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.