[Seminar] Objective Rates from Observation Structures: Continuum Mechanics in Constructive Tensor Theory

Title:

Objective Rates from Observation Structures: Continuum Mechanics in Constructive Tensor Theory

Abstract:

Science is usually built on reproducibility and objectivity, yet actual phenomena do not always appear in exactly the same way. This broader gap motivates Constructive Tensor Theory (CTT), a framework that asks how lawful structures depend on the way a world is constructed and compared. In this talk, I focus on one local appearance of this question in continuum mechanics: the non-uniqueness of objective rates.
In classical continuum mechanics, several time derivatives are called objective, including upper-convected and corotational forms, although they are not identical. I argue that this multiplicity should not be viewed merely as a collection of ad hoc corrections. Instead, it reflects differences in the underlying observation structure, namely, in how tensorial quantities are identified and compared across time. From this viewpoint, objective rates are induced by explicit comparison rules rather than patched in afterward.
Based on this idea, I introduce Constructive Continuum Mechanics (CCM), a specification-first framework in which identification and transport are treated explicitly before material response is prescribed. I will show how familiar classical rates can be reinterpreted within this constructive picture, and I will briefly indicate how this local result fits into the broader CTT program.

Speaker:

Mr Hiroki Endo, PhD.Student at Nagaoka University of Technology, Japan.