On May 22nd, 2023 at 10.30 am Michael A. Slawinski, Professor at Department of Earth Sciences of Memorial University, Canada, will hold a seminar on "On Hookean Solids: Mathematical Models of Physical Objects" in DEIB Beta Room.

Commonly, in spite of many of constraints, linear operations are empirically adequate mathematical analogies of physical phenomena.
In this seminar, we discuss Hookean solids, which are mathematical entities that relate linearly stress and strain, which are second-rank symmetric tensors; hence—under the assumption of hyperelasticity—in three spatial dimensions, a Hookean solid is a fourth-rank tensor with twenty-one independent components. These components allow us to model eight symmetry classes of anisotropic behaviour, including isotropy, which is represented by two components, and general anisotropy, which is represented by twenty-one. Since no physical material belongs to any of these classes, the question is to find the class that is its best representation. For that purpose, we formulate the notion of distance in the twenty-one dimensional space of fourth-rank tensors, which allows us to quantify the proximity of measurements, including their experimental errors, to a given symmetry class. Once this is achieved, we have an abstract model to examine quantitatively the behaviour of a physical object, be that a crystal, a rock, a piece of wood or carbon fiber.

The event will be held online by Webex.