Covid-19 rules for Italy require GREEN PASS for all participants. 

Schedule: March 2022;

Four lectures on Tue 1, Thu 3, Tue 8, Thu 10, from 15:00 to 18:00 (break included).

Venue: Lab Informatico, nuovo padiglione aule,

Dip. Matematica e Fisica, Università Roma Tre, Largo S. Leonardo Murialdo 1, Roma

Goal: understand the fundamentals of continuum mechanics through worked examples. Participants will tackle some typical problems of continuum mechanics, and will learn to implement a given problem using the weak formulation into the COMSOL software and to discuss the solution.

Synopsis of lectures

1) Browse a model of nonlinear solid mechanics, from the implementation to the solution.

A first glance at the fundamentals of continuum mechanics: Kinematics, Constitutive, Balance laws.

Differential form (strong) versus Integral form (weak).

Worked example: large deformations of a hyperelastic solid under loadings.

2) Material Versus Spatial description.

A continuum body as a differentiable manifold.

Tell the difference between tensors: strain tensor versus stress tensor.

Pull back & push forward of scalar, vector and tensor fields.

Geometric elements; change of densities.

3) Solid mechanics versus Fluid mechanics

Kinematical constraints; isochoric motion.

Reference stress (Piola) & Actual stress (Cauchy).

Polar decomposition theorem; eigenspace of the stress tensor and of the strain tensor

4) Non linear solid mechanics

Worked example: large deformations of a hyperelastic solid under distortions. The notion of Target metric.

5) Material response

Worked example: from elastic energy  to the constitutive law for the stress.

Transversely isotropic materials. Fiber reinforced materials.

Worked example: fiber reinforced hyperelastic solid under traction.

6) Fluid dynamics

Tackling Navier Stokes equations.

Worked examples: fluid in a channel; fluid around an obstacle.

7) Fluid-Structure interactions - theory

Worked examples: understand the moving mesh technique; how to write the problem of a beam immersed in a fluid.

8) Fluid-Structure interactions - practice

Worked example: implement and solve the problem of an oscillating beam immersed in a fluid.