COURSE - Hands on Continuum Mechanics with COMSOL

The goal of this course is to 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.

March 1-3-8-10, 2022 - 3:00pm - 6:00pm

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 and distortions. 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.

© Università degli Studi di Roma "La Sapienza" - Piazzale Aldo Moro 5, 00185 Roma