On the modelling of materials and interactions with thermoelectromechanical constraints
type: Item
instance of: scholarly article
title: On the modelling of materials and interactions with thermoelectromechanical constraints
zbMATH Open document ID: 0577.73120
author: Czesław Woźniak
published in: Bulletin of the Polish Academy of Sciences. Technical Sciences
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74Axx
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 3924325
zbMATH Keywords: thermoelectromechanical constraints
zbMATH Keywords: internal constraints
zbMATH Keywords: properties of materials
zbMATH Keywords: external constraints
zbMATH Keywords: mode of interaction between the material body and its exterior
zbMATH Keywords: nonempty set collecting thermomechanical states
zbMATH Keywords: rates of states
zbMATH Keywords: internal and external responses
zbMATH Keywords: two linear topological spaces
zbMATH Keywords: power
zbMATH Keywords: duality pairing between these spaces
zbMATH Keywords: Hidden variables also constitute a given set
zbMATH Keywords: mathematical model
zbMATH Keywords: as a relation in the Cartesian product of all four sets
zbMATH Keywords: constraint is defined as a relation in the Cartesian product of
zbMATH Keywords: the first two sets
zbMATH Keywords: constraint is defined as a relation in the Cartesian product of the first two sets
reviewed by: Erdoğan S. Şuhubi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3924325