Аннотация:Abstract The traditional principles of the theory of constitutive relations in classical continuum mechanics are
discussed. In light of the approaches by A. A. Ilyushin and by W. Noll, the equivalence and the completeness of
their general reduced forms of constitutive relations for simple classical media are noted. First, it is mentioned that
a possible presence of internal kinematic constraints is rarely taken into account and needs special modifications
in formulating the principles and relations. Secondly, a systematic study of internal body forces in constitutive
relations has not been done before. Here a unified approach to the theory of constitutive relations is proposed to
describe properties of deformation resistance of a body including both internal kinematic constraints and internal
body forces. The general reduced forms of the system of constitutive relations are derived in terms of different
definitions of a dynamical process in a body. The case of a simple body is considered in detail in view of the theory
of objective tensors, their diagrams and frame-independent relations between objective tensors. The completeness
of Ilyushin’s and Noll’s types of relations for the most general constitutive formulations is noted and confirmed by
examples.
Keywords Classical continuum mechanics · Constitutive relations · New principles
Cited 1 time.
http://www.scopus.com/inward/record.url?eid=2-s2.0-84871893032&partnerID=40&md5=77f427616102795c541ebd5d5c44821f
DOCUMENT TYPE: Article
SOURCE: Scopus
Scopus
EXPORT DATE:17 Feb 2014