The Slow March towards an Analytical Mechanics of Dissipative Materials

The concern of this work is the derivation of material balance laws for the Green-Naghdi (G-N) theory of dissipationless thermoelasticity. The lack of dissipation allows for a physically meaningfal variational formulation which is used for the application of Noether’s theorem. The balance laws on the material manifold are derived and the extact conditions under which they hold are rigorously studied

CONTRIBUTION TO THE STUDY OF PROBLEMS OF COUPLED AND GENERALIZED THEORY OF THERMOELASTICITY

IN THIS THESIS AN ATTEMPT HAS BEEN MADE TO REPRESENT THE MATHEMATICAL DESCRIPTION OF THE PROBLEM OF COUPLED AND GENERALIZED THEORY OF THERMOELASTICITY. IN THEFRAMEWORK OF THE COUPLED THERMOELASTICITY THE PROBLEMS OF VIBRATION OF BERNOULLI- EULER AND TIMOSHENKO BEAM AND THE PROBLEM OF AN INFINITE MEDIUM (X1, X2 [- , ], X3 FINITE) HAVE BEEN STUDIED BY USING INTEGRAL AND FINITE FOURIER TRANSFORMS. THE GENERALIZED THEORY OF LORD AND SHULMAN HAS BEEN USED TO STUDY THE CHARACTERISTICS OF THE WAVE MOTION IN A THIN PLATE OF INFINITE LENGTH UNDER PLANE STRESS STATE. FINALLY THE THREE-DIMENSIONAL GENERALIZED THERMOELASTICITY IS USED TO THE STUDY OF THE PROPAGATION OF HARMONIC WAVES IN A WAVEGUIDE. IN THE PROBLEMS UNDER DISCUSSION THE ROLE OF THE ENTERING PARAMETERS EXTENSIVELLY DISCUSSED.Σ'ΑΥΤΗ ΤΗΝ ΕΡΓΑΣΙΑ ΕΠΙΧΕΙΡΕΙΤΑΙ ΜΙΑ ΠΑΡΟΥΣΙΑΣΗ ΤΗΣ ΜΑΘΗΜΑΤΙΚΗΣ ΠΕΡΙΓΡΑΦΗΣ ΤΟΥ ΠΡΟΒΛΗΜΑΤΟΣ ΤΗΣ ΖΕΥΓΜΕΝΗΣ ΚΑΙ ΓΕΝΙΚΕΥΜΕΝΗΣ ΘΕΡΜΟΕΛΑΣΤΙΚΟΤΗΤΑΣ. ΜΕ ΒΑΣΗ ΤΗ ΖΕΥΓΜΕΝΗ ΘΕΡΜΟΕΛΑΣΤΙΚΟΤΗΤΑ ΔΙΕΡΕΥΝΟΥΝΤΑΙ ΟΙ ΤΑΛΑΝΤΩΣΕΙΣ ΔΟΚΟΥ ΤΩΝ BERNAULLI-EULER ΚΑΙTIMOSHENKO ΚΑΙ ΤΟ ΠΡΟΒΛΗΜΑ ΕΝΟΣ ΑΠΕΙΡΟΥ ΜΕΣΟΥ (Χ1,Χ2 [- , ], Χ3 ΠΕΠΕΡΑΣΜΕΝΟ), ΜΕ ΤΗ ΒΟΗΘΕΙΑ ΟΛΟΚΛΗΡΩΤΙΚΩΝ ΚΑΙ ΠΕΠΕΡΑΣΜΕΝΩΝ ΜΕΤΑΣΧΗΜΑΤΙΣΜΩΝ FOURIER. ΜΕ ΒΑΣΗ ΤΗ ΓΕΝΙΚΕΥΜΕΝΗ ΘΕΩΡΙΑ ΤΩΝ LORD ΚΑΙ SHULMAN ΕΞΕΤΑΖΟΝΤΑΙ ΤΑ ΧΑΡΑΚΤΗΡΗΣΤΙΚΑ ΤΗΣ ΚΥΜΑΤΙΚΗΣ ΚΙΝΗΣΗΣ ΓΙΑ ΜΙΑ ΛΕΠΤΗ ΠΛΑΚΑ ΑΠΕΙΡΟΥ ΜΗΚΟΥΣ ΣΤΗΝ ΕΠΙΠΕΔΗ ΕΝΤΑΤΙΚΗ ΚΑΤΑΣΤΑΣΗ. ΤΕΛΟΣ ΕΞΕΤΑΖΕΤΑΙ Η ΔΙΑΔΟΣΗ ΑΡΜΟΝΙΚΩΝ ΚΥΜΑΤΩΝ Σ'ΕΝΑ ΚΥΜΑΤΟΔΗΓΟ ΜΕ ΒΑΣΗ ΤΗ ΤΡΙΣΔΙΑΣΤΑΤΗ ΓΕΝΙΚΕΥΜΕΝΗ ΘΕΡΜΟΕΛΑΣΤΙΚΟΤΗΤΑ. Σ'ΟΛΑ ΤΑ ΠΑΡΑΠΑΝΩ ΠΡΟΒΛΗΜΑΤΑ ΔΙΕΡΕΥΝΑΤΑΙ ΑΝΑΛΥΤΙΚΑ Η ΕΠΙΔΡΑΣΗ ΤΩΝ ΠΑΡΑΜΕΤΡΩΝ ΠΟΥ ΥΠΕΙΣΕΡΧΟΝΤΑΙ ΣΤΟ ΠΡΟΒΛΗΜΑ

Configurational balance laws for dynamical fracture

In the spirit of modern continuum mechanics, global balance laws for momentum, angular momentum, energy and pseudomomentum are formulated for an elastic body in the presence of a moving crack. Upon localization, the corresponding balance equations in the bulk and at the crack tip are simultaneously obtained. The proposed framework is convenient for the derivation of the well-known formula, which relates the crack propagation velocity, the global material force and the energy release rate.