On the modelling of materials and interactions with thermoelectromechanical constraints
In this short note a mathematical framework is proposed to model material systems in which the actual values and the rates of field variables are subject to constraints which can be internal constraints due to properties of materials and external constraints which describe the mode of interaction between the material body and its exterior. The behaviour of the material is defined by a nonempty set collecting thermomechanical states. The rates of states and internal and external responses are assumed to be in two linear topological spaces and the power is defined as a duality pairing between these spaces. Hidden variables also constitute a given set. A mathematical model is then defined as a relation in the Cartesian product of all four sets. On the other hand a constraint is defined as a relation in the Cartesian product of the first two sets. There are three propositions concerning the nature of constraints. However for the proof of them the reader is referred elsewhere. It is shown that for fiber reinforced materials the present approach leads exactly to previous forms for responses.
mode of interaction between the material body and its exterior
nonempty set collecting thermomechanical states
Hidden variables also constitute a given set
as a relation in the Cartesian product of all four sets
constraint is defined as a relation in the Cartesian product of
constraint is defined as a relation in the Cartesian product of the first two sets
scientific article; zbMATH DE number 3924325