19:30  (2 hours) together with Theoretical Biomechanics
Thursday 2/12  10:00-13:00  (3 hours) only for PhD students

Abstract: 

The course addresses the kinematics, statics and constitutive equations of continua subject to large strain and fracture.
Strain measures. Stress measures. Work conjugacy.
Rigid-body motion. Spatial and material quantities.
Motion, velocity and acceleration. Gradient of velocity, Eulerian strain rate and spin.
Cauchy stress. Kirchhoff Stress. First and second Piola-Kirchhoff stress. Objectivity and material frame indifference. Constitutive equations. Krichhoff-Saint-Venant material. Incompressibility and Lagrangian multipliers. Mooney-Rivlin.
Application of nonlinear Solid Mechanics to the deformation of the arteries and possible aneurysm formation. Large deformations of an incompressible tube made up of neo-Hookean material. Fracture mechanics. Stiffness, failure and toughness. Singular solutions in elasticity. Critical stress intensity factor. The toughness of bone, nacre and horn. Ashby diagrams.
Kinematics of a circular rod subject to large deformation. Referential and spatial descriptions. Statics of the rod, constitutive equations and prestress states.

Duration: 16 hours (2 credits)

Registration: in order to register for the course please send an email to dicamphd [at] unitn.it